Question

A random sample of size 15 is obtained from a normal population yielding a sample standard deviation of 20. Test the null hypothesis that the unknown population variance is greater than or equal to 162 versus the alternative that the unknown population variance is less than 162 using a 5% level of significance

a. Set up the null and alternative hypotheses, clearly defining any unknown parameters. Note the “=” value is always in the null hypothesis.

b. Find a test statistic: i. Sensitive to the unknown parameter with ii. Known distribution under the “=” value of the unknown parameter. iii. First state and clearly label the distribution fact that you are using and then state and clearly label the test statistic

c. Look at the test statistic and alternative hypothesis and decide what values of the test statistics would tend to indicate that the alternative hypothesis is true (general direction)

d. Use the results of B and C along with the value of the probability of a type I error to find the cutoff points for the acceptance and rejection regions

e. Clearly state your decision rules

f. Calculate your test statistic and using D, decide whether you will accept or reject the null hypothesis. Interpret your results.

Answer 1

(c)

Values less than equal to 6.57

(d-e)

The level of significance is 0.05

Rejection region:

If test statistics is less than equal to 6.57, reject H0