Question

Question 1: For each of the following below you should decide
a) What test would you use?
b) Why would you use this test?

1. You wish to test the hypothesis that introverted people earn less money than extroverted people. You sample 27 people from your graduating class and ask them how much money they make and also give them a test to determine how introverted they are. This test of introversion yields a score from 0 to 100 with 0 being not introverted at all (i.e. extroverted) and 100 being very introverted.

2. There are 2 washing machines in your apartment building and you think that the time it takes to wash your clothes varies depending on which machine you use. You decide to test this and spend one afternoon in your laundry room. You record the time it takes to wash one load each time a person does their laundry and end up with the following data. Machine 1 was used 14 times and the mean time for 1 wash was 22.1 minutes with a standard deviation of 2.2 minutes. Machine 2 was used 17 times and took an average of 21.0 minutes per wash with a standard deviation of 1.6 minutes

3. You have developed a new treatment for Alzheimer’s and wish to test it. You give your treatment to 15 patients with suspected Alzheimer’s disease and a placebo to 15 other patients with suspected Alzheimer’s disease. Your treatment is inexpensive, and has few side effects. You give each person a memory test after 3 months of treatment. Scores on this test are based on number of items remembered from a list after a delay of 1 hour.

Answer 1

1st problem:

a) I will do t test.

b) At first I try to fit linear regression. Response variable is the money earned and explanatory variable is the introvert score. By least square technique we can estimate 0 and 1. Now null hypothese, H0:  1=0, Alternate hypotheses, H1:  1 <0. test statistics would be estimated value of  1 divided by standard error of  1..So it would be one tail t test. If t test is not signifcant then  1=0 i.e there is no significant correlation between money earned and introvert score. But if  1 <0 then there is relation between money earned and introvert score. If the value of 1 comes negative then we can conclude introvert people earn less money than extroverted people.

2nd problem:

a) I will do t test

b) Here two population( Washing machine) means to be compaired. samples are taken from both the population. sample mean and standard deviation data is there. The best test here to do is t test. We assumed standard deviations are different . Rejecting the null hypotheses concludes two washing machine has different washing time.

3rd problem:

a) t test

b) Here also we have to compare 2 populations ( new treatment vs placebo). We have mean score and standard deviation of score for patients getting treatment and and for patients getting placebo. H0: , H1:. two tail t test best suited here. Rejecting the null hypotheses colucludes that treatment is working.