Question

Suppose the national average for fees paid on a parking ticket (not including any court involvement) is $24 with a standard deviation of $6. Your local police department feels that they charge less than this on average. Of the next 132 parking tickets awarded, the average fee due is $23.

A)What type of hypothesis test should be performed here?

B)State the null hypothesis. and the alternative hypothesis.

C)State the p-value for your test.

D)Choose the appropriate conclusion for this test with significance level 0.01.

1. We reject the null hypothesis because the p-value is greater than the significance level.

2. We reject the null hypothesis because the p-value is less than the significance level.

3.We fail to reject the null hypothesis because the p-value is greater than the significance level.

4. We fail to reject the null hypothesis because the p-value is less than the significance level.

E) Interpret your conclusion.

Answer 1

A) Type of hypothesis test: z test for single mean because the sample size is large and we know the population standard deviation.

B) Null and alternative hypotheses:

Ho: = 24

Ha: < 24

C) Test statistic

z = -1.91

So,

p - Value = P(z < -1.91) = 0.0278

D) We fail to reject the null hypothesis because the p-value is greater than the significance level. Option 3 is correct.

E) Interpretation: We do not have sufficient evidence to conclude that they charge less than this on average.