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Chapter 10: Q. 10.118 (page 441)

$H_{2} : μ_{1} < μ_{2}$

Short Answer

Expert verified

Since the value of the test statistic is fall in the accepted region. Thus, the null hypothesis is not rejected.

Step by step solution

01

Given Information

The hypothesis is

$H_{0} : μ_{1} = μ_{2}, H_{a} : μ_{1} < μ_{2}$

and the level of significance is 0.1.

02

Explanation

Compute the sample mean as follow:

$\bar{d} = \frac{\sum d}{n}$

$= \frac{- 17}{7}$

$= - 1.714$

The value of the standard deviation is given below:

$s_{d} = \sqrt{\frac{\sum d_{i}^{2} - \frac{{(\sum d_{i})}^{2}}{n}}{n - 1}}$

$= \sqrt{\frac{122 - \frac{(- 12)^{2}}{7}}{7 - 1}}$

$= 4.1115$

The test statistics are,

$t = \frac{\bar{d}}{\frac{s_{d}}{\sqrt{\bar{n}}}}$

Replace the above value in the given equation

$z = \frac{- 1.714}{\frac{4.1115}{\sqrt{7}}} = - 1.1$

The value of the degree of freedom is,

$d f = n - 1 = 7 - 1 = 6$

The critical value for the level of significance of $0.1$ is $- 1.44 .$

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Most popular questions from this chapter

In Exercise $10.83$ , you conducted a nonpooled $t$ -test to decide whether the mean number of acute postoperative days spent in the hospital is smaller with the dynamic system than with the static system. Use the technology of your choice to perform the following tasks.

a. Using a pooled $t$ -test, repeat that hypothesis test.

b. Compare your results from the pooled and nonpooled $t$ -tests.

c. Which test do you think is more appropriate, the pooled or nonpooled $t$ -test? Explain your answer.

Give an example of interest to you for comparing two population means. Identify the variable under consideration and the two populations.

Two-Tailed Hypothesis Tests and CIs. As we mentioned on page 413, the following relationship holds between hypothesis tests and confidence intervals: For a two-tailed hypothesis test at the significance level $α$ , the null hypothesis $H_{0} : μ_{1} = μ_{2}$ will be rejected in favor of the alternative hypothesis $H_{a} : μ_{1} \neq μ_{2}$ if and only if the ( $1 - α$ )-level confidence interval for $μ_{1} - μ_{2}$ does not contain $0$ . In each case, illustrate the preceding relationship by comparing the reults of the hypothesis test and confidence interval in the specified xercises.

a. Exercises 10.48 and 10.54.

b. Exercises 10.49 and 10.55.

Discuss the basic strategy for performing a hypothesis test to compare the means of two populations, based on independent samples.

Discuss the basic strategy for comparing the means of two populations based on independent simple random samples.

See all solutions

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