Let x represent the average annual salary of college and university professors (in thousands of dollars) in the United States. For all colleges and universities in the United States, the population variance of x is approximately σ2 = 47.1. However, a random sample of 11 colleges and universities in Kansas showed that x has a sample variance s2 = 86.8. Use a 5% level of significance to test the claim that the variance for colleges and universities in Kansas is greater than 47.1. Find a 95% confidence interval for the population variance. (a) What is the level of significance? State the null and alternate hypotheses. Ho: σ2 < 47.1; H1: σ2 = 47.1Ho: σ2 = 47.1; H1: σ2 ≠ 47.1    Ho: σ2 = 47.1; H1: σ2 > 47.1Ho: σ2 = 47.1; H1: σ2 < 47.1 (b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.) What are the degrees of freedom? What assumptions are you making about the original distribution? We assume a uniform population distribution.We assume a normal population distribution.    We assume a exponential population distribution.We assume a binomial population distribution. (c) Find or estimate the P-value of the sample test statistic. P-value > 0.1000.050 < P-value < 0.100    0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-value < 0.005

A researcher takes sample temperatures in Fahrenheit of 16 days from Miami and 14 days from Atlanta. Use the sample data shown in the table. Test the claim that the mean temperature in Miami greater than the mean temperature in Atlanta. Use a significance level of α=0.10α=0.10.Assume the populations are approximately normally distributed with unequal variances.Note that list 1 is longer than list 2, so these are 2 independent samples, not matched pairs.   Miami Atlanta 68.3 73.6 83.1 69.3 79.1 54.9 72 81.1 72.8 78.6 83.3 54 82.7 36.1 80.7 44.3 87 58.4 83.1 50.8 77.4 60.5 86.1 61.2 76.3 46.8 74.5 54.4 83.3   78.5     The Null Hypotheses is: H0: μ1 - μ2 = 0 What is the alterative hypothesis? Select the correct symbols for each space. (Note this may view better in full screen mode.)HA: μ1 - μ2            Based on these hypotheses, find the following. Round answers to 4 decimal places. Test Statistic =  p-value =  The p-value is     The correct…

A researcher takes sample temperatures in Fahrenheit of 17 days from New York City and 18 days from Phoenix. Test the claim that the mean temperature in New York City is different from the mean temperature in Phoenix. Use a significance level of α=0.05. Assume the populations are approximately normally distributed with unequal variances. You obtain the following two samples of data. New York City Phoenix 99 94.2 95.5 72 93.2 86.8 102 122.1 85.4 114.4 80 94.7 86.4 89.7 75.4 104.7 79.5 77.6 83.4 106.8 64.3 98.6 65.5 91.5 87.7 82 104 97.7 74.3 64.9 59.5 82 82.8 72   116.2 The Hypotheses for this problem are: H0: μ1 = μ2 H1: μ1μ2 Find the p-value. Round answer to 4 decimal places. Make sure you put the 0 in front of the decimal. p-value =

Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The mean shopping time, u, spent by customers at the supermarkets has been reported to be 35 minutes, but executives hire a statistical consultant and ask her to determine whether it can be concluded that u is greater than 35 minutes. To perform her statistical test, the consultant collects a random sample of shopping times at the supermarkets. She computes the mean of these times to be 42 minutes and the standard deviation of the times to be 10 minutes. Based on this information, answer the questions below. What are the null hypothesis (H,) and the alternative hypothesis (H,) that should be used for the test? H: u is ? H: u is ? In the context of this test, what is a Type I error? A Type I error is ? fact, u is ? ? v when, in v the hypothesis that u is? v? v. Suppose that the consultant decides to reject the null hypothesis. What sort of error might she be…