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Chapter 10: Q.10.127 (page 442)

Glaucoma and Corneal Thickness. Glaucoma is a leading cause of blindness in the United States. N. Ehlers measured the corneal thickness of eight patients who had glaucoma in one eye but not in the other. The results of the study were published as the paper "On Corneal Thickness and Intraocular Pressure, II" (Acta Opthalmologica, Vol. 48, pp. 1107-1112). The data on corneal thickness, in microns, are shown in the following table.

At10%significance level, do the data provide sufficient evidence to conclude that mean conceal thickness is greater in normal eyes than a eyes with glaucoma.

Short Answer

Expert verified

The null hypothesis is not rejected, and the data are sufficient to indicate that mean corneal thickness in normal eyes is bigger than in glaucoma eyes.

Step by step solution

01

Given Information

Given data is :

We have to explain whether the data provide sufficient evidence to conclude that mean corneal thickness is greater in normal eyes than in eyes with glaucoma.

02

Explanation

The null and alternative hypothesis are:

H0:渭1=渭2

Ha:渭1>渭2

The table is shown below:

The mean and standard deviation are computed as follows:

Mean:

d炉=鈭�dn=328=4

Standard deviation:

sd=鈭�di2-鈭�di2nn-1=936-(32)288-1=10.74

The formula of test statistics is: t=d炉sdn

Substitute the given values:

t=410.746=1.05

The degree of freedom is :

dof=n-1=8-1=7

The critical value for the level of significance is1.415

Since, the value of test statistic is not fall in the rejection region.

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Most popular questions from this chapter

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?

The primary concern is deciding whether the mean of Population 2 is less than the mean of Population1.

In this Exercise, we have provided summary statistics for independent simple random samples from two populations. In each case, use the pooled t-test and the pooled t-interval procedure to conduct the required hypothesis test and obtain the specified confidence interval.

x炉1=20,s1=4,n1=10,x炉2=23,s2=5,n2=15

a. Left-tailed test,伪=0.05

b. 90%confidence interval

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 伪, the null hypothesis H0:渭1=渭2will be rejected in favor of the alternative hypothesis Ha:渭1鈮�渭2if and only if the ( 1-伪)-level confidence interval for 渭1-渭2does 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.

In each of Exercises 10.75-10.80, we have provided summary statistics for independent simple random samples form non populations. In each case, use the non pooled t-fest and the non pooled t-interval procedure to conduct the required hypothesis test and obtain the specified confidence interval.

x~1=20,s1=4,n1=10,x~2=18,s2=5,n2=15.

a. Right-tailed test,localid="1651298373729" 伪=0.05.

b. 90%confidence interval.
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