Suppose the age that children learn to walk is normally distributed with mean 11 months and standard deviation 1 month. 10 randomly selected people were asked what age they learned to walk. Round all answers to 4 decimal places where possible.
a. What is the distribution of XX? XX ~ N( , )
b. What is the distribution of ¯xx¯? ¯xx¯ ~ N( , )
c. What is the probability that one randomly selected person learned to walk when the person was between 10.5 and 12.5 months old?
d. For the 10 people, find the probability that the average age that they learned to walk is between 10.5 and 12.5 months old.
e. For part d), is the assumption that the distribution is normal necessary? Yes No
f. Find the IQR for the average first time walking age for groups of 10 people.
Q1 = months
Q3 = months
IQR: months
The average price of a college math textbook is $153 and the standard deviation is $20. Suppose that 40 textbooks are randomly chosen. Round all answers to 4 decimal places where possible.
a. What is the distribution of ¯xx¯? ¯xx¯ ~ N( , )
b. For the group of 40, find the probability that the average price is between $149 and $154.
c. Find the first quartile for the average textbook price for this sample size. $ (round to the nearest cent)
d. For part b), is the assumption that the distribution is normal necessary? Yes No
The average production cost for major movies is 59 million dollars and the standard deviation is 18 million dollars. Assume the production cost distribution is normal. Suppose that 16 randomly selected major movies are researched. Answer the following questions. Round all answers to 4 decimal places where possible.
a. What is the distribution of XX? XX ~ N( , )
b. What is the distribution of ¯xx¯? ¯xx¯ ~ N( , )
c. For a single randomly selected movie, find the probability that this movie’s production cost is between 56 and 61 million dollars.
d. For the group of 16 movies, find the probability that the average production cost is between 56 and 61 million dollars.
e. For part d), is the assumption of normal necessary? No Yes
The average amount of money spent for lunch per person in the college cafeteria is $6.41 and the standard deviation is $2.78. Suppose that 8 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible.
a. What is the distribution of XX? XX ~ N( , )
b. What is the distribution of ¯xx¯? ¯xx¯ ~ N( , )
c. For a single randomly selected lunch patron, find the probability that this patron’s lunch cost is between $7.5357 and $8.1272.
d. For the group of 8 patrons, find the probability that the average lunch cost is between $7.5357 and $8.1272.
e. For part d), is the assumption that the distribution is normal necessary? Yes No
Each sweat shop worker at a computer factory can put together 4.4 computers per hour on average with a standard deviation of 0.9 computers. 11 workers are randomly selected to work the next shift at the factory. Round all answers to 4 decimal places where possible and assume a normal distribution.
a. What is the distribution of XX? XX ~ N( , )
b. What is the distribution of ¯xx¯? ¯xx¯ ~ N( , )
c. What is the distribution of ∑x∑x? ∑x∑x ~ N( , )
d. If one randomly selected worker is observed, find the probability that this worker will put together between 4.2 and 4.4 computers per hour.
e. For the 11 workers, find the probability that their average number of computers put together per hour is between 4.2 and 4.4.
f. Find the probability that a 11 person shift will put together between 49.5 and 52.8 computers per hour.
g. For part e) and f), is the assumption of normal necessary? Yes No
h. A sticker that says “Great Dedication” will be given to the groups of 11 workers who have the top 20% productivity. What is the least total number of computers produced by a group that receives a sticker? minutes (round to the nearest computer)
Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 49 minutes and standard deviation 20 minutes. A researcher observed 18 students who entered the library to study. Round all answers to 4 decimal places where possible.
a. What is the distribution of XX? XX ~ N( , )
b. What is the distribution of ¯xx¯? ¯xx¯ ~ N( , )
c. What is the distribution of ∑x∑x? ∑x∑x ~ N( , )
d. If one randomly selected student is timed, find the probability that this student’s time will be between 51 and 58 minutes.
e. For the 18 students, find the probability that their average time studying is between 51 and 58 minutes.
f. Find the probability that the randomly selected 18 students will have a total study time less than 810 minutes.
g. For part e) and f), is the assumption of normal necessary? Yes No
h. The top 10% of the total study time for groups of 18 students will be given a sticker that says “Great dedication”. What is the least total time that a group can study and still receive a sticker? minutes
The number of seconds XX after the minute that class ends is uniformly distributed between 0 and 60. Round all answers to 4 decimal places where possible.
a. What is the distribution of XX? XX ~ U( , )
then the sampling distribution is
b. Suppose that 37 classes are clocked. What is the distribution of ¯xx¯ for this group of classes? ¯xx¯ ~ N( , )
c. What is the probability that the average of 37 classes will end with the second hand between 23 and 31 seconds?
