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Erin is the Human Resources Director at Amalgamated Rat Trap. The company is contemplating extending medical insurance to employees’ dependents and wants an estimate of the likely cost. Erin believes that the number of dependents employees claim is uniformly distributed between one and four – that is, the same proportion of all employees claim one dependent as claim two, three or four. Unfortunately, the number of dependents isn’t in ART’s computer system, so the only evidence Erin can get is to take a sample of the company’s 12,438 employees. In a sample of one hundred employees, she finds the following: No. of Dep.1234 No. of Employees Do these data support Erin’s belief?

1.What is the null hypothesis? 2.What is the test statistic? 3.If the null hypothesis is true, how many employees would we expect to have each number of dependents? 4.What is the calculated value of the test statistic? 5.How many degrees of freedom does this statistic have? 6.Should we reject or not reject the null hypothesis? 7.What’s our conclusion about Erin’s belief?

Darby has caught one hundred sea bass today. Surveying his catch, it seems to him that the weight of sea bass is normally distributed. Since he can regard his hundred as a sample, he decides to use the sample to test his hypothesis. In the sample, he finds an average weight of fourteen ounces with standard deviation five ounces; he will use these statistics in his calculations.

1.What is the null hypothesis? 2.If Darby divides his sample into eight weight ranges and counts the number of fish in each range, how many degrees of freedom will his  2 statistic have? 3.In the event, Darby’s  2 = What is our conclusion about the null hypothesis? 5.Can we assume that fish weights are normally distributed?

Clifford Kent (left) and Darby Grover conducting a  2 test.

Darby believes that the kind of fish caught depends on the depth below the boat; using today’s catch as a sample, he develops the following contingency table: Fish   Depth Sea BassRed Snapper Shallow4060 Deep6040

Formally, what is the null hypothesis? What is the test statistic? How many degrees of freedom does this statistic have? How many sea bass would we expect to catch at shallow depth? What is the calculated value of the test statistic? If the critical value for this statistic = 3.84, what is the conclusion about the null hypothesis? Do the evidence support Darby’s theory?

At what depth were we probably fishing?

Gary would like to know whether the proportion of gun owners is the same across geographic regions of the United States. In a national sample of 1200 households, the proportion answering “yes” to the question “do you own a gun?” is as follows: RegionEastSouthMidwestWest Percentage yes njnj

What is the null hypothesis? What is the test statistic? How many degrees of freedom does the statistic have? What does the table look like? How can we use Excel to help us work this problem?

Darlene’s in the quality assurance department at ART. The company wants to run its equipment as fast as possible, but Darlene’s concerned that stepping up the cycle rate on spring winder increases the variability of the springs’ strength. So she takes two samples: one at 30 springs per minute and one at 70 springs per minute. For the first sample of 41 springs, s = 2 psi; for the second sample of 51 springs, s = 3.5 psi. Calculate confidence intervals for the springs’ standard deviation at each speed. 1.If we want a 95% confidence interval, what Excel expression would yield  2 U? ? 2.What Excel expression would yield  2 L ?

Calculate the intervals. Do the data support Darlene’s fears?