Question

Proffesor. R wants to know if the GPA of foreign students is higher than the GPA of American students. He collects data on a random sample of 500 students and finds that the GPA of foreign students is 0.13 points higher than the GPA of American students (standard error 0.08). What is the null hypothesis? What is the alternative hypothesis? Can we reject the null hypothesis at the 5% level? Explain how you arrive at your answer. If your answer to b) was that we can reject the null hypothesis, answer the following: Does this show that the GPA of foreign students is higher than the GPA of American students in the population? Why or why not? If your answer to b) was that we cannot reject the null hypothesis, answer the following: Does this show that there is no difference between the GPA of foreign students and the GPA of American students in the population? Why or why not?

Answer #1

Let D= GPA of foreign students-GPA of American students

We are testing,

H0: Ud=0 vs H1: Ud>0

Test statistic: 0.13/0.08= 1.625

p-value of this one sided test is: (z test since n>120)

P(z>1.625) = 0.0521 (from standard normal distribution tables)

Since the p-value of this test>significance level of 0.05, we have insufficient evidence to Reject H0 at the 5% significance level.

So, since we fail to Reject H0, we conclude:

b) There is no difference between the GPA scores of foreign and American students.

Test the claim that the mean GPA of night students is smaller
than 3 at the .05 significance level.
The null and alternative hypothesis would be:
H0:p=0.75
H1:p≠0.75
H0:μ=3
H1:μ>3
H0:p=0.75
H1:p>0.75
H0:μ=3
H1:μ<3
H0:p=0.75
H1:p<0.75
H0:μ=3
H1:μ≠3
The test is:
left-tailed
right-tailed
two-tailed
Based on a sample of 35 people, the sample mean GPA was 2.97 with a
standard deviation of 0.08
The test statistic is: (to 2 decimals)
The critical value is: (to 2 decimals)
Based on this we:
Fail...

Test the claim that the mean GPA of night students is larger
than the mean GPA of day students at the 0.10 significance
level.
The null and alternative hypothesis would be:
H0:μN≤μD
H1:μN>μD
H0:μN≥μD
H1:μN<μD
H0:pN≤pD
H1:pN>pD
H0:μN=μD
H1:μN≠μD
H0:pN=pD
H1:pN≠pD
H0:pN≥pD
H1:pN<pD
The test is:
two-tailed
left-tailed
right-tailed
The sample consisted of 35 night students, with a sample mean GPA
of 2.74 and a standard deviation of 0.07, and 35 day students, with
a sample mean GPA of 2.73...

Test the claim that the mean GPA of night students is smaller
than 2 at the 0.10 significance level.
The null and alternative hypothesis would be:
H0H0:?pσμsx̄p̂ ?=≠≥≤<> Select an answer20.04351.950.10
H1H1:?σsx̄μp̂p ?≠=<>≤≥ Select an
answer0.040.101.95352
The test is:
right-tailed
two-tailed
left-tailed
Based on a sample of 35 people, the sample mean GPA was 1.95 with a
standard deviation of 0.04
The p-value is: (to 4 decimals)
Based on this we:
Reject the null hypothesis
Fail to reject the null...

Test the claim that the mean GPA of night students is
significantly different than the mean GPA of day students at the
0.2 significance level.
The null and alternative hypothesis would be:
H0:pN=pD
H1:pN<pD
H0:pN=pD
H1:pN≠pD
H0:pN=pD
H1:pN>pD
H0:μN=μD
H1:μN≠μD
H0:μN=μD
H1:μN<μD
H0:μN=μD
H1:μN>μD
The test is:
two-tailed
right-tailed
left-tailed
The sample consisted of 25 night students, with a sample mean GPA
of 2.01 and a standard deviation of 0.08, and 60 day students, with
a sample mean GPA of...

