Question

test H : μ-: 25 vs. H: μ >25. An SRS of size . continue to favor Ho? Explain your decision. Answer: The critical n 16 is taken. Assume 4 value is 26.645. 26, would you continue to favor H? Explain your decision. (c) For a pre-set α of 0. 01 and 26, what would be your decision? (8.3.1) 23.613

Answer 1

a) The mean of SRS is 28 which is greater than the population mean, since the calculated value is greater than the critical value we reject null hypothesis and we conclude that there is a statistically significant evidence that sample mean is more than the population mean.

b) Now the mean of sample is 26, which is lesser than the population mean, since the calculated value is lesser than the critical value we fail to reject null hypothesis and there is a no statistically significant evidence to conclude that sample mean is more than the population mean.

c) given $\alpha$ = 0.01

$\bar{x}$ = 26. $\sigma$ = 4, n =16

it is one-tailed test for a hypothesis in the question

test statistic Z = $\frac{\bar{x}-\mu}{\sigma/\sqrt{n}}$ = = 1

26 -25 4/V16

critical z-value for $\alpha$ = 0.01 is 2.33

test statistic is less than the critical Z value, we fail to reject null hypothesis and there is a no statistically significant evidence to conclude that sample mean is more than the population mean.