The average time to run the 5K fun run is 25 minutes and the standard deviation is 2.4 minutes. 12 runners are randomly selected to run the 5K fun run. Round all answers to 4 decimal places where possible and assume a normal distribution.
a. What is the distribution of XX? XX ~ N( , )
b. What is the distribution of ¯xx¯? ¯xx¯ ~ N( , )
c. What is the distribution of ∑x∑x? ∑x∑x ~ N( , )
d. If one randomly selected runner is timed, find the probability that this runner’s time will be between 24.2608 and 25.2608 minutes.
e. For the 12 runners, find the probability that their average time is between 24.2608 and 25.2608 minutes.
f. Find the probability that the randomly selected 12 person team will have a total time less than 306.
g. For part e) and f), is the assumption of normal necessary? Yes No
h. The top 15% of all 12 person team relay races will compete in the championship round. These are the 15% lowest times. What is the longest total time that a relay team can have and still make it to the championship round? minutes
Each sweat shop worker at a computer factory can put together 4.4 computers per hour on average with a standard deviation of 0.7 computers. 12 workers are randomly selected to work the next shift at the factory. Round all answers to 4 decimal places where possible and assume a normal distribution.
a. What is the distribution of XX? XX ~ N( , )
b. What is the distribution of ¯xx¯? ¯xx¯ ~ N( , )
c. What is the distribution of ∑x∑x? ∑x∑x ~ N( , )
d. If one randomly selected worker is observed, find the probability that this worker will put together between 4.5 and 4.6 computers per hour.
e. For the 12 workers, find the probability that their average number of computers put together per hour is between 4.5 and 4.6.
f. Find the probability that a 12 person shift will put together between 49.2 and 50.4 computers per hour.
g. For part e) and f), is the assumption of normal necessary? Yes No
h. A sticker that says “Great Dedication” will be given to the groups of 12 workers who have the top 15% productivity. What is the least total number of computers produced by a group that receives a sticker? minutes (round to the nearest computer)
Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 45 minutes and standard deviation 17 minutes. A researcher observed 40 students who entered the library to study. Round all answers to 4 decimal places where possible.
a. What is the distribution of XX? XX ~ N( , )
b. What is the distribution of ¯xx¯? ¯xx¯ ~ N( , )
c. What is the distribution of ∑x∑x? ∑x∑x ~ N( , )
d. If one randomly selected student is timed, find the probability that this student’s time will be between 41 and 45 minutes.
e. For the 40 students, find the probability that their average time studying is between 41 and 45 minutes.
f. Find the probability that the randomly selected 40 students will have a total study time more than 1920 minutes.
g. For part e) and f), is the assumption of normal necessary? No Yes
h. The top 15% of the total study time for groups of 40 students will be given a sticker that says “Great dedication”. What is the least total time that a group can study and still receive a sticker? minutes
The average amount of money that people spend at Don Mcalds fast food place is $7.5400 with a standard deviation of $1.8600. 41 customers are randomly selected. Please answer the following questions, and round all answers to 4 decimal places where possible and assume a normal distribution.
a. What is the distribution of XX? XX ~ N( , )
b. What is the distribution of ¯xx¯? ¯xx¯ ~ N( , )
c. What is the distribution of ∑x∑x? ∑x∑x ~ N( , )
d. What is the probability that one randomly selected customer will spend more than $7.4143?
e. For the 41 customers, find the probability that their average spent is more than $7.4143.
f. Find the probability that the randomly selected 41 customers will spend more than $303.9863.
g. For part e) and f), is the assumption of normal necessary? No Yes
h. The owner of Don Mcalds gives a coupon for a free sundae to the 3% of all groups of 41 people who spend the most money. At least how much must a group of 41 spend in total to get the free sundae? $
The average score for games played in the NFL is 22.3 and the standard deviation is 9.1 points. 17 games are randomly selected. Round all answers to 4 decimal places where possible and assume a normal distribution.
