Chpt9 part 2 (problems 3 and 6)

Research was conducted on whether drinking chamomile tea helped students get to sleep faster. The amount of time in minutes it took students to get to sleep in each group was recorded below. Students drinking chamomile tea: n=20, xˉ=5.5, s=0.9 Students not drinking chamomile tea: n=25, xˉ=7.8, s=1.4 Test the claim that drinking chamomile tea helped students get to sleep faster using a 0.05 significance level. What is the t-value, P-value, and conclusion of this t-test?

• t-value: -6.424, P-value: 0.99999; Fail to reject the null hypothesis; does not support the claim

• t-value: -2.01, P-value: 0.05; Fail to reject the null hypothesis; does not support the claim

• t-value: -2.01, P-value: 0.05; Reject the null hypothesis; supports the claim

• t-value: -6.424, P-value: 5.40e-08; Reject the null hypothesis; supports the claim

Research was conducted on whether using a white noise machine helped students get to sleep faster. The amount of time (in minutes) it took students to fall asleep was recorded for two groups: Students using a white noise machine: n=18, xˉ=6.3, s=0.8 Students not using a white noise machine: n=22, xˉ=8.5, s=1.5 Use a 0.05 significance level to test the claim that using a white noise machine helps students fall asleep faster. What is the t-value, P-value, and conclusion of this t-test?

• t-value: -5.926, P-value: 5.90e-07; Reject the null hypothesis; supports the claim

• t-value: -5.926, P-value: 0.99; Fail to reject the null hypothesis; does not support the claim

• t-value: -2.01, P-value: 0.05; Fail to reject the null hypothesis; does not support the claim

• t-value: -2.01, P-value: 0.05; Reject the null hypothesis; supports the claim

Research was conducted on whether reading a book before bed helped students get to sleep faster. The amount of time (in minutes) it took students to fall asleep was recorded for two groups: Students reading a book before bed: n=16, xˉ=5.0, s=0.7 Students not reading a book before bed: n=24, xˉ=7.0, s=1.3 Use a 0.05 significance level to test the claim that reading a book before bed helps students fall asleep faster. What is the t-value, P-value, and conclusion of this t-test?

• t-value: -2.01, P-value: 0.05; Reject the null hypothesis; supports the claim

• t-value: -6.292, P-value: 0.99; Fail to reject the null hypothesis; does not support the claim

• t-value: -2.01, P-value: 0.05; Fail to reject the null hypothesis; does not support the claim

• t-value: -6.292, P-value: 1.30e-07; Reject the null hypothesis; supports the claim

A coach wants to see if a new strength training program affects the vertical jump height of their basketball players. The vertical jump height of 15 basketball players is measured again. Before Training (Group 1): (Assume we have the raw data for 15 players) with a calculated sample mean (x̄₁) and sample standard deviation (s₁). After Training (Group 2): (Assume we have the raw data for the same 15 players) with a calculated sample mean (x̄₂) and sample standard deviation (s₂). Test the claim, using a 0.05 significance level, that the new strength training program has increased the vertical jump height of the basketball players (i.e., their jump height after training is greater than before training). What type of data and test statistic would be used for this hypothesis test?

• Independent data; t-test

• Independent data; Z-test

• Dependent data; t-test

• Dependent data; F-test

The average score of 25 students in math is 85 with a deviation of 5. The average score of 28 students in science is 78 with a deviation of 6. Group 1: n=25, xˉ=85, s=5 Group 2: n=28, xˉ=78, s=6 Test the claim using a 0.05 significance level. What type of data and test statistic would be used for this hypothesis test?

• Independent data; t-test

• Independent data; Z-test

• Dependent data; t-test

• Dependent data; F-test

A researcher wants to investigate the effect of a new aerodynamic bicycle design on a group of athletes' cycling speed compared to their running speed over a fixed distance. Ten athletes each complete a race distance by running, and then, on a separate occasion, complete the same race distance by cycling using the new aerodynamic bicycle. The time taken (in minutes) for each athlete in both the running and cycling trials is recorded. Running Times (Group 1): (Assume we have the raw data for 10 athletes) with a calculated sample mean (x̄₁) and sample standard deviation (s₁). Cycling Times (Group 2): (Assume we have the raw data for the same 10 athletes) with a calculated sample mean (x̄₂) and sample standard deviation (s₂). Test the claim, using a 0.05 significance level, that the new aerodynamic bicycle helps these athletes complete the distance faster (i.e., their cycling time is less than their running time). What type of data and test statistic would be used for this hypothesis test?

• Independent data; t-test

• Dependent data; Z-test

• Dependent data; t-test

• Dependent data; F-test

The average number of books read by 15 adults in a year is 10 with a deviation of 3 books. The average number of books read by 20 teenagers in a year is 7 with a deviation of 2 books. Group 1: n=15, xˉ=10, s=3 Group 2: n=20, xˉ=7, s=2 Test the claim using a 0.05 significance level. What type of data and test statistic would be used for this hypothesis test?

• Independent data; Z-test

• Independent data; t-test

• Dependent data; t-test

• Dependent data; F-test