Question

1. A fire insurance company thought that the mean distance from a home to the nearest fire department in a suburb of Chicago was at least 5.3 miles. It set its fire insurance rates accordingly. Members of the community set out to show that the mean distance was less than 5.3 miles. This, they thought, would convince the insurance company to lower its rates. They randomly indentified 57 homes and measured the distance to the nearest fire department from each. The resulting sample mean was 4.8 miles. If σ = 2.4 miles, does the sample show sufficient evidence to support the community's claim at the α = .05 level of significance?

(a) What is the appropriate alternate hypothesis? H_a:μ  ---Select--- > 4.8 > 5.3  < 5.3 < 4.8
(b) Find the p-value. (Give your answer correct to four decimal places.)

(c) State the appropriate conclusion.

Reject the null hypothesis, there is not significant evidence that the mean distance is less than 5.3 miles.

Reject the null hypothesis, there is significant evidence that the mean distance is less than 5.3 miles.    

Fail to reject the null hypothesis, there is significant evidence that the mean distance is less than 5.3 miles.

Fail to reject the null hypothesis, there is not significant evidence that the mean distance is less than 5.3 miles.

2.

While writing an article on the high cost of college education, a reporter took a random sample of the cost of new textbooks for a semester. The random variable x is the cost of one book. Her sample data can be summarized by the following. The sample size is 31; the sample mean is 119.31, and the sample standard deviation is 17.97. (Give your answers correct to two decimal places.)

(a) Find the critical value for the sampling distribution for a 99% confidence interval.  

(b) Find the standard error for the sampling distribution for the confidence interval.  

(c) Find he margin of error for the confidence interval.  

(d) Find the 99% confidence interval to estimate the true mean textbook cost for the semester based on this sample.

Lower Bound	$
Upper Bound	$

(e) The reason that a t-distribution is required for the sampling distribution is:

Because the population mean is unknownBecause the population standard deviation in unknown    Because the sample mean is unknownBecause the sample standard deviation is known

(f) Which of the following a correct description of the confidence interval? (More than one may apply)

If we took 100 samples and constructed 100 confidence intervals, approximately 99 of them will contain the population mean

There is a 99% probability that the cost of a given text book is in the interval

We are 99% confident that the population mean is in the interval

99% of all the textbook costs are in the interval

Answer 1