Question

# The average age for livmcensed drivers in purple county is u=42.6 years with a standard deviation...

The average age for livmcensed drivers in purple county is u=42.6 years with a standard deviation of sigma sub xbar=12.The local police want to know if drivers who received tickets on the day of the concert differ in age from licensed drivers in Purple County .If so,they would use that as evidence that the event should not be held next year.Below are the ages of the six individuals who received tickets on the day of the concert .
20,23,51,46,31,18

Please state the alternative & null hypothesis in words and symbols .

Find Z obtained
Find Z critical
Is the test statistic in the critical region ?
Retain Ho or Reject Ho?
What’s the conclusion ?
What type of error could you have made ?(type 1 or 2)

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u = 42.6
Alternative hypothesis: u 42.6

Note that these hypotheses constitute a two-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample z-test.

Analyze sample data. Using sample data, we compute the standard error (SE), z statistic test statistic (z).

SE = s / sqrt(n)

S.E = 5.7082

z = (x - u) / SE

z = - 1.944

zcritical = + 1.96

where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.

Since we have a two-tailed test, the P-value is the probability that the z statistic less than -1.944 or greater than 1.944.

Thus, the P-value = 0.052.

Interpret results. Since the P-value (0.052) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Retain the null hypothesis.

From the above test we do not have sufficient evidence in the favor of the claim that drivers who received tickets on the day of the concert differ in age from licensed drivers in Purple County.

We would made type II error.

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