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# Hypothesis testing problem

1. A researcher conducts a two tailed two sample t test on 28 subjects (14 subjects in each Group) and finds that t=1.986.
a. How many degrees of freedom are there in this study?
b. Estimate the actual type 1 error for this study.
c. If the researcher decides to reject the null hypothesis, how confident can the researcher be that the results are due to the treatment and not due to mere sampling error?
d. Report the results as they would appear in an academic journal.

2. Researcher conducts a one tailed two sample t test on 32 subjects (16 subjects in each group) and finds that t=2.182.

a. How many degrees of freedom are there in this study?
b. Estimate the actual type 1 error for this study.
c. If the researcher decides to reject the null hypothesis, how confident can the researcher
be that the results are due to the treatment and not due to mere sampling error?
d. Report the results as they would appear in an academic journal.

3. You read a study that reports p=.07.

a. What confidence can you have that the results are due to the treatment rather than to mere
sampling error?
b. What additional information would you need before deciding, whether to put the finding to your own use?

4. A collage is expecting an entering freshman class of 700. The sex ratio of the incoming class is exactly 350 women and 350 men. The mean score on a test of writing skills for 70 incoming female freshmen attending one of several collage orientation sessions is 84 the mean score for 70 incoming male freshman on the same writing test at the same orientation sessions is 78. The &#963; µ1-µ2 for the writing test is 2.15 points.

b. In constructing an interval estimate for the difference in writing score between men and Women in the entire incoming freshman class, what difference score will fall in the Center of the interval?
d.If the admissions officer were willing to be only 90% confident, would the confidence Interval be larger or smaller? Why?

5. A social psychologist measures the average time what 20 new transfer students at an orientation party mingle with other new transfer students before selecting a chair or corner in which to settle. Ten of the new transfer students are from nearby colleges, and 10 are from distant colleges. The average mingle time for students transferring from nearby colleges is 6.2 min. the average mingle time for students transferring from distant colleges is 5.4 min. The &#963;µ1- µ2 for mingle time .47 min.
b) In constructing an interval estimate for the difference in mingle time between the nearby and distant transferees, what time difference will fall in the center of the interval?

7. Exercise 3 in module 20 addressed the rated effectiveness of two of the Shine Company's cleaning products: one with a fragrance added and one without a fragrance added. Twenty four subjects rated the scented cleaner as 17/2 points more effective than the unscented cleaner. The value of &#963;µ1- µ2 was 0.50.
a) What is the best point estimated for the difference in effectiveness ratings of the ext group of 24 participants who are asked to rate the effectiveness of the scented versus unscented cleaners?
b) In constructing an interval estimate for the difference in effectiveness ratings for the scented versus unscented cleaners, what difference score will fall in the center of the interval?
c) The Shiny Company can be 95% confident that the true difference in effectiveness ratings between the scented and unscented cleaners falls between which two values?

8. Exercise 4 in module 20 addressed the number of large verses small posters displayed by homeowners supporting the candidate Elena Martin. Posters of each type were sent to homeowners supporting her in each of 10 districts. On average, supporting displayed 8.2 more small posters than large posters. The value of &#963;µ1- µ2 was 2.62.
a) What is the best point estimate for the difference in number of large versus small posters displayed by the next group of Elena Martin's supporters in the 10 districts?
b) In constructing an interval estimate for the difference in number of large versus small posters displayed by the next group of Elena Martin's supporters, what score will fall in the center of the interval?
c) Elena Martin can be 99% confident that the true difference in the number of posters displayed by any 100 supportive homeowners sent each type of poster fails between which two values?

#### Solution Summary

The solution provides step by step method for the calculation of test statistic . Formula for the calculation and Interpretations of the results are also included.

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