Final Exam Practice Solutions
Use the following scenario and Excel output to answer the next six questions.
A student organization was interested in studying the amount spent on textbooks by college students. The organization
obtained a random sample of 25 female and male students. The Excel output below compares the average amount spent
on books by male students compared with the average amount spent by female students.
t-Test: Two-Sample Assuming Unequal Variances
α = .05
Male Book $
Female Book $
Mean
200.72
189.56
Variance
5683.126667
5469.09
Observations
25
25
Hypothesized Mean Difference
0
df
48
t Stat
0.528388795
P(T<=t) one-tail
0.299832091
t Critical one-tail
1.677224197
P(T<=t) two-tail
0.599664183
t Critical two-tail
2.010634722
1. What is the sample variance of the amount spent on books by male students?
The s2 = 5683.13
2. Suppose you wish to conduct a hypothesis test to determine if there is a difference between females and males in the
average amount spent on books. State the null and alternative hypothesis for this test.
Ho: male = female
Ha: male ≠ female
3. What is the test statistic and p-value for a test of the hypothesis that there are differences between females and males
in the average amount spent on books?
The value of the test statistic is 0.5284 found on the printout next to “t stat.”
The p-value for the test is 0.599664 using the Satterthwaite approximation and is listed in the printout next to
“P(T<=t) two-tail” which gives the p-value for a two-sided alternative hypothesis.
4. Using = .05, what is your decision and conclusion for the hypothesis test that there is a difference between females
and males in the average amount spent on books.
Because the p-value of 0.5997 is greater than of .05, do not reject the Ho. There is NOT sufficient evidence to
show that males and females differ in the amount they spend on books.
5. What is the margin of error in a 95% confidence interval to estimate the population difference in the average amount
spent on books between females and males?
A confidence level of .95 (1 - ) was used to obtain the Excel printout. The “t Critical two tail” is the t needed
to calculate the margin of error for a 95% confidence interval for the population difference in the average
amount spent on books. The margin of error is:
t
s12
n1
s 22
n2
Final Exam Practice Solutions
2.0106
5,683.13
25
5469.09
25
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± 2.0106(21.12)
± 42.27
6. Compute and interpret a 99% confidence interval to estimate the population difference in the average amount spent on
books between females and males.
The t-value for this confidence interval must be obtained from Table B. The Excel printout gives the
Satterthwaite approximation for the df as 48. The closest listed df in Table B is 50. The t at 99% confidence and
50 df is 2.678.
( x1
s12
x2 ) t
n1
s 22
n2
(200.72 189.56) 2.678
5683.13
25
5469.09
25
11.16 2.678(21.12)
11.16 56.56
( 45.40, 67.72)
We are 99% confident that the population difference in the average amount spent by males may be from $45.40
less than the average amount spent by females to $67.72 more than the average amount spent by females.
Because zero is included in the interval, we would conclude that males and females do not differ in the amount
they spend on books.
Use the following information to answer the next three questions.
A consumer electronics chain store is interested in studying the relationship between the number of advertisements run
during a week and the weekly sales of stores in an area. The chain collects a random sample of stores in cities of similar
size and records the number of advertisements run on local television during the week and the total dollar amount of sales
for the local store. A regression analysis was conducted and the Excel output is given below. The variables included in
the analysis are:
Ads – the number of television ads run during the week
Sales – the total amount of weekly sales in thousands (1,000s)
Regression Statistics
Multiple R
R Square
Adjusted R Square
0.63132666
Standard Error
Observations
55
ANOVA
df
Regression
Residual
Total
Intercept
Ads
1
53
54
SS
MS
F
Significance F
1277.584204 1277.584 93.47113 2.70272E-13
724.4157956 13.66822
2002
Coefficients Standard Error
t Stat
P-value
8.59233449
1.093331683 7.858854 1.88E-10
1.2775842
0.132145016 9.668047 2.7E-13
Final Exam Practice Solutions
Lower 95%
Upper 95%
6.399389889 10.7852791
1.012534993 1.54263342
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7. Conduct a test of the hypothesis that the number of television ads has a significant impact on weekly sales (is a
significant linear predictor of weekly sales), using α = .05. State the null and alternative hypotheses. Report the test
statistic and p-value of the test. What is your decision and conclusion?
Ho: = 0
Ha:
0
Obtain the information for the hypothesis test from the printout in the line next to “Ads”
Test statistic: 9.668
p-value: 2.7E-13 or p < .0001
Decision: Since p-value < , reject Ho: conclude that the number of television ads run weekly is a significant
linear predictor of weekly sales.
8. Obtain and interpret a 95% confidence interval to estimate the population slope coefficient for the number of
television ads run weekly.
Obtain the lower and upper limits of the 95% confidence interval from the printout in the line next to “Ads”
The upper and lower limits of the interval are 1.013 and 1.543.
Interpretation: We are 95% confident that weekly sales increase between $1,013 and $1,543, on average, for
each additional television ad run during the week.
9. What is the margin of error for a 90% confidence interval to estimate the population slope coefficient for the number
of television ads run weekly?
The margin of error to estimate a slope coefficient is:
t(SEads)
The standard error from the printout is 0.1321
The critical t value must be obtained from the t-distribution table with df= n – 2 = 53. The closest df in the t table
is 50 df. The t value for a 90% confidence interval at 50 df is 1.676
1.676(0.1321) = 0.2214 The margin of error for a 90% confidence interval is 0.2214
Final Exam Practice Solutions
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