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It is often useful for companies to know who their customers are and how they became customers. A credit card company is interested in whether the owner of the card applied for the card on his or her own or was contacted by a telemarketer. The company obtained the following sample information regarding end-of-the-month balances for the two groups.
Is it reasonable to conclude the
- (a) State the null hypothesis and the alternate hypothesis.
- (b) How many degrees of freedom are there?
- (c) What is the decision rule?
- (d) What is the value of the test statistic?
- (e) What is your decision regarding the null hypothesis?
- (f) Interpret the result.
a.
![Check Mark](/static/check-mark.png)
State the null and the alternative hypothesis.
Answer to Problem 3SR
The null hypothesis is
The alternative hypothesis is
Explanation of Solution
In this context,
The hypotheses are given below:
In this context,
Null hypothesis:
Alternative hypothesis:
Thus, the null hypothesis is
b.
![Check Mark](/static/check-mark.png)
Find the number of degrees of freedom.
Answer to Problem 3SR
Thus, the number of degrees of freedom is 8.
Explanation of Solution
Calculation:
For t distribution with the two independent random samples, the degrees of freedom is as follows:
Substitute
Thus, the number of degrees of freedom is 8.
c.
![Check Mark](/static/check-mark.png)
Determine the decision rule.
Explanation of Solution
Step-by-step procedure to obtain the critical value using MINITAB software:
- Choose Graph > Probability Distribution Plot choose View Probability > OK.
- From Distribution, choose ‘t’ distribution.
- In Degrees of freedom, enter 8.
- Click the Shaded Area tab.
- Choose Probability and left Tail for the region of the curve to shade.
- Enter the Probability value as 0.05.
- Click OK.
Output obtained using MINITAB software is given below:
From the MINITAB output, the critical value is –1.860.
The decision rule is as follows:
If
d.
![Check Mark](/static/check-mark.png)
Find the value of test statistic.
Answer to Problem 3SR
Thus, the value of the test statistic is –1.234.
Explanation of Solution
Calculation:
Test statistic:
The test statistics is obtained as follows:
Thus, the test statistic is –1.234.
e.
![Check Mark](/static/check-mark.png)
Determine the decision regarding
Answer to Problem 3SR
The decision is that fail to reject the null hypothesis
Explanation of Solution
Decision:
The critical value is –1.860 and the value of test statistic is –1.234.
The value of test statistic is greater than the critical value.
That is,
From the decision rule, fail to reject the null hypothesis.
f.
![Check Mark](/static/check-mark.png)
Determine the interpretation of the study.
Answer to Problem 3SR
The interpretation is that there is no evidence that the mean balance is larger for the credit card holders contacted by telemarketers than those who applied on their won for the card.
Explanation of Solution
Interpretation:
From the decision rule, fail to reject the null hypothesis.
Therefore, there is no evidence that the mean balance is larger for the credit card holders contacted by telemarketers than those who applied on their won for the card.
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Chapter 11 Solutions
Loose Leaf for Statistical Techniques in Business and Economics (Mcgraw-hill/Irwin Series in Operations and Decision Sciences)
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