Question

3. Testing a population mean The test statistic (Chapter 11) Aa Aa You conduct a hypothesis test about a population mean u with the following null and alternative hypotheses: Ho: u-25.8 H1: <25.8 Suppose that the population standard deviation has a known value of a observations, which provides a sample mean of % 30.7. 17.8. You obtain a sample of n =62 Since the sample size large enough, you assume that the sample mean X follows a normal distribution. Let po denote the hypothesized value of the population mean u when the null hypothesis is true. Click on the blue dropdown menus that follow, and select the appropriate expressions to obtain the correct formula for the test statistic for your hypothesis test: When the null hypothesis is true, the test statistic for this hypothesis test follows which of the following distributions? OAt distribution with 62 degrees of freedom O At distribution with 61 degrees of freedom O A normal distribution with mean 0 and standard deviation 1 A normal distribution with mean 25.8 and standard deviation 17.8 The value of the test statistic is

Answer 1

Here we have to test that

$H_0:\mu=25.8$

$H_1:\mu<25.8$

$\bar{x}=30.7,n=62$

$\sigma =17.8$,$\mu_0=25.8$

Here population standard deviation $\sigma$ is known so we will use here one sample z test.

Since the sample size n = 62 is large enough, you can assume that sample mean has normal distribution

Test statistic:

Here test statistic z follows normal distribution with mean 0 and standard deviation 1

$z=\frac{\bar{x}-\mu_0}{\sigma /\sqrt{n}}$

$z=\frac{30.7-25.8}{17.8 /\sqrt{62}}$

z = 2.17                     (Round to 2 decimal)

Test statistic = 2.17