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# Multiple t test based questions

1.) A spelling test is given to random samples of size 6 from executive secretaries at each of two large insurance companies. The results (in errors/document are:

Company A Company B
Subject 1 5 3
2 9 4
3 2 9
4 0 8
5 6 2
6 8 2

Test, at a.05 level of significance, the hypothesis that executive secretaries from Company A have more errors per document than executive secretaries from company B.

2.) Seven seniors at MTSU were randomly selected and the amount they spent for books and the amount they spent for University fees were ascertained. The table below presents the results:

Student # Book \$ Fee \$
1 117 273
2 119 181
3 128 190
4 116 179
5 220 181
6 113 160
7 215 175
Assuming that both dollar amounts are normally distributed test, at a .05 level of significance, the hypothesis that the amount spent on books and the amount spent on fees are, on average, the same.

3.) A weight-reduction clinic claims that their program provides a loss of at least 10 pounds in 20 days. A random sample of 7 members yielded the following data:
Individual 1 2 3 4 5 6 7
Initial Weight 130 180 110 250 150 165 170
Weight After 20 days 122 176 105 230 130 166 160
Test the claim at a .05 level of significance.

4.) An wholesaler of novelty items sells her products to stores in enclosed malls and to stores in strip malls. She suspects that the average mark-up is significantly higher in those stores which are in enclosed malls. She decides to test the hypothesis by taking two samples drawn at random from her customer list. The results were:
Enclosed Malls Strip Malls
Sample Size 25 30
Average Mark-up .55 .48
Standard Deviation .10 .14
Test, at a .05 level of significance, her hypothesis that the mark- up is higher for enclosed than for strip malls if it is known that mark-ups are normally distributed.

5.) An identical keyboarding test is given to random samples of size 40 from each of two large insurance companies. The results (in words/minute) are:

Company A Company B
Mean 50 53
Standard Deviation 7.874 6.693
Test, at a .05 level of significance, the hypothesis that typists from the two companies average the same speed.

6.) Studies at a prominent medical school indicate that the typical individual with back problems will take at least a week to have ease of their back pain, with a standard deviation of 2.25 days. A chiropractic clinic advertises that its services will alleviate your back problems (almost) immediately. A random sample of 9 individuals with back problems who were patients of the clinic and a control group of 9 individuals with back problems who received no treatment reported ease of back pain in the following number of days;

Individual 1 2 3 4 5 6 7 8 9
Clinic Patients 6 8 3 10 5 6 7 7 5
Control Group 6 7 10 2 3 6 6 5 8
Test the hypothesis that on average the two groups received ease of back pain in the same number of days (use a .05 level of significance and assuming normality).

#### Solution Summary

The solution gives detailed explanations as to how to use t test to evaluate the claims.

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