1. ## Please help! I am failing my stats class and have a few more assignments to help me!

4.4 Find the p-value. An independent random sample is selected from an approximately normal
population with an unknown standard deviation. Find the p-value for the given set of hypotheses
and T test statistic. Also determine if the null hypothesis would be rejected at α = 0.05.

(a) HA : μ > μ0, n = 11, T = 1.91
(b) HA : μ < μ0, n = 17, T = −3.45

(c) HA : μ 6= μ0, n = 7, T = 0.83
(d) HA : μ > μ0, n = 28, T = 2.13

2. ## Re: Please help! I am failing my stats class and have a few more assignments to help

a) This is a one sided test with the upper tail as the rejection region.

note that with n=11 (I assume this is the sample size) the number of degrees of freedom $\nu=n-1=10$

Using a table or software we find (and you can enter the bit in italics directly in at wolframalpha.com)

p-value = 1-CDF[StudentTDistribution[10]=0.0426

0.0426 < 0.05 so we would reject the Null hypothesis

b) This is a one sided test with the lower tail as the rejection region

See if you can follow what I did in (a) to solve this one. Just use the CDF directly rather than 1-CDF since this is the lower tail.

c) This is a two tailed test

We calculate the critical points of the test, $p_{lo},p_{hi}$ for $\alpha =0.05$ such that

$p_{lo}$ corresponds to probability 0.025, and $p_{hi}$ corresponds to probability 1-0.025 = 0.975

$p_{lo}$ = InverseCDF[StudentTDistribution[6],0.025] = -2.44691

$p_{hi}= -p_{lo}= 2.44691$

we reject if $p_{val} < p_{lo} \vee p_{hi}< p_{val}$

The p-value for this problem is found as

p-value =CDF[StudentTDistribution[6],0.83] = 0.780846

This falls within the acceptance region so we do not reject the null hypothesis

d) just do what I did in problem (a) with the different numbers