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# Graphical Devices for Checking Test Results

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1. A random sample of 10 college students was drawn from a large University. Their ages are 22, 17, 27, 20, 23, 19, 24, 18, 19, and 24 years. What is the required condition to test to determine if we can infer that the population mean is not equal.

What graphical device can you use to check to see if that required condition is satisfied?

2. Construct a 95% confidence interval estimate for the population variance of the weight if a random sample of 25 fish showed a variance of 20.

3. Thirty-five employees who completed two years of college were asked to take a basic mathematics test The mean and standard deviation of their scores were 75.1 and 12.8, respectively. In a random sample of 50 employees who only completed high school, the mean and standard deviation of the test scores were 72.1 and 14.6 respectively. Estimate with 90% confidence the difference in mean scores between the two groups of employees. Explain how to use the interval to test the hypotheses.

4. An investor is considering two types of investment. She is quite satisfied that the expected return on investment 1 is higher than the expected return on investment 2. However, she is quite concerned that the risk associated with investment 1 is higher than that of investment 2. To help make her decision, she randomly selects seven monthly returns on investment 1 and ten monthly returns on investment 2. She finds that the sample variances of investments 1 and 2 are 225 and 118, respectively. Estimate with 95% confidence the ratio of the two population variances. Briefly describe what the interval estimate tells you.