Statistics Exam
ahmd54
final_examination_part_2___9.docFINAL EXAMINATION
Part (2) (9)Name _________
Statistics Quantitative Methods
Score __________
Department of Economics, Loyola Marymount University
Dr. Jian Xu
(I) Excel coding question:
1) (5 points)The average cost of a hotel room in New York is said to be $168 per night. To determine if this is true, a random sample of 200 hotels is taken and resulted in a sample mean of $172.50 and an S of $15.40. Test the appropriate hypotheses at α = 0.05.
a. Please write Excel coding to complete this Hypothesis test using T approach.
b. Please write Excel coding to complete this Hypothesis test using P approach. Write a complete coding, no calculation is needed.
2) (5 points) A marketing company claims that it receives 8% responses from its mailing. To test this claim, a random sample of 500 were surveyed with 25 responses. Test at the α = 0.05 significance level by the following coding:
H0: π = 0.08
H1: π ≠ 0.08
Z* = -2.47
=if (normsinv(Z*)<α/2, “reject H0”, ”accept H0 ”) Please check to see anything is wrong. If so, do your correction to make the coding work.
(II) Calculation for short essay questions: (Your answers should be specified with steps and explanations to get full credit)
.
1. (2 points for each question) Following is a multiple regression output with Y = % Passing as the dependent variable,
1
X
=:% Attendance,2
X
= Salaries and3
X
= Spending:Table(3)
|
Regression Statistics |
|
|
|
|
|
|
|
Multiple R |
0.7930 |
|
|
|
|
|
|
R Square |
0.6288 |
|
|
|
|
|
|
Adjusted R Square |
0.6029 |
|
|
|
|
|
|
Standard Error |
10.4570 |
|
|
|
|
|
|
Observations |
47 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
ANOVA |
|
|
|
|
|
|
|
|
df |
SS |
MS |
F |
Significance F |
|
|
Regression |
3 |
7965.08 |
2655.03 |
24.2802 |
2.3853E-09 |
|
|
Residual |
43 |
4702.02 |
109.35 |
|
|
|
|
Total |
46 |
12667.11 |
|
|
|
|
|
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|
|
|
|
|
|
|
Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
|
Intercept |
-753.4225 |
101.1149 |
-7.4511 |
2.88E-09 |
-957.3401 |
-549.5050 |
|
% Attendance |
8.5014 |
1.0771 |
7.8929 |
6.73E-10 |
6.3292 |
10.6735 |
|
Salary |
6.85E-07 |
0.0006 |
0.0011 |
0.9991 |
-0.0013 |
0.0013 |
|
Spending |
0.0060 |
0.0046 |
1.2879 |
0.2047 |
-0.0034 |
0.0153 |
1.1 Referring to Table (3), interpret how the Attendance can affect to the percentage of students passing the proficiency test.
1.2 Referring to Table (3), explain the implication of Multiple R Square and Adjusted R Square.
1.3 What is the difference between them?
1.4 Referring to Table (3), what is the value of the test statistics when testing whether instructional spending per pupil has any effect on percentage of students passing the proficiency test? Using this test statistics to complete your hypothesis test and describe the test steps and your conclusion.
1.5 Referring to Table (3), what is the p-values of the test statistics when testing whether instructional spending per pupil, has any effect on percentage of students passing the proficiency test?
1.6 Referring to Table (3) perform a null hypothesis to test whether daily average of the percentage of students attending class has any effect on percentage of students passing the proficiency test? WHAT IS YOUR CONCLUSION? Specify and explain your reasons.
1.7 After the two hypothesis tests for
3
1
,
b
b
, re-estimate to improve the regression model.Please conduct a F-test for this regression model for the significance of all coefficients
3
2
1
,
,
b
b
b
of the independent variables using the F-test information from above table. What is your result? Is it consistent with the results from T-tests?1. (8 points) As an aid to the establishment of personnel requirements, the director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a 24-hour period. The director randomly selects 64 different 24-hour periods and determines the number of admissions for each. For this sample, and S2 = 25. If the director wishes to estimate the mean number of admissions per 24-hour period to within 1 admission with 99% reliability, what size sample should she choose?
2. (8 points) Pizza shop delivers pizza to students DOM. The shop manage intended to speed up the delivery time of a trip by paying tips for each trip. The records shows that up to current, the average time for each trip is 25 minutes. For a sample of 25, we calculated that the sample mean is 23.5, the sample standard deviation is 7. At the critical level of 5 percent, please conduct a Hypothesis Test for the above issue: If the tips have successfully speeded up the delivery? Please specify the complete process for each of the 6 steps of a Hypothesis Test.
3. (10 points) For long time people believe that college participation rate for male and female suppose to be equal. Recently, there is a impression that the participation rate for girls is significantly higher than the rate of boys. A 200 sample is collected and the sample rate for boys is 0.48. At a confidence level of 95%, please use Hypothesis tests for boys and girls to find out if this participation rate has been significantly changed.
Extra Credit Question. (10 point)
Using the given data set, develop a simple OLS regression model and evaluate the model in terms of:
1. Fitness,
2. Significance,
3. If the model meet the 4 assumptions: linearity, independence, homogeneity, normality). Show your result with graph and convincing, specific explanations.
DATA:
|
Hours |
Feet |
|
24.00 |
545 |
|
13.50 |
400 |
|
26.25 |
562 |
|
25.00 |
540 |
|
9.00 |
220 |
|
20.00 |
344 |
|
22.00 |
569 |
|
11.25 |
340 |
|
50.00 |
900 |
|
12.00 |
285 |
|
38.75 |
865 |
|
40.00 |
831 |
|
19.50 |
344 |
|
18.00 |
360 |
|
28.00 |
750 |
|
27.00 |
650 |
|
21.00 |
415 |
|
15.00 |
275 |
|
25.00 |
557 |
|
45.00 |
1028 |
|
29.00 |
793 |
|
21.00 |
523 |
|
22.00 |
564 |
|
16.50 |
312 |
|
37.00 |
757 |
|
32.00 |
600 |
|
34.00 |
796 |
|
25.00 |
577 |
|
31.00 |
500 |
|
24.00 |
695 |
|
40.00 |
1054 |
|
27.00 |
486 |
|
18.00 |
442 |
|
62.50 |
1249 |
|
53.75 |
995 |
|
79.50 |
1397 |
