Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)
Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)
6th Edition
ISBN: 9781337115186
Author: David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, Jeffrey D. Camm, James J. Cochran
Publisher: Cengage Learning
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Chapter 9.4, Problem 26E

a.

To determine

Find the p-value and state the conclusion.

a.

Expert Solution
Check Mark

Answer to Problem 26E

The p-value is 0.039.

The conclusion is “reject the null hypothesis”.

Explanation of Solution

Calculation:

The given information is the sample size is n=65, the sample mean is x¯=103, and the sample standard deviation is s=11.5.

The hypotheses are given below:

Null hypothesis: H0:μ=100

Alternative hypothesis: Ha:μ100

Test statistic:

The formula for finding test statistic is as follows:

t=x¯μ0sn

Here, x¯ represents the sample mean, μ0 represents the hypothesized value of the population mean, s represents the sample standard deviation, and n represents the sample size.

Substitute x¯=103, μ0=100, s=11.5 and n=65 in t formula.

t=10310011.565=311.58.0623=31.4264=2.10

Thus, the value of the test statistic is 2.10.

The degrees of freedom is,

df=n1=651=64

Software Procedure:

Step-by-step procedure to obtain the probability value using Excel:

  • Open an EXCEL sheet and select the cell A1.
  • Enter the formula =T.DIST.2T(2.10,64) in the cell A1.
  • Press Enter.

Output using the EXCEL software is given below:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 9.4, Problem 26E , additional homework tip  1

From the output, the exact p-value is approximately 0.040.

Rejection rule:

If p-valueα, reject the null hypothesis.

If p-value>α, do not reject the null hypothesis.

Conclusion:

Here, the p-value is less than the level of significance.

That is, p-value(=0.040)<α(=0.05).

By the rejection rule, the null hypothesis is rejected.

b.

To determine

Calculate the p-value and draw the conclusion.

b.

Expert Solution
Check Mark

Answer to Problem 26E

The p-value is 0.013.

The conclusion is “reject the null hypothesis”.

Explanation of Solution

Calculation:

The given information is that the sample size is n=65, the sample mean is x¯=96.5, and the sample standard deviation is s=11.

Test statistic:

Substitute x¯=96.5, μ0=100, s=11, and n=65 in t formula.

t=96.51001165=3.5118.0623=3.51.3644=2.57

Thus, the value of the test statistic is –2.57.

From part (a), the degrees of freedom is 64.

Software Procedure:

Step-by-step procedure to obtain the probability value using Excel:

  • Open an EXCEL sheet and select the cell A1.
  • Enter the formula =T.DIST.2T(2.57,64) in the cell A1.
  • Press Enter.

Output using the EXCEL software is given below:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 9.4, Problem 26E , additional homework tip  2

From the output, the exact p-value is approximately 0.0125.

Conclusion:

Here, the p-value is less than the level of significance.

That is, p-value(=0.0125)<α(=0.05).

By the rejection rule, the null hypothesis is rejected.

c.

To determine

Obtain the p-value and claim the conclusion.

c.

Expert Solution
Check Mark

Answer to Problem 26E

The p-value is 0.130.

The conclusion is “do not reject the null hypothesis”.

Explanation of Solution

Calculation:

The given information is that the sample size is n=65, the sample mean is x¯=102, and the sample standard deviation is s=10.5.

Test statistic:

Substitute x¯=102, μ0=100, s=10.5 and n=65 in t formula.

t=10210010.565=210.58.0623=21.3024=1.54

Thus, the value of the test statistic is 1.54.

From part (a), the degrees of freedom is 64.

Software Procedure:

Step-by-step procedure to obtain the probability value using Excel:

  • Open an EXCEL sheet and select the cell A1.
  • Enter the formula =T.DIST.2T(1.54,64) in the cell A1.
  • Press Enter.

Output using the EXCEL software is given below:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 9.4, Problem 26E , additional homework tip  3

From the output, the exact p-value is approximately 0.01285.

Conclusion:

Here, the p-value is greater than the level of significance.

That is, p-value(=0.1285)>α(=0.05).

By the rejection rule, the null hypothesis is not rejected.

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Chapter 9 Solutions

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)

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