a. What is the distribution of ¯xx¯? ¯xx¯ ~ N( , )
b. What is the distribution of ∑x∑x? ∑x∑x ~ N( , )
c. P(¯xx¯ > 19.3894) =
d. Find the 70th percentile for the mean score for this sample size.
e. P(22.9894 < ¯xx¯ < 24.8036) =
f. Q3 for the ¯xx¯ distribution =
g. P(∑x∑x > 341.5198) =
h. For part c) and e), is the assumption of normal necessary? No Yes
A computer selects a number XX from 4 to 10 randomly and uniformly. Round all answers to 4 decimal places where possible.
a. What is the distribution of XX? XX ~ U( , )
b. Suppose that the computer randomly picks 35 such numbers. What is the distribution of ¯xx¯ for this selection of numbers. ¯xx¯ ~ N( , )
c. What is the probability that the average of 35 numbers will be more than 6.6?
Treat the number of months X after January 1 that someone is born as uniformly distributed from 0 to 12. Round all answers to 4 decimal places where possible.
a. What is the distribution of XX? XX ~ U( , )
b. Suppose that 38 people are surveyed. What is the distribution of ¯xx¯ for this sample? ¯xx¯ ~ N( , )
c. What is the probability that the average birth month of the 38 people will be more than 5.5?
Suppose that the age of students at George Washington Elementary school is uniformly distributed between 6 and 11 years old. 39 randomly selected children from the school are asked their age. Round all answers to 4 decimal places where possible.
a. What is the distribution of XX? XX ~ U( , )
Suppose that 39 children from the school are surveyed. Then the sampling distribution is
b. What is the distribution of ¯xx¯? ¯xx¯ ~ N( , )
c. What is the probability that the average of 39 children will be between 8 and 8.3 years old?
The number of seconds XX after the minute that class ends is uniformly distributed between 0 and 60. Round all answers to 4 decimal places where possible.
a. What is the distribution of XX? XX ~ U( , )
then the sampling distribution is
b. Suppose that 38 classes are clocked. What is the distribution of ¯xx¯ for this group of classes? ¯xx¯ ~ N( , )
c. What is the probability that the average of 38 classes will end with the second hand between 23 and 28 seconds?
Are freshmen psychology majors just as likely to change their major before they graduate compared to freshmen business majors? 381 of the 619 freshmen psychology majors from a recent study changed their major before they graduated and 386 of the 647 freshmen business majors changed their major before they graduated. What can be concluded at the = 0.05 level of significance?
For this study, we should use
a. The null and alternative hypotheses would be:
b. The test statistic = (please show your answer to 3 decimal places.)
c. The p-value = (Please show your answer to 4 decimal places.)
d. The p-value is
e. Based on this, we should the null hypothesis.
f. Thus, the final conclusion is that …
o The results are statistically insignificant at αα = 0.05, so there is statistically significant evidence to conclude that the population proportion of freshmen psychology majors who change their major is the same as the population proportion of freshmen business majors who change their major.
o The results are statistically significant at αα = 0.05, so there is sufficient evidence to conclude that the proportion of the 619 freshmen psychology majors who changed their major is different from the proportion of the 647 freshmen business majors who change their major.
o The results are statistically insignificant at αα = 0.05, so there is insufficient evidence to conclude that the population proportion of freshmen psychology majors who change their major is different from the population proportion of freshmen business majors who change their major.
o The results are statistically significant at αα = 0.05, so there is sufficient evidence to conclude that the population proportion of freshmen psychology majors who change their major is different from the population proportion of freshmen business majors who change their major.
Are blonde female college students just as likely to have boyfriends as brunette female college students? 408 of the 616 blondes surveyed had boyfriends and 543 of the 748 brunettes surveyed had boyfriends. What can be concluded at the αα = 0.10 level of significance?
