(a) state the decision rule, (b) compute the pooled estimate of the population variance, (c) compute the test statistic, (d) state your decision about the null hypothesis, and (e) estimate the p-value.
The null and alternate hypotheses are:
Ho: µ1 = µ2
Ha: µ1 ≠ µ2
Please use the five-step hypothesis testing procedure for the following exercises. Please use Excel and show all formula outputs.
14. A random sample of 15 observations from the first population revealed a sample mean of 350 and a sample standard deviation of 12. A random sample of 17 observations from the second population revealed a sample mean of 342 and a sample standard deviation of 15. At the .10 significance level, is there a difference in the population means?
18. The Tampa Bay (Florida) Area Chamber of Commerce wanted to know whether the mean weekly salary of nurses was larger than that of school teachers. To investigate, they collected the following information on the amounts earned last week by sample of school teachers and nurses.
School teachers ($) 845 826 827 875 784 809 802 820 829 830 842 832
Nurses ($) 841 890 821 771 850 859 825 829
Is it reasonable to conclude that the mean salary of nurses is higher? Use .01 LOS. What is the P-value?
22. The federal government recently granted funds for a special program designed to reduce crime in high-crime areas. The study of results of the program in eight high-crime areas of Miami, FL, yielded the following results.
Number of Crimes by Area
A B C D E F G H
14 7 4 5 17 12 8 9
2 7 3 6 8 13 3 5
Has there been a decrease in the number of crimes since the inauguration of the program? Use .01 LOS. Estimate P-value.
44. The following data resulted from a taste test of two different chocolate bars. The first number is a rating of the taste, which could range from 0 to 5, with a 5 indicating the person liked the taste. The second number indicates whether a "secret ingredient" was present. If the ingredient was present a code of "1" was used and a "0" otherwise. At the .05 significance level, does this data show a difference in the taste ratings?
Rating "With/Without" Rating "With/Without"
3 1 1 1
1 1 4 0
0 0 4 0
2 1 2 1
3 1 3 0
1 1 4 0
Step by step method for testing the hypothesis under 5 step approach is discussed here. Excel template for each problem is also included. This template can be used to obtain the answers of similar problems.