Question

A medical researcher is investigating the effect of drinking coffee on systolic blood pressure. The researcher assumes the average systolic blood pressure is 120 mmHg. For a random sample of 200 patients, the researcher takes two measurements of systolic blood pressure. The first systolic blood pressure measurement is taken during a week when the patients drink no coffee, and the second systolic blood pressure measurement is taken during a week when the patients drink at least two cups of coffee. The medical researcher wonders whether there is a significant difference between the blood pressure measurements.

Which of the following is the correct null and alternative hypothesis for the medical researcher’s study?

1. H₀: µ = 120; H_a: µ ≠ 120
2. H₀: µ = 0; H_a: µ ≠ 0
3. H₀: µ = 0; H_a: µ ≠ 120

Question 2

In a fictional study, suppose that a psychologist is studying the effect of daily meditation on resting heart rate. The psychologist believes the patients who not meditate have a higher resting heart rate. For a random sample of 45 pairs of identical twins, the psychologist randomly assigns one twin to one of two treatments. One twin in each pair meditates daily for one week, while the other twin does not meditate. At the end of the week, the psychologist measures the resting heart rate of each twin. Assume the mean resting heart rate is 80 heart beats per minute.

The psychologist conducts a T-test for the mean of the differences in resting heart rate of patients who do not meditate minus resting heart rate of patients who do meditate.

Which of the following is the correct null and alternative hypothesis for the psychologist’s study?

1. H₀: µ = 80; H_a: µ > 80
2. H₀: µ = 0; H_a: µ ≠ 0
3. H₀: µ = 0; H_a: µ > 0

Question 3

Facebook friends: According to Facebook’s self-reported statistics, the average Facebook user has 130 Facebook friends. For a statistics project a student at Contra Costa College (CCC) tests the hypothesis that CCC students will average more than 130 Facebook friends. She randomly selects 3 classes from the schedule of classes and distributes a survey in these classes. Her sample contains 45 students.

From her survey data she calculates that the mean number of Facebook friends for her sample is: ¯x= 138.7 with a standard deviation of: s=79.3.

She chooses a 5% level of significance. What can she conclude from her data?

1. Nothing. The conditions for use of a t-model are not met. She cannot trust that the p-value is accurate for this reason.
2. We cannot conclude that the average number of Facebook friends for CCC students is greater than 130. The sample mean of 138.7 is not significantly greater than 130.
3. Her data supports her claim. The average number of Facebook friends for CCC students is significantly greater than 130.

Question 4

According to a 2014 research study of national student engagement in the U.S., the average college student spends 17 hours per week studying. A professor believes that students at her college study less than 17 hours per week. The professor distributes a survey to a random sample of 80 students enrolled at the college.

From her survey data the professor calculates that the mean number of hours per week spent studying for her sample is: ¯x= 15.6 hours per week with a standard deviation of s = 4.5 hours per week.

The professor chooses a 5% level of significance. What can she conclude from her data?

1. The data supports the professor’s claim. The average number of hours per week spent studying for students at her college is less than 17 hours per week.
2. The professor cannot conclude that the average number of hours per week spent studying for students at her college is less than 17 hours per week. The sample mean of 15.6 is not significantly less than 17.
3. Nothing. The conditions for use of a t-model are not met. The professor cannot trust that the p-value is accurate for this reason.

Question 5

An urban planner is researching commute times in the San Francisco Bay Area to find out if commute times have increased. In which of the following situations could the urban planner use a hypothesis test for a population mean? Check all that apply.

1. The urban planner asks a simple random sample of 110 commuters in the San Francisco Bay Area if they believe their commute time has increased in the past year. The urban planner will compute the proportion of commuters who believe their commute time has increased in the past year.
2. The urban planner collects travel times from a random sample of 125 commuters in the San Francisco Bay Area. A traffic study from last year claimed that the average commute time in the San Francisco Bay Area is 45 minutes. The urban planner will see if there is evidence the average commute time is greater than 45 minutes.
3. The urban planner asks a random sample of 100 commuters in the San Francisco Bay Area to record travel times on a Tuesday morning. One year later, the urban planner asks the same 100 commuters to record travel times on a Tuesday morning. The urban planner will see if the difference in commute times shows an increase.

