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Chapter 10: Q.10.135 (page 443)

Font Readability. In the online paper "A Comparison o Two Computer Fonts: Serif versus Ornate Sans Serif" (Usability News, Issue 5.3), researchers S. Morrison and J. Noyes studied whether the type of font used in a document affects reading speed or comprehension. The fonts used for the comparisons were the serif font Times New Roman (TNR) and a more ornate sans serif font called Gigi. The following table gives the times, in seconds, that it took each of the $25$ participants to read paragraphs in the TNR and Gigi fonts.
Suppose that you want to perform a hypothesis test to determine whether, on average, people read faster with the TNR font than with the Gigi font. Conduct preliminary graphical data analyses to decide whether applying the paired $t$ -test is reasonable. Explain your decision.

Short Answer

Expert verified

It is not possible to apply the paired $t$ -test.

Step by step solution

01

Given Information

The sample size is $25$ .

02

Explanation

The probability plot is

The box plot is,

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Most popular questions from this chapter

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 $H_{2} : μ_{1} \neq μ_{2}$ 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 results of the hypothesis test and confidence interval in the specified exercises.

a. Exercises $10.81$ and $10.87$

b. Excrcises $10.86$ and $10.92$

Discuss the basic strategy for comparing the means of two populations based on a simple random paired sample.

Political Prisoners. According to the American Psychiatric Association, posttraumatic stress disorder (PTSD) is a common psychological consequence of traumatic events that involve a threat to life or physical integrity. During the Cold War, some 200,000 people in East Germany were imprisoned for political reasons. Many were subjected to physical and psychological torture during their imprisonment, resulting in PTSD. A. Ehlers et al. studied various characteristics of political prisoners from the former East Germany and presented their findings in the paper "Posttraumatic Stress Dis-order (PTSD) Following Political Imprisonment: The Role of Mental Defeat, Alienation, and Perceived Permanent Change" (Journal of Abnormal Psychology, Vol. 109, pp. 45-55). The researchers randomly and independently selected 32 former prisoners diagnosed with chronic PTSD and 20 former prisoners that were diagnosed with PTSD after release from prison but had since recovered (remitted). The ages, in years, at arrest yielded the following summary statistics.

At the $10 %$ significance level, is there sufficient evidence to conclude that a difference exists in the mean age at arrest of East German prisoners with chronic PTSD and remitted PTSD?

Suppose that you want to perform a hypothesis test to compare the means of two populations, using independent simple random samples. Assume that the two distributions (one for each population) of the variable under consideration are normally distributed and have equal standard deviations. Answer the following questions and explain your answers.

a. Is it permissible to use the pooled $t$ -test to perform the hypothesis test?

b. Is it permissible to use the Mann-Whitney test to perform the hypothesis test?

c. Which procedure is preferable, the pooled $t$ -test or the Mann-Whitney test?

The intent is to employ the sample data to perform a hypothesis test to compare the means of the two populations from which the data were obtained. In each case, decide which of the procedures should be applied.

Paired: $n = 18$ .

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