Statistics - Hypothesis Testing Projects

Suppose scores on an exam are normally distributed with a mean of 60 and standard deviation of 8. If you

Suppose scores on an exam are normally distributed with a mean of 60 and standard deviation of 8. If you use the scores to award academic prizes, what cutoff score should you use if you only want to award prizes to the top 1% of the students?
A dietitian wants to test if a new food menu on campus is lowering the weight of students. To investigate, she randomly samples 49 students and records their weights. The scores have a mean of 151 pounds. A recent campus census taken before the new food menu showed the mean weight for students of 157 pounds with a standard deviation of 9 pounds. Can the researcher conclude that students now weigh less? Show all 4 steps of our hypothesis testing procedure.

Of the next problems, problem 1 is to be done by hand and problems 2-5 are to be done using SPSS with the results written out and interpreted by hand.

1. A developmental psychologist would like to determine if depression is affected by age. It is known that the general population averages a mean of 50 and a standard deviation of 10 on a standardized test of depression. The psychologist wished to see if seniors (age greater than or equal to 65) have greater depression on average than the general population. Assuming that depression scores are normally distributed and that the standard deviation remains 10 for seniors, how large a sample must she use to test her directional hypothesis if she wants the probability of a Type I error, alpha to be .01 and she wants the probability of a Type 2 error, Beta to be .05 when Mean1 =65?

2. A school administrator is interested in purchasing a set of teaching aids to supplement classroom instruction. However, before purchasing the aids she wants to make sure student scores on a national standardized test would increase to at least a mean of 85. To asses this, she had 20 students use the teaching aids and recorded their scores (given below). On the basis of this research, would she be justified in purchasing the instructional aids? Use alpha = .05 and show all 4 steps of our hypothesis testing procedure. Interpret your results as if you are addressing a group of other administrators.
Test scores: 82,93,88,98,84,89,90,100,110,79,95,105,91,85,89,86,99,78,97,115
For the data in problem 2, construct the 90% confidence interval for estimating the population mean and interpret your results.
A dental hygienist wants to evaluate the effect of a dental film on the frequency with which children brush their teeth. 30 children were randomly selected and randomly assigned to one of two conditions. One group of 15 children watched the film and the other 15 did not. The number of times the children brushed their teeth over a one month period was recorded and shown below. Can the educator conclude using alpha =.01 that the film has an effect on the frequency with which children brush their teeth. State any assumptions you must make as part of step 2. Show all 4 steps of our hypothesis testing procedure. Interpret your results as if you were addressing a group of parents.

Film No film
22 22
28 25
27 22
30 26
30 28
25 26
25 22
30 30
29 19
29 26
27 25
27 24
30 27
28 25
26 22
For the data in problem 4, construct the 95% confidence interval for the difference between the population means and interpret your results.