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# Pooled variance, Interval data & Hypothesis Testing

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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?