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 121. Sample​ data: nequals13​, x overbarequals122​, sequals13. The significance level is alphaequals0.05.

Answer 1

Answer:

Step-by-step explanation:

Given that for a sample of size n = 13, mean =122 and std dev = 13

STd error of sample = $\frac{13}{\sqrt{13} } =3.61$

Hypotheses:

$H_0: x bar = 121\\H_a: x bar >121$

(One tailed test at 5% sign level)

Mean difference = 1 and test statistic

$t = \frac{1}{3.61} \\=0.2778$

df = n-1 =12

pvalue = 0.3929

Since p > alpha, accept null hypothesis

There is no evidence to prove that mean is greater than 121.