# statistical inference 4

1. A hospital wants to compare the mean length of stay of its patients with the nation-wide (population) mean. Suppose that the nation-wide mean = 3 days, with a standard deviation = 1.5 day. The hospital samples N = 10 of its patients at random and finds that they stayed has mean = 4.3 days. Does mean hospital stay length for patients at this hospital differ from the nation-wide mean?

Conduct a statistical test to answer this question. Use Î± = .05

1. Write down the null and alternative hypotheses using statistical symbols. Explain your symbols

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1. What are the critical values?

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1. What is the test statistic? Show your calculations

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TURN TO NEXT PAGE

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1. Report the results in APA style

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1. Calculate the 95% confidence interval of mean. What does it mean? Show your calculations

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A car company claims that their new car model has 31 mpg (miles per gallon) on local traffic. A researcher in Consumer Reports randomly selects 8 of this cars from the local car dealerships and test their gas mileage on local traffic in NYC. The mean mpg is 29, with SD = 2.78. The researcher wants to claim that the actual mean mpg is less than what the company claims.

Conduct a statistical test to answer this question. Use Î± = .01

1. Write down the null and alternative hypotheses using statistical symbols. Explain your symbols

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1. What are the critical values? Show your calculations

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1. What is the test statistic? Show your calculations

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Report the results in APA style

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Can the reporter claim that the actual mean mpg is less than what the company claims (31 mpg)? YES or NO?

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