7/21/2019 26 June 2014 Recitation Questions

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26 June 2014  –  Statistics Recitation

1. 

An insurance company has operated under the assumption that their average claim is about$1,800. However they are concerned that the PPACA has raised this average. At random, theyselect 40 claims and calculate a sample mean of $1,950. Assuming a standard deviation of $500and a significance level of 95%, test whether the population mean is greater than $1,800.

2. 

A sample of 40 receipts yields an average purchase price of $137 and a standard deviation of$30.20. Test whether the mean sale is different from $150 with a confidence level of 99%.

3. 

BMW manufactures Mini Cooper door panels with a tolerance of 0.50 centimeters. This tolerancefluctuates with a standard deviation of 0.04 centimeters. Assume that a 25 unit sample of this production process found a mean of 0.51. At 95% significance, test whether the manufacturing process is malfunctioning.

4. 

Suppose we’re interested in whether the S&P index moves, on average, up more often than itdeclines. We take a sample of 1,112 trading days to find that the index increased on 573 of thesedays (quite obviously, it declined on the others). What can we conclude? At what level of

significance could we reject our null hypothesis (what is the null hypothesis for that matter)?

5. 

A bourbon distillery produces an 80 proof whiskey and claims that the variance in this figure isno more than 0.25. An independent agency tests the accuracy of this claim by sampling 41 bottlesto measure a variance of 0.27. At a significance level of 95%, test whether there is enoughevidence to reject the distiller ’s claim.

6. 

Textbook question 9.28

7. 

Textbook question 9.49