Test the claim that the mean GPA of night students is larger
than the mean GPA of day students at the .005 significance
level.
The null and alternative hypothesis would be:
H0:pN=pDH0:pN=pD
H1:pN<pDH1:pN<pD
H0:pN=pDH0:pN=pD
H1:pN>pDH1:pN>pD
H0:μN=μDH0:μN=μD
H1:μN≠μDH1:μN≠μD
H0:μN=μDH0:μN=μD
H1:μN>μDH1:μN>μD
H0:pN=pDH0:pN=pD
H1:pN≠pDH1:pN≠pD
H0:μN=μDH0:μN=μD
H1:μN<μDH1:μN<μD
The test is:
left-tailed
two-tailed
right-tailed
The sample consisted of 70 night students, with a sample mean GPA
of 2.58 and a standard deviation of 0.04, and 30 day students, with
a sample mean GPA of 2.53...

Test the claim that the mean GPA of night students is smaller
than 3 at the .10 significance level.
The null and alternative hypothesis would be:
H0:p=0.75H0:p=0.75
H1:p<0.75H1:p<0.75
H0:μ=3H0:μ=3
H1:μ<3H1:μ<3
H0:μ=3H0:μ=3
H1:μ≠3H1:μ≠3
H0:p=0.75H0:p=0.75
H1:p≠0.75H1:p≠0.75
H0:μ=3H0:μ=3
H1:μ>3H1:μ>3
H0:p=0.75H0:p=0.75
H1:p>0.75H1:p>0.75
The test is:
left-tailed
two-tailed
right-tailed
Based on a sample of 35 people, the sample mean GPA was 2.97 with a
standard deviation of 0.08
The test statistic is: (to 2 decimals)
The critical value is: (to 2 decimals)
Based on this we:
Reject...

Test the claim that the mean GPA of night students is
significantly different than 3.2 at the 0.05 significance
level.
The null and alternative hypothesis would be:
H0:μ≥3.2H0:μ≥3.2
H1:μ<3.2H1:μ<3.2
H0:μ≤3.2H0:μ≤3.2
H1:μ>3.2H1:μ>3.2
H0:p=0.8H0:p=0.8
H1:p≠0.8H1:p≠0.8
H0:p≤0.8H0:p≤0.8
H1:p>0.8H1:p>0.8
H0:μ=3.2H0:μ=3.2
H1:μ≠3.2H1:μ≠3.2
H0:p≥0.8H0:p≥0.8
H1:p<0.8H1:p<0.8
The test is:
right-tailed
two-tailed
left-tailed
Based on a sample of 25 people, the sample mean GPA was 3.19 with a
standard deviation of 0.08
The p-value is: (to 2 decimals)
Based on this we:
Reject the null hypothesis
Fail to reject...

Test the claim that the mean GPA of night students is
significantly different than 2.6 at the 0.01 significance
level.
Based on a sample of 50 people, the sample mean GPA was 2.57
with a standard deviation of 0.04
The test statistic is: (to 2 decimals)
The p-value is: (to 2 decimals)
Based on this we:
Reject the null hypothesis
OR
Fail to reject the null hypothesis
(Choose one)

Test the claim that the mean GPA of night students is
significantly different than 2.9 at the 0.1 significance level.
Based on a sample of 20 people, the sample mean GPA was 2.87
with a standard deviation of 0.06
The test statistic is (to 3 decimals)
The positive critical value is (to 3
decimals)
Based on this we
fail to reject the null hypothesis
reject the null hypothesis

Test the claim that the mean GPA of night students is smaller
than 3.1 at the 0.005 significance level. You believe the
population is normally distributed, but you do not know the
standard deviation.
The null and alternative hypothesis would be:
H0:μ≥3.1
H1:μ<3.1
H0:p≥0.775H0
H1:p<0.775H1
H0:p=0.775H0
H1:p≠0.775H1
H0:μ=3.1H0
H1:μ≠3.1H1
H0:μ≤3.1H0
H1:μ>3.1H1
H0:p≤0.775H0
H1:p>0.775H1
The test is:
left-tailed
right-tailed
two-tailed
Based on a sample of 20 people, the sample mean GPA was 3.06
with a standard deviation of 0.05
The test...

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