The average age for licensed drivers in a county isSolution1

The average age for licensed drivers in a county is

Solution

1.    Identify the appropriate hypothesis for analyzing this data including the conditions for using this test.

Let mu be the population mean

The test hypothesis are:

Ho: mu=42.6 (i.e. null hypothesis)

Ha: mu not equal to 42.6 (i.e. alternative hypothesis)

We need to assume that the population follows normal distribution.

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2.    Complete the four steps of hypothesis testing necessary to determine whether this group differs from the population of drivers in the county and include each step in your final study group answer.

The test hypothesis:

Z=(xbar-mu)/(s/vn)

=(40.5-42.6)/(12/sqrt(25))

=-0.875

Assume that the significant level a=0.05

It is a two-tailed test.

The critical values are Z(0.025) = -1.96 or 1.96 (from standard normal table)

The rejection regions are if Z<-1.96 or Z>1.96, we reject HO.

Since Z=-0.875 is between -1.96 and 1.96, we do not reject Ho.

So we can not conclude that the average age of those receiving parking tickets in the county differed from that of the average age of the population of licensed drivers in the county.

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3.    Given the conclusion found in #2, which type of error (Type I or Type II) is a possibility? Why?

Type II error: We do not reject Ho when it is false.

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4.    Given the possible type of error (Type I or Type II) made in this situation, what could researchers do to reduce the risk of this error?

The researchers could collect more sample size to reduce the risk of this error.