A fire insurance company thought that the mean distance from

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 5.6 miles. It set its fire insurance rates accordingly. Members of the community set out to show that the mean distance was less than 5.6 miles. This, they thought, would convince the insurance company to lower its rates. They randomly indentified 69 homes and measured the distance to the nearest fire department from each. The resulting sample mean was 4.6. If = 2.4 miles, does the sample show sufficient evidence to support the community\'s claim at the = .05 level of significance?

(a) Find z. (Give your answer correct to two decimal places.)

(ii) Find the p-value. (Give your answer correct to four decimal places.)

(b) State the appropriate conclusion.

Solution

a.

To find the value of z, do as follows:

Step1. Go to Stat> Basic statistics> one-sample z for mean. Select \'Summarized Data\'.

Step2. Enter 69, 4.6, 2.4 corresponding to \'Sample size\', \'Sample mean\' and \'Known standard deviation\'. Check \'Hypothesis test\' and enter 5.6 in \'Hypothesized mean\' .

Step3. Click OK.

The output displays the required values as follows:

z=-3.46

2.

The p value is 0.001.

3.

Reject nyull hypothesis if p value is less than the given significance level. Here, p valu eis less than 0.05. Therefore, reject null hypothesis to conclude that community\'s claim is valid.