The mean annual premium for automobile insurance in the United States is $1503 (Insure website, March 6, 2014). Being from Pennsylvania, you believe automobile insurance is cheaper there and wish to develop statistical support for your opinion. A sample of 25 automobile insurance policies from the state of Pennsylvania showed a mean annual premium of $1440 with a standard deviation of s = $165.

The mean annual premium for automobile insurance is greater than $1440

Explanation:

Null hypothesis: The mean annual premium for automobile insurance is $1440

Alternate hypothesis: The mean annual premium for automobile insurance is greater than $1440

Z = (sample mean - population mean) / (sd/√n)

sample mean = 1440, population mean = 1503, sd = 165, n = 25

Z = (1440 - 1503) / (65/√25) = - 63/33 = - 1.91

This is a one-tailed test, assuming a 5% significance level, the critical value is 1.645

Since the test statistic - 1.91 is less than the critical value 1.645, reject the null hypothesis

There is sufficient evidence to conclude that the mean annual premium for automobile insurance is greater than $1440