Question

suppose a random sample of 25 is taken from a population that follows a normal distribution...

suppose a random sample of 25 is taken from a population that follows a normal distribution with unknown mean and a known variance of 144. Provide the null and alternative hypothesis necessary to determine if there is evidence that the mean of the population is greater than 100. Using the sample mean ybar as the test statistic and a rejection region of the form {ybar>k} find the value of k so that alpha=.15 Using the sample mean ybar as the test statistic and the rejection region {ybar>k} find the type2 error rate when the true mean of the population is known to be 110. To decrease the type2 error rate we can increase the size of the sample taken. How large would the sample need to be so that alpha=.15 and beta=.05 when using the test statistic ybar, rejection region {ybar>k} and true value of the mean to be 110?

Hypotheses are:

Test is right tailed. The critical value of sample mean for which we will reject the null hypothesis using excel function "=NORMSINV(1-0.15)" is 1.036.

So critical value of sample mean for which we will reject the null hypothesis is

The rejection region is :

The z-score for and is

The type II error is

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