Question

A new SAT study course is tested on 12 individuals. Pre-course and post-course scores are recorded. Of interest is the average increase in SAT scores. The following data is collected. Conduct a hypothesis test at the 5% level.

Pre-course score	Post-course score
1200	1340
910	900
1080	1100
840	880
1100	1070
1250	1320
860	860
1330	1370
790	770
990	1040
1110	1200
740	850

What is the test statistic?

p value?

While her husband spent 2½ hours picking out new speakers, a statistician decided to determine whether the percent of men who enjoy shopping for electronic equipment is higher than the percent of women who enjoy shopping for electronic equipment. The population was Saturday afternoon shoppers. Out of 65 men, 22 said they enjoyed the activity. 8 of the 24 women surveyed claimed to enjoy the activity. Interpret the results of the survey. Conduct a hypothesis test at the 5% level. Let the subscript m = men and w = women.

State the distribution to use for the test. (Round your answer to four decimal places.)

What is the p-value?

Marketing companies have collected data implying that teenage girls use more ring tones on their cellular phones than teenage boys do. In one particular study of 40 randomly chosen teenage girls and boys (20 of each) with cellular phones, the average number of ring tones for the girls was 3.1 with a standard deviation of 1.6. The average for the boys was 1.8 with a standard deviation of 0.8. Conduct a hypothesis test at the 5% level to determine if the averages are approximately the same or if the girls' average is higher than the boys' average.

State the distribution to use for the test. (Enter your answer in the form z or t_df where df is the degrees of freedom. Round your answer to two decimal places.)

What is the test statistic? (Round your answer to two decimal places.)

What is the p-value? (Round your answer to four decimal places.)

Answer 1

We have to test

We test the claim that SAT scores have improved after the cource.

Since the sample sizes are small, , we use T-test.
The test statistic is

Here, the sample means are . The sample standard deviations are . Thus the test statistic is

The P-value of the test is

Since the , we retain the null hypothesis.

We are 95% confident that the SAT scores have not improved after the coures.

We are required to solve only one question. Please post the remaining questions as another post.