# Pooled Variance, Interval Data and Hypothesis Testing

1. What is pooled variance and why is it important?

2. Explain what interval data is and give an example:

3. Write the formula for a problem that has 2 sample populations greater than 30 and the standard deviations are known and equal:

4. Write the formula for pooled variance.

5. Please analyze the following data using the T-test for Unpaired data:

A school district wants to determine if the girls are equal to boys in test scores. They took a random sample of 22 8th grade girls and 24 8th grade boys. The district looked at recent CAT scores and found the mean score for girls to be xbar1 = 25 and the mean score for boys to be xbar2 = 26. The standard deviation for the girls is s1 = 2.2 and for the boys the standard deviation is s2 = 3.4. Is the school district correct in assuming the girls are equal in performance to boys. They are 95% sure their assumption is correct.

6. Please analyze the following data using the Z-test for Unpaired data

A candy company wants to identify whether or not the size of its' candy bars are the same length from one day to another. On day 1 they sample 52 candy bars with an average mean of 5.4 inches and on day 2 they sample 52 bars again with and average mean of 5.6 inches. Both days have sample standard deviations of 3.4. Is the average mean of size different from day 1 to day 2?

7. A sample of 40 observations is selected from one population. The sample mean is 102 and the sample standard deviation is 5. A sample of 50 observations is selected from a second population. The sample mean is 99 and the sample standard deviation is 6. Conduct the following test using 95% level of confidence. Z-test for Unpaired data

A. Is it a 1 or 2 tail test

B. Compute the statistical calculation

C. What is your decision regarding H1

8. A sample of 65 observations is selected from one population. The sample mean is 2.67 and the sample standard deviation is .75. A sample of 50 observations is selected from a second population. The sample mean is 2.59 and the sample standard deviation is .66. Conduct the following test using 95% level of confidence. Z-test for Unpaired data

a. Is it a 1 or 2 tail test

b. Compute the statistical calculation

c. What is your decision regarding H1?

d. What is the P-value?

9. The Gibbs Baby Food Company wishes to compare the weight gain of infants using their brand versus their competitor's brand. A sample of 40 babies using the Gibbs products revealed a mean weight gain of 7.6 pounds in the first 3 months after birth. The standard deviation of this sample is 2.3 pounds. A sample of 55 babies using the competitors brand revealed a mean increase of 8.8 pounds with a standard deviation of 2.9 pounds. At 95% level of confidence, can we conclude that the babies using the Gibbs product gained LESS weight? Z-test for Unpaired data

10. What key words tell you that the Hypothesis is to be set up as a 1 Tail UPPER?

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#### Solution Summary

The solution provides a step by step method for the calculation of testing of hypotheses. The solution also provides information on pooled variance, its importance, interval data and formula for pooled variance. Formula for the calculation and interpretations of the results are also included. An interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.