For this study, we should use
a. The null and alternative hypotheses would be:
H0:H0:
H1:H1:
b. The test statistic = (please show your answer to 3 decimal places.)
c. The p-value = (Please show your answer to 4 decimal places.)
d. The p-value is αα
e. Based on this, we should the null hypothesis.
f. Thus, the final conclusion is that …
o The results are statistically insignificant at αα = 0.10, so there is insufficient evidence to conclude that the population proportion of blonde college students who have a boyfriend is different from the population proportion of brunette college students who have a boyfriend.
o The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the population proportion of blonde college students who have a boyfriend is different from the population proportion of brunette college students who have a boyfriend.
o The results are statistically insignificant at αα = 0.10, so we can conclude that the population proportion of blonde college students who have a boyfriend is equal to the population proportion of brunette college students who have a boyfriend.
o The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the proportion of the 616 blonde college students who have a boyfriend is different from the proportion of the 748 brunette college students who have a boyfriend.
g. Interpret the p-value in the context of the study.
o There is a 1.1% chance that blonde and brunette college students differ by at least 6.4% when it comes to having a boyfriend.
o If the percent of all blonde college students who have a boyfriend is the same as the percent of all brunette college students who have a boyfriend and if another 616 blonde college students and 748 brunette college students are surveyed then there would be a 1.1% chance that the percent of the surveyed blonde and brunette college students who have a boyfriend differ by at least 6.4%
o If the sample proportion of blonde college students who have a boyfriend is the same as the sample proportion of brunette college students who have a boyfriend and if another another 616 blonde college students and 748 brunette college students are surveyed then there would be a 1.1% chance of concluding that blonde and brunette college students differ by at least 6.4% when it comes to having a boyfriend
o There is a 1.1% chance of a Type I error.
h. Interpret the level of significance in the context of the study.
o If the percent of all blonde college students who have a boyfriend is the same as the percent of all brunette college students who have a boyfriend and if another 616 blonde college students and 748 brunette college students are surveyed then there would be a 10% chance that we would end up falsely concuding that the population proportion of blonde college students who have a boyfriend is different from the population proportion of brunette college students who have a boyfriend
o If the percent of all blonde college students who have a boyfriend is the same as the percent of all brunette college students who have a boyfriend and if another 616 blonde college students and 748 brunette college students are surveyed then there would be a 10% chance that we would end up falsely concuding that the proportion of these surveyed blonde and brunette college students who have a boyfriend differ from each other.
o There is a 10% chance that there is a difference in the proportion of blonde and brunette college students who have a boyfriend.
o There is a 10% chance that you will never get a boyfriend unless you dye your hair blonde.
Do political science classes require less writing than history classes? The 45 randomly selected political science classes assigned an average of 19.3 pages of essay writing for the course. The standard deviation for these 45 classes was 4.4 pages. The 45 randomly selected history classes assigned an average of 21.4 pages of essay writing for the course. The standard deviation for these 45 classes was 4.2 pages. What can be concluded at the αα = 0.10 level of significance?
For this study, we should use
a. The null and alternative hypotheses would be:
H0:H0:
H1:H1:
b. The test statistic = (please show your answer to 3 decimal places.)
c. The p-value = (Please show your answer to 4 decimal places.)
d. The p-value is αα
e. Based on this, we should the null hypothesis.
f. Thus, the final conclusion is that …
o The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the mean number of required pages for the 45 political science classes that were observed is less than the mean number of required pages for the 45 history classes that were observed.
o The results are statistically insignificant at αα = 0.10, so there is statistically significant evidence to conclude that the population mean number of pages of writing that political science classes require is equal to the population mean number of pages of writing that history classes require.
o The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the population mean number of pages of writing that political science classes require is less than the population mean number of pages of writing that history classes require.
o The results are statistically insignificant at αα = 0.10, so there is insufficient evidence to conclude that the population mean number of pages of writing that political science classes require is less than the population mean number of pages of writing that history classes require.
Male: 55 74 80 58 91 92 78 56 88 84 71 84 62
Female: 48 80 67 80 69 52 49 68 48 64 51 85 50
Assume both follow a Normal distribution. What can be concluded at the the αα = 0.05 level of significance level of significance?
