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Chapter 10: Q.10.69 (page 427)

You know that the population standard deviations are equal.

Short Answer

Expert verified

For the current circumstance, a pooled $t$ test should be utilized.

Step by step solution

01

Given Information

The standard deviations of the population are the same.

02

Explanation

The following are the assumptions of the pooled $t$ test: - The sample should be a simple random sampling from two populations.

Each sample is distinct from the others.
The population is roughly normal.
Population standard deviations are the same.

The non-pooled $t$ assumption is that the chosen sample should be a simple random sampling from two populations.

The samples are unrelated to each other.
The population is rather normal.
The sample size is substantial.

The two standard deviations values are similar in the present circumstance.

For the pooled $t$ test, this is the assumption.

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Most popular questions from this chapter

In each of Exercises 10.35-10.38, we have provided summary statistics for independent simple random samples from two populations. Preliminary data analyses indicate that the variable under consideration is normally distributed on each population. Decide, in each case, whether use of the pooled $t$ -test and pooled $t$ -interval procedure is reasonable. Explain your answer.

10.38 $x_{1} = 39.04, s_{1} = 18.82, n_{1} = 51$

$x_{2} = 49.92, s_{2} = 18.97, n_{2} = 53$

In each of exercise 10.13-10.18, we have presented a confidence interval for the difference, $μ_{1} a n d μ_{2}$ , between two population means. interpret each confidence interval.

$95 %$ CI is from $- 20 t o - 15$

In this section, we introduced the pooled t-test, which provides a method for comparing two population means. In deriving the pooled f-test, we stated that the variable

z = \frac{({\hat{f}}_{1} - {\hat{x}}_{2}) - (μ_{1} - μ_{2})}{σ \sqrt{(1 / n_{1}) + (1 / n_{2})}}

cannot be used as a basis for the required test statistic because $σ$ is unknown. Why can't that variable be used as a basis for the required test statistic?

Stressed-Out Bus Drivers. An intervention program designed by the Stockholm Transit District was implemented to improve the work conditions of the city's bus drivers. Improvements were evaluated by G. Evans et al., who collected physiological and psychological data for bus drivers who drove on the improved routes (intervention) and for drivers who were assigned the normal routes (control). Their findings were published in the article "Hassles on the Job: A Study of a Job Intervention with Urban Bus Drivers" (Journal of Organizational Behavior, Vol. 20, pp. 199-208). Following are data, based on the results of the study, for the heart rates, in beats per minute, of the intervention and control drivers.

a. At the $5 %$ significance level, do the data provide sufficient evidence to conclude that the intervention program reduces mean heart rate of urban bus drivers in Stockholm? (Note; $x_{1} = 67.90$ , $s_{1} = 5.49,$ ${\bar{x}}_{2} = 66.81$ and $s_{2} = 9.04$ .

b. Can you provide an explanation for the somewhat surprising results of the study?

c. Is the study a designed experiment or an observational study? plain your answer.

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

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