3. The average age for licensed drivers in a county is = 42.6, = 12, and the dis

Question

3. The average age for licensed drivers in a county is = 42.6, = 12, and the distribution is approximately normal. A county police officer was interested in whether the average age of drivers receiving speeding tickets differed from the average age of the driving population. She obtained a sample of n = 16 drivers receiving speeding tickets. The average age for this sample wasX 41.4. What is t p-value? What is your decision regarding the claim? |8% = 0.98 =conf)dence hevel 2%-b02 = level of Sonihcore

Explanation / Answer

Given:-

sample mean is X¯=41.4 and the known population standard deviation is =12, and the sample size is n=16.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: =42.6

Ha: 42.6

This corresponds to a two-tailed test, for which a z-test for one mean, with known population standard deviation will be used.

(2) Rejection Region

Consider the significance level is

=0.05, and the critical value for a two-tailed test is zc=1.96.

The rejection region for this two-tailed test is R={z:|z|>1.96}

(3) Test Statistics

The z-statistic is computed as follows:

z=[(X¯–0) / (/n) ] = [ (41.4–42.6) / (12/16) ]=0.4

(4) Decision about the null hypothesis

Since it is observed that |z|=0.4zc=1.96, it is then concluded that the null hypothesis is not rejected.

Using the P-value approach: The p-value is p=0.6892, and since p=0.6892 alpha =0.05, it is concluded that the null hypothesis is not rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean is different than 42.6, at the consider 0.05 significance level.

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