Answer to Question #339816 in Statistics and Probability for None

Question

1. Data from the school clinic shows that the average height of grade 11 students is 160 cm with a population standard deviation of 1.5. A sample of 50 students has an average height of 164 cm. Test the hypothesis that the average height is 160 cm.

a) formulate the null and alternative hypothesis

b) Determine what test statistic to use

c) Calculate the test statistic value

Answer 1

a) The following null and alternative hypotheses need to be tested:

$H_0:\mu_1=160$

$H_a:\mu_1\not=160$

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

The rejection region for this left-tailed test is $R = \{z: |z| >z_c\}.$

c) The z-statistic is computed as follows:

$$z=\dfrac{\bar{X}-\mu}{\sigma/\sqrt{n}}$$

$$=\dfrac{164-160}{1.5/\sqrt{50}}=18.8562$$