I need to answers this for my review but I also need the phstat output or at lea
ID: 3322600 • Letter: I
Question
I need to answers this for my review but I also need the phstat output or at least what function to use for the phstat output.
4. Using your sample data, test this hypothesis at the alpha = 0.01 significance level. You may assume that the population standard deviation is not known and that the population is approximately normally distributed.
(a) Is there sufficient evidence to conclude that the mean GPA for all students is more than 3.2?
(b) Test the hypothesis again, changing alpha to 0.05 but not changing anything else.
PASTE PHSTAT OUTPUT BELOW: Now mark all of the following statements about the two hypothesis tests either T(TRUE) or F(FALSE). _________ The p-value is the probability that the null hypothesis will be rejected. _________ The second test has a smaller “reject” region than the first. _________ The test statistic measures the distance between the mean being tested and the sample mean. _________ The null hypothesis will be rejected provided alpha exceeds the p-value. _________ The critical value is the boundary between the “reject” region and the “do not reject” region. _________ The p-value is the probability of getting a test statistic equal to, or more extreme than the sample result, if the null hypothesis is true.
5. Suppose it is known that 8 out of the 20 students in the sample are women.
(a) Find a 95% confidence interval for the true proportion of all MBA students who are women.
PASTE PHSTAT OUTPUT BELOW:
(b) What is your opinion of the precision of this confidence interval? Give a reason for your answer.
6. Assume that the population proportion is 0.45, and find the sample size that would be required to determine a 95% confidence interval if we want to be within 0.05 of the true proportion of women MBA students. That is, we want the margin of error, e, to not exceed 0.05.
PASTE PHSTAT OUTPUT BELOW:
LINEAR REGRESSION – Use the sample to complete this section. Remember, the X variable is GMAT SCORE, and the Y variable is GPA 7.
PASTE A SCATTER PLOT BELOW:
8. Perform the regression analysis using PHSTAT and PASTE THE PRINTOUT BELOW:
9. The regression output. i. The regression equation is: ____________________________________ ii. The slope of the equation is: ___________________________________ iii. The y-intercept of the equation is: ________________________________ iv. The standard error of the estimate is: ____________________________ v. The coefficient of determination is: _____________________________
10. Using the Excel printout from Question 8, test the hypothesis that there is no linear relationship between X and Y. Test at alpha = 0.05 significance level.
i. State the null hypothesis: _______________________ ii. State the alternate hypothesis: ___________________ iii. p-value: __________________________________ iv. Test result and reason for test result: ________________________________ 11. Interpretation. [6 POINTS] (a) What does the y-intercept of this regression equation represent? (b) State the exact meaning of the slope in this regression equation. (c) Predict the GPA of a student with a GMAT score of 600. _______________
12. (a) PASTE RESIDUAL PLOT BELOW: (b) From the residual plot, do you think that the two regression assumptions listed below are satisfied? Give the reason for your conclusion. Linearity: ___________________________________ Reason: ____________________________________ Equal Variance: ______________________________ Reason: ____________________________________
13. (a) PASTE A NORMAL PROBABILITY PLOT OF RESIDUALS BELOW: (b) From the normal probability plot, do you think the normality assumption for regression is satisfied? Give the reason for your conclusion.
14. Determine 95% confidence and prediction intervals for X = 600. PASTE PHSTAT OUTPUT BELOW:
15. Discuss this model. How good do you think the model is for predicting GPA? Give reasons for your answer. Then state at least two other possible independent variables that you think would be useful for predicting GPA.
GMAT (X) 688 647 652 608 680 617 557 599 616 594 567 542 551 573 536 639 619 694 718 759Explanation / Answer
Result:
firast two questions answered.
4. Using your sample data, test this hypothesis at the alpha = 0.01 significance level. You may assume that the population standard deviation is not known and that the population is approximately normally distributed.
(a) Is there sufficient evidence to conclude that the mean GPA for all students is more than 3.2?
t Test for Hypothesis of the Mean
Data
Null Hypothesis m=
3.2
Level of Significance
0.01
Sample Size
20
Sample Mean
3.3335
Sample Standard Deviation
0.337409247
Intermediate Calculations
Standard Error of the Mean
0.0754
Degrees of Freedom
19
t Test Statistic
1.7695
Upper-Tail Test
Upper Critical Value
2.5395
p-Value
0.0464
Do not reject the null hypothesis
(b) Test the hypothesis again, changing alpha to 0.05 but not changing anything else.
t Test for Hypothesis of the Mean
Data
Null Hypothesis m=
3.2
Level of Significance
0.05
Sample Size
20
Sample Mean
3.3335
Sample Standard Deviation
0.337409247
Intermediate Calculations
Standard Error of the Mean
0.0754
Degrees of Freedom
19
t Test Statistic
1.7695
Upper-Tail Test
Upper Critical Value
1.7291
p-Value
0.0464
Reject the null hypothesis
PASTE PHSTAT OUTPUT BELOW: Now mark all of the following statements about the two hypothesis tests either T(TRUE) or F(FALSE).
TRUE The p-value is the probability that the null hypothesis will be rejected.
FALSE The second test has a smaller “reject” region than the first.
TRUE The test statistic measures the distance between the mean being tested and the sample mean.
FALSE The null hypothesis will be rejected provided alpha exceeds the p-value
. TRUE The critical value is the boundary between the “reject” region and the “do not reject” region.
TRUE The p-value is the probability of getting a test statistic equal to, or more extreme than the sample result, if the null hypothesis is true.
5. Suppose it is known that 8 out of the 20 students in the sample are women.
(a) Find a 95% confidence interval for the true proportion of all MBA students who are women.
PASTE PHSTAT OUTPUT BELOW:
Confidence Interval Estimate for the Proportion
Data
Sample Size
20
Number of Successes
8
Confidence Level
95%
Intermediate Calculations
Sample Proportion
0.4
Z Value
-1.9600
Standard Error of the Proportion
0.1095
Interval Half Width
0.2147
Confidence Interval
Interval Lower Limit
0.1853
Interval Upper Limit
0.6147
(b) What is your opinion of the precision of this confidence interval? Give a reason for your answer
Margin of error is 0.2147. we are 95% confident that the true proportion will fall in the interval.
t Test for Hypothesis of the Mean
Data
Null Hypothesis m=
3.2
Level of Significance
0.01
Sample Size
20
Sample Mean
3.3335
Sample Standard Deviation
0.337409247
Intermediate Calculations
Standard Error of the Mean
0.0754
Degrees of Freedom
19
t Test Statistic
1.7695
Upper-Tail Test
Upper Critical Value
2.5395
p-Value
0.0464
Do not reject the null hypothesis
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