For this study, we should use
a. The null and alternative hypotheses would be:
H0:H0:
H1:H1:
b. The test statistic = (please show your answer to 3 decimal places.)
c. The p-value = (Please show your answer to 4 decimal places.)
d. The p-value is αα
e. Based on this, we should the null hypothesis.
f. Thus, the final conclusion is that …
o The results are statistically insignificant at αα = 0.05, so there is insufficient evidence to conclude that the population mean statistics final exam score for men is not the same as the population mean statistics final exam score for women.
o The results are statistically significant at αα = 0.05, so there is sufficient evidence to conclude that the population mean statistics final exam score for men is not the same as the population mean statistics final exam score for women.
o The results are statistically insignificant at αα = 0.05, so there is statistically significant evidence to conclude that the population mean statistics final exam score for men is equal to the population mean statistics final exam score for women.
o The results are statistically significant at αα = 0.05, so there is sufficient evidence to conclude that the mean final exam score for the thirteen men that were observed is not the same as the mean final exam score for the thirteen women that were observed.
Is a weight loss program based on exercise less effective than a program based on diet? The 41 overweight people put on a strict one year exercise program lost an average of 24 pounds with a standard deviation of 5 pounds. The 42 overweight people put on a strict one year diet lost an average of 25 pounds with a standard deviation of 7 pounds. What can be concluded at the αα = 0.05 level of significance?
a. For this study, we should use
b. The null and alternative hypotheses would be:
H0:H0:
H1:H1:
c. The test statistic = (please show your answer to 3 decimal places.)
d. The p-value = (Please show your answer to 4 decimal places.)
e. The p-value is αα
f. Based on this, we should the null hypothesis.
g. Thus, the final conclusion is that …
o The results are statistically insignificant at αα = 0.05, so there is insufficient evidence to conclude that the population mean weight loss on the exercise program is less than the population mean weight loss on the diet.
o The results are statistically significant at αα = 0.05, so there is sufficient evidence to conclude that the mean weight loss for the 41 participants on the exercise program is less than the mean weight loss for the 42 participants on the diet.
o The results are statistically significant at αα = 0.05, so there is sufficient evidence to conclude that the population mean weight loss on the exercise program is less than the population mean weight loss on the diet.
o The results are statistically insignificant at αα = 0.05, so there is statistically significant evidence to conclude that the population mean weight loss on the exercise program is equal to the population mean weight loss on the diet.
h. Interpret the p-value in the context of the study.
o There is a 22.77% chance that the mean weight loss for the 41 participants on the exercise program is at least 1 pounds less than the mean weight loss for the 42 participants on the diet.
o If the population mean weight loss on the exercise program is equal to the population mean weight loss on the diet and if another 41 and 42 participants on the exercise program and on the diet are observed then there would be a 22.77% chance that the mean weight loss for the 41 participants on the exercise program would be at least 1 pounds less than the mean weight loss for the 42 participants on the diet.
o There is a 22.77% chance of a Type I error.
o If the sample mean weight loss for the 41 participants on the exercise program is the same as the sample mean weight loss for the 42 participants on the diet and if another 41 participants on the exercise program and 42 participants on the diet are weighed then there would be a 22.77% chance of concluding that the mean weight loss for the 41 participants on the exercise program is at least 1 pounds less than the mean weight loss for the 42 participants on the diet
i. Interpret the level of significance in the context of the study.
o There is a 5% chance that you are such a beautiful person that you never have to worry about your weight.
o If the population mean weight loss on the exercise program is equal to the population mean weight loss on the diet and if another 41 and 42 participants on the exercise program and on the diet are observed then there would be a 5% chance that we would end up falsely concluding that the sample mean weight loss for these 41 and 42 participants differ from each other.
o There is a 5% chance that there is a difference in the population mean weight loss between those on the exercise program and those on the diet.
o If the population mean weight loss on the exercise program is equal to the population mean weight loss on the diet and if another 41 and 42 participants on the exercise program and on the diet are observed then there would be a 5% chance that we would end up falsely concluding that the population mean weight loss on the exercise program is less than the population mean weight loss on the diet
Is the average time to complete an obstacle course shorter when a patch is placed over the right eye than when a patch is placed over the left eye? Thirteen randomly selected volunteers first completed an obstacle course with a patch over one eye and then completed an equally difficult obstacle course with a patch over the other eye. The completion times are shown below. “Left” means the patch was placed over the left eye and “Right” means the patch was placed over the right eye.
