Question

W71) I am study Excel Functions. Please answer in detail using Excel functions.

Parking Tickets – The Chicago police department claims that it issues an average of only 60 parking tickets per day. The data below, reproduced in your Excel answer workbook, show the number of parking tickets issued each day for a randomly selected period of 30 days. Assume σ =13.42.   State the null and alternate hypotheses, as well as the claim, which (hint!) is in the null hypothesis. Is there enough evidence to reject the group’s claim at α = .05?   (As with all of these exercises, use the P-value method, rounding to 4 digits.) (Hint: so since we know the population standard deviation, use the standard normal distribution z-test .) (Monday class)

              79         78         71         72         69         71              57         60

              83         36         60         74         58         86              48         59

              70         66         64         68         52         67              67

              68         73         59         83         85         34              73

Answer 1

Solution:

Here, we have to use one sample z test for population mean. The null and alternative hypotheses are given as below:

Null hypothesis: H₀: The Chicago police department issues an average of only 60 parking tickets per day. (Claim)

Alternative hypothesis: H_a: The Chicago police department issues parking tickets with an average different than 60 per day.

H₀: µ = 60 versus H_a: µ ≠ 60

This is two tailed test.

We are given

Level of significance = α = 0.05

The test statistic formula is given as below:

Z = (Xbar - µ)/[σ/sqrt(n)]

From given data, we have

n = 30

Xbar = 66.33

(Use excel command =average() )

σ = 13.42

Z = (66.33 – 60)/[13.42/sqrt(30)]

Z = 2.5849

P-value = 0.0097

[by using excel command =2*(1-NORMSDIST(2.5849))]

P-value < α = 0.05

So, we reject the null hypothesis

There is insufficient evidence to conclude that the Chicago police department issues an average of only 60 parking tickets per day.