Question

Question 1

Select one answer.

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 2

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 3

A group of 51 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 51 students in the study reported an average of 4.35 drinks per with a standard deviation of 3.88 drinks.

Find the p-value for the hypothesis test.

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

Question 4

Commute times in the U.S. are heavily skewed to the right. We select a random sample of 510 people from the 2000 U.S. Census who reported a non-zero commute time.

In this sample, the mean commute time is 28.0 minutes with a standard deviation of 19.1 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 5

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 31 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 31 students studied each week was 18.9 hours. The sample standard deviation of 3.7 hours.

Find the p-value.

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

Question 6

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 increases blood pressure. At the end of 4 weeks, 31 subjects in the study had an average change in blood pressure of 2.9 with a standard deviation of 5.3.

Find the p-value for the hypothesis test

Your answer should be rounded to 4 decimal places.

Question 7

Find the p-value for the hypothesis test. A random sample of size 54 is taken. The sample has a mean of 426 and a standard deviation of 82.

H0: µ = 400

Ha: µ > 400

The p-value for the hypothesis test is

Your answer should be rounded to 4 decimal places.

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 37 expectant mothers have mean weight increase of 16.0 pounds in the second trimester, with a standard deviation of 6.1 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

Question 1

This option is correct

{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.}

___________________________________________________________________________________________

Question 2

This option is correct

{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.}

___________________________________________________________________________________________

Question 3

The p-value is p = 0.4875

___________________________________________________________________________________________

Question 4

The p value is p= 0.0092