Mid-Term EXAM
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Mid-Term EXAM
Problem 1 (25 points): Independent random samples of 17 sophomores and 13 juniors attending a large university yield the following data on grade point averages:
Sophomore Junior
|
3.04 |
|
2.56 |
|
1.71 |
|
2.77 |
|
3.3 |
|
2.7 |
|
2.88 |
|
3 |
|
2.11 |
|
2.98 |
|
2.6 |
|
3.47 |
|
2.92 |
|
3.26 |
|
3.6 |
|
3.2 |
|
2.28 |
|
3.19 |
|
2.82 |
|
2.65 |
|
3.03 |
|
3 |
|
3.13 |
|
3.39 |
|
2.86 |
|
2.58 |
|
3.49 |
||
|
3.11 |
||
|
2.13 |
||
|
3.27 |
||
At the 5% significance level, do the data provide sufficient evidence to conclude that the mean GPAs of juniors is more than sophomores at this university?
a) What are the null and alternate hypotheses?
H0: The average GPA of a junior at this school is no greater than the average GPA of a sophomore at this university
H1: The average GPA of a junior at this school is greater than the average GPA of a sophomore at this university
b) What is the critical value?
The 0.05 significance level is stated in the problem.
c) What is the Decision Rule?
Reject H0 if Z > 1.96
Reject H1 if Z < 1.96
d) What is the test statistic?
The computed value of Z = 1.98 is larger than the
critical value of 1.96
e) What is the decision?
We reject H0.
f) What does the decision infer?
We have sufficient evidence to show that juniors in this school have higher GPA than sophomores.
Problem 2 (25 points ): The data below compares the prices of a single hot dog and a medium soft drink at all the Major League Baseball stadia.
|
$ |
$ |
|
Hot Dog |
Soft Drink |
|
1 |
1 |
|
1.5 |
1.5 |
|
2.75 |
1.5 |
|
3 |
3 |
|
3.25 |
3.25 |
|
3.5 |
2.5 |
|
3.75 |
4 |
|
3.75 |
4.5 |
|
4 |
4 |
|
4 |
4.5 |
|
4.25 |
5.25 |
|
4.5 |
2.75 |
|
4.5 |
4.25 |
|
4.5 |
4.5 |
|
4.75 |
3.25 |
|
4.75 |
4.5 |
|
4.75 |
4.75 |
|
5 |
4.75 |
|
5 |
5 |
|
5 |
5.25 |
|
5.25 |
4.5 |
|
5.25 |
4.75 |
|
5.5 |
4 |
|
5.5 |
5.75 |
|
6 |
4.5 |
|
6.25 |
5 |
a) Draw a scatter Diagram. Let Hot price be the X Variable. Draw a “best fit” or “good fit” line on the scatter plot.
b)What is the coefficient of Correlation?
c)What is the Coefficient of Determination?
d)What is the Coefficient of Non-determination?
e)What is the Regression Equation? This means find the equation for the function that predicts the price of a medium soft drink, S, as a function of the price of a single hot dog, H. In other words, find the equation for the function S(H).
Use your equation to predict the price of a medium soft drink if the price of a single hot dog is $7.
Problem 3 (25 points ) A group of 5 statistics students received the following grades on a test: 81, 74, 62, 92, and 76. An intervention plan is used and the students were hopeful to increase their scores on a retest. They received the following grades in retest: 89, 78, 59, 98 and 75. At the 0.025 significance level, is the intervention plan helpful in increasing the grades?
a. State the null and alternate hypotheses
Ho : H1:
b.State the decision rule.
c. Compute the value of the test statistic.
d. Estimate the p-value.
e. What is your decision regarding the null hypothesis? Interpret the result.
Problem 4 (25 points)
Problem 4 (25 points): Time magazine reported the result of a telephone poll of 800 adult Americans. The question posed of the Americans who were surveyed was: "Should the federal tax on cigarettes be raised to pay for health care reform?" The results of the survey were:
|
|
|
|
Non-Smokers |
Smokers |
|
Sampled: 605 |
Sampled: 195 |
|
351 said Yes |
41 said Yes |
|
|
Is there sufficient evidence at the α = 0.05 level, to conclude that the two populations — smokers and non-smokers are different from each other with respect to their opinions? Find the p-value and re-affirm the result of the Hypothesis testing.
a. State the null and alternate hypotheses
Ho : H1:
b.State the decision rule.
c. Compute the value of the test statistic.
d. Estimate the p-value.
e. What is your decision regarding the null hypothesis? Interpret the result.
2023-06-16