For the following claim, find the null and alternative hypotheses, test statisti
ID: 3325006 • Letter: F
Question
For the following claim, find the null and alternative hypotheses, test statistic, critical value, and draw a conclusion. Assume that a simple random sample has been selected from a normally distributed population. Answer parts a-d. Claim: The mean IQ score of statistics professors is greater than 135. Sample data: n-29, x= 136·s-13. The significance level is -0.05. Click the icon to view a table of critical t-values a. Choose the correct null hypothesis (H aternative hypothesis (H1) OA. Ho : =135 H1 : #135 B. Ho : =135 H1 : >135 C. Ho : > 135 H1 : 135 H1 : =135 b. Determine the test statistic t. t-D (Round to three decimal places as needed.) c. Find the critical value using a t-distribution table. The critical value is (Round to three decimal places as needed.) d. What is the conclusion? ( A. B. ° C. ( D. Fail to reject the null hypothesis and support the claim that > 135. Reject the null hypothesis and do not support the claim that > 135. Fail to reject the null hypothesis and do not support the claim that > 135. Reject the null hypothesis and support the claim that > 135.Explanation / Answer
Part a
The null and alternative hypothesis is given as below:
H0: µ = 135 versus H1: µ > 135
So, correct answer is B.
Part b
Test statistic = t = (Xbar - µ) / [S/sqrt(n)
We are given
Xbar = 136
S = 13
n = 29
df = n – 1 = 28
= 0.05
t = (136 – 135) / [13/sqrt(29)]
t = 0.414
Part c
Critical value = 1.701
(by using t-table)
Part d
Here, test statistic value is less than critical value, so we fail to reject the null hypothesis and do not support alternative hypothesis or claim.
So, correct answer is C.
C. Fail to reject the null hypothesis and do not support the claim that µ > 135.