Question 6

The Food and Drug Administration (FDA) is a U.S. government agency that regulates (you guessed it) food and drugs for consumer safety. One thing the FDA regulates is the allowable insect parts in various foods. You may be surprised to know that much of the processed food we eat contains insect parts. An example is flour. When wheat is ground into flour, insects that were in the wheat are ground up as well.

The mean number of insect parts allowed in 100 grams (about 3 ounces) of wheat flour is 75. If the FDA finds more than this number, they conduct further tests to determine if the flour is too contaminated by insect parts to be fit for human consumption.

The null hypothesis is that the mean number of insect parts per 100 grams is 75. The alternative hypothesis is that the mean number of insect parts per 100 grams is greater than 75.

Is the following a Type I error or a Type II error or neither?

The test fails to show that the mean number of insect parts is greater than 75 per 100 grams when it is.

1. Type I error
2. Type II error
3. Neither

Question 7

Child Health and Development Studies (CHDS) has been collecting data about expectant mothers in Oakland, CA since 1959. One of the measurements taken by CHDS is the age of first time expectant mothers. Suppose that CHDS finds the average age for a first time mother is 26 years old. Suppose also that, in 2015, a random sample of 50 expectant mothers have mean age of 26.5 years old, with a standard deviation of 1.9 years. At the 5% significance level, we conduct a one-sided T-test to see if the mean age in 2015 is significantly greater than 26 years old. Statistical software tells us that the p-value = 0.034.

Which of the following is the most appropriate conclusion?

1. There is a 3.4% chance that a random sample of 50 expectant mothers will have a mean age of 26.5 years old or greater if the mean age for a first time mother is 26 years old.
2. There is a 3.4% chance that mean age for all expectant mothers is 26 years old in 2015.
3. There is a 3.4% chance that mean age for all expectant mothers is 26.5 years old in 2015.
4. There is 3.4% chance that the population of expectant mothers will have a mean age of 26.5 years old or greater in 2015 if the mean age for all expectant mothers was 26 years old in 1959.

Question 8

Child Health and Development Studies (CHDS) has been collecting data about expectant mothers in Oakland, CA since 1959. One of the measurements taken by CHDS is the weight increase (in pounds) for expectant mothers in the second trimester. In a fictitious study, suppose that CHDS finds the average weight increase in the second trimester is 14 pounds. Suppose also that, in 2015, a random sample of 40 expectant mothers have mean weight increase of 16 pounds in the second trimester, with a standard deviation of 6 pounds. At the 5% significance level, we can conduct a one-sided T-test to see if the mean weight increase in 2015 is greater than 14 pounds. Statistical software tells us that the p-value = 0.021.

Which of the following is the most appropriate conclusion?

1. There is a 2.1% chance that a random sample of 40 expectant mothers will have a mean weight increase of 16 pounds or greater if the mean second trimester weight gain for all expectant mothers is 14 pounds.
2. There is a 2.1% chance that mean second trimester weight gain for all expectant mothers is 14 pounds in 2015.
3. There is a 2.1% chance that mean second trimester weight gain for all expectant mothers is 16 pounds in 2015.
4. There is 2.1% chance that the population of expectant mothers will have a mean weight increase of 16 pounds or greater in 2015 if the mean second trimester weight gain for all expectant mothers was 14 pounds in 1959.

Question 9

A researcher conducts an experiment on human memory and recruits 15 people to participate in her study. She performs the experiment and analyzes the results. She uses a t-test for a mean and obtains a p-value of 0.17.

Which of the following is a reasonable interpretation of her results?

1. This suggests that her experimental treatment has no effect on memory.
2. If there is a treatment effect, the sample size was too small to detect it.
3. She should reject the null hypothesis.
4. There is evidence of a small effect on memory by her experimental treatment.

Question 10

A criminal investigator conducts a study on the accuracy of fingerprint matching and recruits a random sample of 35 people to participate. Since this is a random sample of people, we don’t expect the fingerprints to match the comparison print. In the general population, a score of 80 indicates no match. Scores greater than 80 indicate a match. If the mean score suggests a match, then the fingerprint matching criteria are not accurate.

The null hypothesis is that the mean match score is 80. The alternative hypothesis is that the mean match score is greater than 80.

The criminal investigator chooses a 5% level of significance. She performs the experiment and analyzes the results. She uses a t-test for a mean and obtains a p-value of 0.04.

Which of the following is a reasonable interpretation of her results?

