Calculate the test statistic, 2. Calculate the P-value. What is the conclusion f

Question

Calculate the test statistic, 2.

Calculate the P-value.

What is the conclusion for this hypothesis test?

what is fundamental error with this analysis?

A police department released the numbers of calls for the different days of the week during the month of october as shown in the table to the right Use a 0.01 significance level to test the claim that the different days af the week have the same frequencies of police calls What is the fundamental error with this analysis? Day Sun Mon Tues Wed Thurs Fri Frequency 206 220 250 234

Explanation / Answer

Solution:

Here, we have to use Chi square test for goodness of fit.

The test statistic formula is given as below:

Chi square test statistic = [(O –E)^2/E]

There are total 7 days, so expected frequency for each day will be

E = Sum of observed frequency * (1/7) for each cell.

The calculation table is given as below:

Day

Freq. O

Exp. E

(O - E)

(O - E)^2

(O - E)^2/E

Sun

157

208.2857

-51.2857

2630.22449

12.62796394

Mon

206

208.2857

-2.28571

5.2244898

0.025083284

Tues

220

208.2857

11.71429

137.22449

0.65882814

Wed

250

208.2857

41.71429

1740.08163

8.354301391

Thurs

180

208.2857

-28.2857

800.081633

3.841269841

Fri

211

208.2857

2.714286

7.36734694

0.03537135

Sat

234

208.2857

25.71429

661.22449

3.174603175

Total

1458

1458

28.71742112

Chi square test statistic = 28.71742112

Number of categories = n = 7

Degrees of freedom = n – 1 = 7 – 1 = 6

Level of significance = alpha = 0.01

Chi square critical value = 16.81189383

P-value = 0.0000688

(By using Chi square table or excel)

Here, we have P-value < Alpha value

So, we reject the null hypothesis

We conclude that there is insufficient evidence that different days of week have the same frequency of police calls.

Day

Freq. O

Exp. E

(O - E)

(O - E)^2

(O - E)^2/E

Sun

157

208.2857

-51.2857

2630.22449

12.62796394

Mon

206

208.2857

-2.28571

5.2244898

0.025083284

Tues

220

208.2857

11.71429

137.22449

0.65882814

Wed

250

208.2857

41.71429

1740.08163

8.354301391

Thurs

180

208.2857

-28.2857

800.081633

3.841269841

Fri

211

208.2857

2.714286

7.36734694

0.03537135

Sat

234

208.2857

25.71429

661.22449

3.174603175

Total

1458

1458

28.71742112

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