Question

From the list given to you for each of the following hypothesis testing situations, indicate the test you would use and the reason (e.g., One sample test for the variance of a normal distribution)

1) One sample z test for the mean of a normal distribution with known variance (Test 1*)

2) One-Sample T-Test for the Mean of a Normal Distribution with unknown Variance (Test 2)

3) The paired t-test (Test 3)

a) A major portion of waiters’ and waitresses’ incomes is derived from tips. The IRS assumes that the average weekly total of tips is $100. A tax accountant who formerly worked as a waitress believes that this figure underestimates the true value. As a result, she conducts a survey among 150 randomly selected waitresses and finds the mean to be $104. Assuming that the population standard deviation is $22, can the researcher determine whether there is sufficient evidence to show that the average weekly tip total exceeds $100? Assume a normal distribution ( Test______________ Why?____________________

b) A manufacturer of automobile seats has a production line that produces an average of 100 seats per day. Because of new government regulations, a new safety device has been installed, which the manufacturer believes will reduce average daily output. A random sample of 15 day’s output after the installation of the safety device is shown below: 93, 103, 95, 101, 91, 105, 96, 94, 101, 88, 98, 94, 101, 92, 95 Assuming the daily output is normally distributed, is there sufficient evidence to conclude the average daily output has decreased following the installation of the safety device ( Test______________ Why?____________________

c) Suppose that it is known that the average lifetime of a 50-year old in 1945 is 18.5 years. Twenty persons age 50 who have been working for at least 20 years in a potentially hazardous industry are ascertained in 1945, and upon follow-up, it is found that their average lifetime is 16.2 years with standard deviation 7.3 years. If we assume that the lifetime of a 50-year-old is approximately normally distributed, then test if the average lifetime of this group is lower than would be expected. Test______________ Why?____________________ d) In order to help children rest night, 10 children were asked to rate their bedtime anxiety due to fear of nighttime monsters on a 1 to 10 scale (1 = not afraid at all, 10 = very afraid), then Acme Monster Spray, an inert sweet-smelling mist was administered by their parents, after which children were asked to rate their anxiety level. Upon spraying, children reported a .30-point average drop in anxiety (5.70 before spraying, down to 5.40 after spraying) Test______________ Why?____________________

Answer 1

a) We will use Test 1 - One sample z test for the mean because the population standard deviation is mentioned in the question

b) We will use Test 2 -  One-Sample T-Test for the Mean because though we have assumed that the data is normally distributed but the variance for the population is not given, hence One-Sample T test.

c) We will use Test 2 -  One-Sample T-Test for the Mean because though we have assumed that the data is normally distributed but the variance for the population is not given, hence One-Sample T test.

d) We will use Test 3 - Paired sample T test, because the subjects in the study is same BEFORE AND AFTER