Time to Complete the Course
Right 43 47 41 48 42 42 43 44
Left 42 50 42 49 45 44 45 46
Assume a Normal distribution. What can be concluded at the the αα = 0.10 level of significance level of significance?
For this study, we should use
a. The null and alternative hypotheses would be:
H0:H0:
H1:H1:
b. The test statistic = (please show your answer to 3 decimal places.)
c. The p-value = (Please show your answer to 4 decimal places.)
d. The p-value is αα
e. Based on this, we should the null hypothesis.
f. Thus, the final conclusion is that …
o The results are statistically insignificant at αα = 0.10, so there is insufficient evidence to conclude that the population mean time to complete the obstacle course with a patch over the right eye is less than the population mean time to complete the obstacle course with a patch over the left eye.
o The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the eight volunteers that were completed the course faster on average with the patch over the right eye compared to the left eye.
o The results are statistically insignificant at αα = 0.10, so there is statistically significant evidence to conclude that the population mean time to complete the obstacle course with a patch over the right eye is equal to the population mean time to complete the obstacle course with a patch over the left eye.
o The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the population mean time to complete the obstacle course with a patch over the right eye is less than the population mean time to complete the obstacle course with a patch over the left eye.
Is memory ability before a meal worse than after a meal? Ten people were given memory tests before their meal and then again after their meal. The data is shown below. A higher score indicates a better memory ability.
Score on the Memory Test
Before a Meal 66 70 46 71 81 83 71 70 67 64
After a Meal 71 74 48 86 79 97 74 79 78 68
Assume a Normal distribution. What can be concluded at the the αα = 0.10 level of significance?
For this study, we should use
a. The null and alternative hypotheses would be:
H0:H0:
H1:H1:
b. The test statistic = (please show your answer to 3 decimal places.)
c. The p-value = (Please show your answer to 4 decimal places.)
d. The p-value is αα
e. Based on this, we should the null hypothesis.
f. Thus, the final conclusion is that .
g.
a. The results are statistically insignificant at αα = 0.10, so there is insufficient evidence to conclude that the population mean memory score before a meal is lower than the population mean memory score after a meal.
b. The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the population mean memory score before a meal is lower than the population mean memory score after a meal
c. The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the ten memory scores from the memory tests that were taken before a meal are lower on average than the ten memory scores from the memory tests that were taken after a meal.
d. The results are statistically insignificant at αα = 0.10, so there is statistically significant evidence to conclude that the population mean memory score before a meal is equal to the population mean memory score after a meal.
h. Interpret the p-value in the context of the study.
a. If the sample mean memory score for the 10 people who took the test before a meal is the same as the sample mean memory score for the 10 people who took the test after a meal and if another 10 people are given a memory test before and after a meal then there would be a 0.24% chance of concluding that the mean memory score for the 10 people who took the test before a meal is at least 6.5 points lower than the mean memory score for the 10 people who took the test after a meal.
b. There is a 0.24% chance of a Type I error.
c. There is a 0.24% chance that the mean memory score for the 10 people who took the test before a meal is at least 6.5 points lower than the mean memory score for the 10 people who took the test after a meal.
d. If the population mean memory score before a meal is the same as the population mean memory score after a meal and if another 10 people are given a memory test before and after a meal then there would be a 0.24% chance that the mean memory score for the 10 people who took the test before a meal would be at least 6.5 points lower than the mean memory score for the 10 people who took the test after a meal.
Interpret the level of significance in the context of the study.
• If the population mean memory score before a meal is the same as the population mean memory score after a meal and if another 10 people are given a memory test before and after a meal, then there would be a 10% chance that we would end up falsely concuding that the population mean memory score before a meal is lower than the population mean memory score after a meal
• There is a 10% chance that your memory is so bad that you have already forgotten what this chapter is about.
• There is a 10% chance that the population mean memory score is the same before and after a meal.
• If the population mean memory score before a meal is the same as the population mean memory score after a meal and if another 10 people are given a memory test before and after a meal, then there would be a 10% chance that we would end up falsely concuding that the sample mean memory scores before and after a meal for these 10 people who were part of the study differ from each other.
