Question

Test the claim that the mean GPA of night students is significantly different than 3 at the 0.1 significance level.

The null and alternative hypothesis would be:

a. H0:μ≤3H0:μ≤3
H1:μ>3H1:μ>3

b. H0:μ=3H0:μ=3
H1:μ≠3H1:μ≠3

c. H0:p≤0.75H0:p≤0.75
H1:p>0.75H1:p>0.75

d. H0:μ≥3H0:μ≥3
H1:μ<3H1:μ<3

e. H0:p≥0.75H0:p≥0.75
H1:p<0.75H1:p<0.75

f. H0:p=0.75H0:p=0.75
H1:p≠0.75H1:p≠0.75

The test is:

two-tailed

right-tailed

left-tailed

Based on a sample of 40 people, the sample mean GPA was 3.01 with a standard deviation of 0.05

The test statistic is:  (to 2 decimals)

The p-value is:  (to 2 decimals)

Based on this we:

• Fail to reject the null hypothesis
• Reject the null hypothesis

2. A shareholders' group is lodging a protest against your company. The shareholders group claimed that the mean tenure for a chief exective office (CEO) was at least 8 years. A survey of 82 companies reported in The Wall Street Journal found a sample mean tenure of 6.7 years for CEOs with a standard deviation of s=s= 4.6 years (The Wall Street Journal, January 2, 2007). You don't know the population standard deviation but can assume it is normally distributed.

You want to formulate and test a hypothesis that can be used to challenge the validity of the claim made by the group, at a significance level of α=0.02α=0.02. Your hypotheses are:

      Ho:μ=8Ho:μ=8
      Ha:μ<8Ha:μ<8

What is the test statistic for this sample?
test statistic =  (Report answer accurate to 3 decimal places.)

What is the p-value for this sample?
p-value =  (Report answer accurate to 4 decimal places.)   

Answer 1

1)

b. H0:μ=3
H1:μ≠3

The test is:

two-tailed

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (3.01 - 3)/(0.05/sqrt(40))
t = 1.26

P-value Approach
P-value = 0.22

Fail to reject the null hypothesis

2)
Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (6.7 - 8)/(4.6/sqrt(82))
t = -2.559

P-value Approach
P-value = 0.0062
As P-value < 0.02, reject the null hypothesis.