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# Hypothesis Testing & Confidence Interval

See attached file.

I do not have the capabilty to use Microsoft Word's Equation Editor and on some of these questions the "x" should have a line over it.

1. Write a hypothesis to test the differences between two populations.

2. (STATISTICAL INFERENCES ABOUT TWO POPULATIONS) Use the following sample information to construct a 90% confidence interval for the difference in the two population means.

Sample 1 Sample 2
n&#305; = 32 n2 = 31
x&#305; = 70.4 x2 = 68.7
&#963;1 = 5.76 &#963;2 = 6.1

3. (STATISTICAL INFERENCES ABOUT TWO POPULATIONS) A. Use the following data and a = .10 to test the stated hypotheses. Assume x is normally distributed in the populations and the variances of the populations are approximately equal. H0: µ1 - µ2 = 0 Ha: µ1 - µ2 = 0

Sample 1 Sample
2 n1 = 20 n2 = 20
x1 = 118 x2 = 113
s 1 = 23.9 s 2 = 21.6

B. Use these data to construct a 90% confidence interval to estimate µ1 - µ2.

4. What is a matched-pairs test

5. When does one use an F test?

6. (TESTING HYPOTHESES ABOUT TWO POPULATION VARIANCES) Test the following hypotheses by using the given sample information and a = .05. Assume the populations are normally distributed. H0: s 2 1 = s 2 2 Ha: s 2 1 = s 2 2 n1 = 5, n2 = 19, s1 = 4.68, s2 = 2.78

7. (ANALYSIS OF VARIANCE AND DESIGN OF EXPERIMENTS) Compute a one- way ANOVA on the following data. (use Excel)
1 2 3 4 5
14 10 11 16 14
13 9 12 17 12
10 12 13 14 13
9 12 16 13
10 17 12
14
Determine the observed F value. Compare the observed F value with the critical table F value and decide whether to reject the null hypothesis. Use a = .01.

#### Solution Summary

The solution provides step by step method for the calculation of testing of hypothesis, ANOVA and confidence interval for difference in two population means. The solution also provides a brief explanation on he use of paired t test and F test. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

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