Question

Ch6 Sec2: Problem 3 PreviousProblem List Next (1 point) A random sample of 100 observations from a population with standard deviation 9.13 yielded a sample mean of 91.6 1. Given that the null hypothesis is--90 and the alternative hypothesis is μ > 90 using a) Test statistic- (b) P- value: (c) The conclusion for this test is: 05, find the following: A. Reject the null hypothesis B. There is insufficient evidence to reject the null hypothesis C. None of the above 2. Given that the null hypothesis is μ-90 and the alternative hypothesis is μ (a) Test statistic (b) P -value: (c) The conclusion for this test is: 90 using a-.05, find the following: A. There is insufficient evidence to reject the null hypothesis B. Reject the null hypothesis C. None of the above

Answer 1

Here

sample mean $\bar{x}= 91.6$

population standard deviation $\sigma = 9.13$

and sample size $n = 100$

The test statistic can be written as

$z = \frac{\sqrt{n}(\bar{x} - 90)}{\sigma }$ which under H₀ follows a standard normal distribution.

We reject H₀ at 5% level of significance if P-value < 0.05

Now,

The value of the test statistic = $z_{obs} = 1.75246$

and P-value = $P(Z>z_{obs}) = P(Z>1.75246) = 1 - 0.960153 = 0.0398470$

Since P-value < 0.05, so we reject the null hypothesis.

2. The value of the test statistic = $z_{obs} = 1.75246$

and P-value = $P(|Z|>z_{obs}) = 2*P(Z>1.75246) = 2(1 - 0.960153) =2* 0.0398470 = 0.079694$

Since P-value > 0.05, so

ans-> A) There is insufficient evidence to reject the null hypothesis.