1. This suggests that there is evidence that the mean match score is greater than 80. This suggests that the fingerprint matching criteria are not accurate.
2. If there is a treatment effect, the sample size was too small to detect it. This suggests that we need a larger sample to determine if the fingerprint matching criteria are not accurate.
3. She cannot reject the null hypothesis. This suggests that the fingerprint matching criteria could be accurate.
4. This suggests that there is evidence that the mean match score is equal to 80. This suggests that the fingerprint matching criteria is accurate.

Question 11

A group of 42 college students from a certain liberal arts college were randomly sampled and asked about the number of alcoholic drinks they have in a typical week. The purpose of this study was to compare the drinking habits of the students at the college to the drinking habits of college students in general. In particular, the dean of students, who initiated this study, would like to check whether the mean number of alcoholic drinks that students at his college in a typical week differs from the mean of U.S. college students in general, which is estimated to be 4.73.

The group of 42 students in the study reported an average of 5.31 drinks per with a standard deviation of 3.93 drinks.

Find the p-value for the hypothesis test.

The p-value should be rounded to 4-decimal places.

Question 12

Commute times in the U.S. are heavily skewed to the right. We select a random sample of 240 people from the 2000 U.S. Census who reported a non-zero commute time.

In this sample the mean commute time is 28.9 minutes with a standard deviation of 19.0 minutes. Can we conclude from this data that the mean commute time in the U.S. is less than half an hour? Conduct a hypothesis test at the 5% level of significance.

What is the p-value for this hypothesis test?

Your answer should be rounded to 4 decimal places.

Question 13

Dean Halverson recently read that full-time college students study 20 hours each week. She decides to do a study at her university to see if there is evidence to show that this is not true at her university. A random sample of 35 students were asked to keep a diary of their activities over a period of several weeks. It was found that the average number of hours that the 35 students studied each week was 18.5 hours. The sample standard deviation of 4.3 hours.

Find the p-value.

The p-value should be rounded to 4-decimal places.

Question 14

A medical researcher is studying the effects of a drug on blood pressure. Subjects in the study have their blood pressure taken at the beginning of the study. After being on the medication for 4 weeks, their blood pressure is taken again. The change in blood pressure is recorded and used in doing the hypothesis test.

Change: Final Blood Pressure - Initial Blood Pressure

The researcher wants to know if there is evidence that the drug affects blood pressure. At the end of 4 weeks, 36 subjects in the study had an average change in blood pressure of 2.4 with a standard deviation of 4.5.

Find the p-value for the hypothesis test.

Your answer should be rounded to 4 decimal places.

Question 15

Find the p-value for the hypothesis test. A random sample of size 54 is taken. The sample has a mean of 375 and a standard deviation of 83.

H0: µ = 400

Ha: µ< 400

The p-value for the hypothesis test is .

Your answer should be rounded to 4 decimal places.

Question 16

Child Health and Development Studies (CHDS) has been collecting data about expectant mothers in Oakland, CA since 1959. One of the measurements taken by CHDS is the weight increase (in pounds) for expectant mothers in the second trimester.

In a fictitious study, suppose that CHDS finds the average weight increase in the second trimester is 14 pounds. Suppose also that, in 2015, a random sample of 39 expectant mothers have mean weight increase of 15.9 pounds in the second trimester, with a standard deviation of 6.0 pounds.

A hypothesis test is done to see if there is evidence that weight increase in the second trimester is greater than 14 pounds.

Find the p-value for the hypothesis test.

The p-value should be rounded to 4 decimal places.

Answer 1

1)

1. H₀: µ = 120; H_a: µ ≠ 120

2)

1. H₀: µ = 0; H_a: µ > 0

3)

Ho :   µ =   130                  
Ha :   µ >   130       (Right tail test)          
                          
Level of Significance ,    α =    0.05                  
sample std dev ,    s =    79.3000                  
Sample Size ,   n =    45                  
Sample Mean,    x̅ =   138.7000                  
                          
degree of freedom=   DF=n-1=   44                  
                          
Standard Error , SE = s/√n =   79.3   / √    45   =   11.8213      
t-test statistic= (x̅ - µ )/SE = (   138.700   -   130   ) /    11.821   =   0.736
                          
  
p-Value   =   0.2328   [Excel formula =t.dist(t-stat,df) ]              
Decision:   p-value>α, Do not reject null hypothesis                       

answer:

1. We cannot conclude that the average number of Facebook friends for CCC students is greater than 130. The sample mean of 138.7 is not significantly greater than 130.