This is an Econometrics problem. For the following problem state (i) all relevan

Question

This is an Econometrics problem. For the following problem state (i) all relevant null and alternative hypothesis (ii) the relevant parameters of the sampling distribution(s), (iii) whether the sample distribution is distributed normally, as a t distribution, F distribution, or Chi square (iv) whether this is a one-tailed or two-tailed test and v) what significance level you use and why. Then test the null hypothesis and state your conclusion(s). Show every step of every calculation or inference upon which you based your answer.

The New York police department has decided that traffic officers should write an average of 27 traffic tickets per month. If individual officers write more than that, they are likely too zealous in the performance of their duties, but if fewer tickets are handed out, the officer may not be doing a thorough job. To evaluate the officers, the police chief checked on the number of tickets written in a particular month by random sample of 15 officers. The results are shown here.

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A) Does it appear the police force is performing satisfactorily in the area of traffic enforcement?

B) Redo this if overzealousness would lead to censure by the US justice department, traffic monitoring defaulting to the state, and the entire police force losing their jobs. Discuss any changes you made.

C) Redo this if instead of the conditions of B a lack of thoroughness yields higher levels of obesity among officers but no other consequences. Discuss any changes you made.

D) Redo this if instead of B and C a lack of thoroughness would result in a bloodbath in the streets as drug dealers and terrorists take over Ferguson.

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Explanation / Answer

Solution:

Here, we have to check the hypothesis or claim whether the traffic officers write an average of 27 traffic tickets per month or not. For checking this hypothesis we have to use the one sample t test for the population mean.

i

The null and alternative hypothesis for this test is given as below:

Null hypothesis: H0: The traffic officers write an average of 27 traffic tickets per month.

Alternative hypothesis: Ha: The traffic officers write an average other than 27 tickets per month.

Symbolically the null and alternative hypotheses are given as below:

H0: µ = 27 v/s Ha: µ 27

ii

The relevant parameters of the sampling distribution are sample mean, sample size and sample standard deviation or standard error.

iii

The sample distribution is distributed as a t distribution. We have to use a one sample t test for the population mean for checking the given claim.

iv

This is a two tailed test. (Alternative hypothesis is of ‘not equal to’ type)

v

We will use the 5% level of significance or alpha = 0.05. We usually use the 5% level of significance because for this level of significance the results are more reliable.

Now, we have to test the above hypothesis.

The test statistic formula is given as below:

Test statistic = t = (Xbar - µ) / [S / sqrt(n)]

From the given data, we have

Test statistic = t = (29.27 – 27) / [4.30/sqrt(15)]

Test statistic = t = 2.0413

Degrees of freedom = n – 1 = 15 – 1 = 14

Critical value = 2.1448 and -2.1448

P-value = 0.0605

Alpha value = 0.05

P-value > alpha value

So, we do not reject the null hypothesis

We conclude that there is sufficient evidence that the traffic officers write an average of 27 traffic tickets per month.

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