Concept explainers
Tom Sevits is the owner of the Appliance Patch. Recently Tom observed a difference in the dollar value of sales between the men and women he employs as sales associates. A sample of 40 days revealed the men sold a mean of $1,400 worth of appliances per day. For a sample of 50 days, the women sold a mean of $1,500 worth of appliances per day. Assume the population standard deviation for men is $200 and for women $250. At the .05 significance level, can Mr. Sevits conclude that the mean amount sold per day is larger for the women?
- (a) State the null hypothesis and the alternate hypothesis.
- (b) What is the decision rule?
- (c) What is the value of the test statistic?
- (d) What is your decision regarding the null hypothesis?
- (e) What is the p-value?
- (f) Interpret the result.
a.
State the null and the alternative hypothesis.
Answer to Problem 1SR
The null hypothesis is
The alternative hypothesis is
Explanation of Solution
In this context,
The hypotheses are given below:
Null hypothesis:
Alternative hypothesis:
Thus, the null hypothesis is
b.
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 ‘Normal’ distribution.
- Enter the Mean as 0 and Standard deviation value as 1
- Click the Shaded Area tab.
- Choose Probability and Right Tails 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 1.645.
The decision rule is as follows:
If
c.
Find the value of the test statistics.
Answer to Problem 1SR
The value of the test statistics is 2.108.
Explanation of Solution
The test statistics is obtained as follows:
Thus, the value of test statistics is 2.108.
d.
Determine the decision regarding
Answer to Problem 1SR
The decision is that reject the null hypothesis
Explanation of Solution
Decision:
The critical value is 1.645 and the value of test statistic is 2.108.
The value of test statistic is greater than the critical value.
That is,
From the decision rule, reject the null hypothesis.
e.
Find the p-value.
Answer to Problem 1SR
The p-value is 0.0175.
Explanation of Solution
p-value:
Step-by-step procedure to obtain the p-value using MINITAB software:
- Choose Graph > Probability Distribution Plot choose View Probability> OK.
- From Distribution, choose ‘Normal’ distribution.
- Enter the Mean as 0 and Standard deviation value as 1.
- Click the Shaded Area tab.
- Choose X Value and right tails for the region of the curve to shade.
- Enter the X value as 2.108.
- Click OK.
Output obtained using MINITAB software is given below:
From the MINITAB output, the p-value is 0.0175.
Thus, the p-value is 0.0175.
f.
Interpret the result.
Explanation of Solution
Interpretation:
Here, the null hypothesis is rejected.
Therefore, there is evidence that the mean amount of sales per day by woman is greater than that of women.
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Chapter 11 Solutions
Statistical Techniques in Business and Economics
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt