Homework 4 (Individual Exercise)

This document provides solutions for Homework 4 (Individual Exercise) in Statistics. It includes answers to questions on t-test, regression analysis, scatter plot, and correlation analysis. The document also includes hypothesis testing, interpretation of results, and recommendations for hiring a new manager.

Homework 4 (Individual Exercise)
Statistics
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Homework 4 (Individual Exercise)
Question 1:
In a press conference, the provost of a university told the public that the average GPA of their students
is 3.5. A reporter is skeptical about the provost’s statement. He surveyed a random sample of 100
students on campus. The mean GPA from the sample is 3.4 and the standard deviation is 0.4.
Please do a t-test to test the following research hypothesis. You need to first write down the null and
alternative hypotheses.
1. Whether the average GPA of the university students is equal to 3.5?
a. Research Hypotheses (H0 and Ha):
Hypothesis
H0: Mean GPA for the students is equal to 3.5
Versus
H1: Mean GPA for the students is not equal to 3.5
b. T-test:
tcalc= X −μ
sX
where sX= s
√n (d.f.=n-1)
tcalc= X −μ
s
√ n
tcalc= 3.5−3.4
0.4
√ 100
=2.5
However t0.95 , 99=2.5
It can be observed that T > t0.95 , 99 that is 1.98 < 2.05
The null hypothesis is rejected. The conclusion is that the areas with greater levels of collective
efficacy will have significantly different mean juvenile crime rate.
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tcalc= X −μ
sX
where sX= s
√n (d.f.=n-1)

Homework 4 (Individual Exercise)
c. Interpret the results using 0.05 significance level (critical value is 1.98 for two-tailed,
α=.05, d.f. = 99, and critical value is 1.66 for one-tailed, α=.05, d.f. = 99).
tcalc=2.5
However t0.95 , 99=1.98
It can be observed therefore that T > t0.95 , 99 that is 1.98 < 2.05
The null hypothesis is not rejected. The conclusion is that the Mean GPA for the students is
equal to 3.5.
Question 2: The Human Resources department of XYZ Company wants to example the relationship
between manager characteristics and performance rating. Interpret the following regression results.
Here are variable information.
 PERFORMANCE: Performance rating for a business unit manager
 SALES: average sales for that unit
 EXPERIENCE: the number of years the manager has been in the industry
 DUMMY: =1 if the manager has an MBA, =0 if the manager has no MBA.
1. What are the dependent and independent variables?
Dependent variable: Performance
Independent variables: Sales, experience & dummy
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Homework 4 (Individual Exercise)
2. What are the null and alternative hypotheses?
Hypothesis
H0: There is no significant prediction of manager performance by sales, experience and dummy
Versus
H1: There is a significant prediction of manager performance by sales, experience and dummy
3. List the independent variables in order from greatest to least in terms of how strong the
relationship is with performance.
 Dummy
 Experience
 Sales
4. Interpret the regression results (F-value, model fit, and parameter estimate/regression
coefficient).
Since the p-value calculated (0.00) is less than the level of significance (0.05), it can be
concluded that the sample data has sufficient evidence to conclude that the model fits the data
well.
For the regression coefficients, it can be concluded that a unit change in dummy causes 3.8 units
change in performance. To add on, a unit change in experience causes a 0.03 unit change in
performance. Lastly, a unit change in sales causes a 0.00038 unit change in performance.
5. Based on the results, what is the prediction equation for manager performance
(PERFORMANCE)?
Performance=0.03 ( experience ) +3.8 ( dummy ) +0.00038 ( sales )+¿72.68
6. Based on the results, what would you tell the human resources department who is hiring a
new manager?
I will tell the manager to put more weight on dummies as opposed to experience and average
sales units when hiring a new manager.
7. When might one prefer to use an ANOVA program instead of a multiple regression analysis?
ANOVA program is appropriate where the independent variable has more than one
level.
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Homework 4 (Individual Exercise)
Question 3: SPSS Exercise
Download “Store data.sav” from Canvas. Make sure you include the SPSS output in your homework
submission.
A store wants to know how advertising spending relate with store traffic. The manager randomly
selected 20 stores and recorded the following variables: the number of people entering the store on a
given Sunday (TRAFFIC), the advertising spending the previous week (ADV). Answer the following
questions.
1. Draw a scatter plot between TRAFFIC and ADV.
Figure 1
It can be observed that there is a linear relationship between advertising spending and store
traffic. It can also be concluded that since R2 is 0.74, 74% of the changes that occur in store
traffic is due to advertising spending.
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Homework 4 (Individual Exercise)
2. Run a Pearson correlation analysis of TRAFFIC and ADV.
Correlation results table
Correlations
Store traffic Advertising
spending
Store traffic
Pearson Correlation 1 .863**
Sig. (2-tailed) .000
N 20 20
Advertising spending
Pearson Correlation .863** 1
Sig. (2-tailed) .000
N 20 20
**. Correlation is significant at the 0.01 level (2-tailed).
Table 1
The Pearson correlation coefficient r is 0.86. This indicates that there is a strong
relationship between store traffic and advertising spending. The correlation is also significant
since the p-value is 0.00 less than the level of significance.
3. Write the null and alternative hypotheses.
Hypothesis
H0: There is no relationship between store traffic and advertising spending.
Versus
H1: There is a significant relationship between store traffic and advertising spending
4. Run a simple regression analysis and interpret the results. (F-value, model fit, and parameter
estimate / regression coefficient).
Simple linear regression result table
ANOVAa
Model Sum of Squares df Mean Square F Sig.
1
Regression 2496109.538 1 2496109.538 52.329 .000b
Residual 858604.212 18 47700.234
Total 3354713.750 19
a. Dependent Variable: Store traffic
b. Predictors: (Constant), Advertising spending
Table 2
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Homework 4 (Individual Exercise)
Coefficientsa
Model Unstandardized Coefficients Standardized
Coefficients
t Sig.
B Std. Error Beta
1 (Constant) 148.642 100.103 1.485 .155
Advertising spending 1.541 .213 .863 7.234 .000
a. Dependent Variable: Store traffic
Table 3
Since the p-value calculated (0.00) is less than the level of significance (0.05), it can be concluded that
the sample data has sufficient evidence to conclude that the model fits the data well.
For the regression coefficients, it can be concluded that a unit change in advertising spending causes
1.54 units change in store traffic.
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