Sociologists want to test whether the number of homeless people in a particular urban area is increasing. In 2010, the average number of homeless people per day who sought shelter was 42.3 (σ = 6.2). Data from the current year reveal that the mean number of people seeking shelter per day is 45.3. Compute the test statistic using an alpha = .01 and n = 1000.

Using the z-distribution, it is found that the test statistic is of z = 15.3.

At the null hypothesis, it is tested if the mean number has not increased, that is, it still is of 42.3, hence:

At the alternative hypothesis, it is tested if it has increased, that is, the mean is greater than 42.3, hence:

We have the standard deviation for the population, hence, the z-distribution is used.

The test statistic is:

The parameters are:

For this problem, the values of the parameters are:

Hence:

The test statistic is of z = 15.3.

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The test statistic value is 15.3.

Step-by-step explanation:

The hypothesis for this test is:

H₀: The average number of homeless people is not increasing, i.e. μ = 42.3.

Hₐ: The average number of homeless people is increasing, i.e. μ > 42.3.

Given:

As the population standard deviation is provided use a single mean z-test for the hypothesis testing.

The test statistic is:

Thus, the test statistic value is 15.3.

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step-by-step explanation: