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Recall that the researchers reported the mean and the standard deviation of the anxiety scale for the sample (M= 33.56, SD = 19.40) as well as for the population (µ = 14.20, o = 9.70), and that the sample size was N= 92. As mentioned on a previous screen, the researchers reported, “A single sample z test revealed that the average score on the SCAS-P for the sample of children with AS significantly differed from the mean of the normative sample, z= 19.15, p< .05" (pp. 364–365). One assumption when performing a z test is that scores in the underlying population from which the sample is drawn are approximately normally distributed. These researchers did not report any tests of this assumption. Let's assume the worst-case scenario-that the anxiety scores in the population are not normally distributed.

Recall that the researchers reported the mean and the standard deviation of the anxiety scale for the sample (M= 33.56, SD = 19.40) as well as for the population (µ = 14.20, o = 9.70), and that the sample size was N= 92. As mentioned on a previous screen, the researchers reported, “A single sample z test revealed that the average score on the SCAS-P for the sample of children with AS significantly differed from the mean of the normative sample, z= 19.15, p< .05" (pp. 364–365). One assumption when performing a z test is that scores in the underlying population from which the sample is drawn are approximately normally distributed. These researchers did not report any tests of this assumption. Let's assume the worst-case scenario-that the anxiety scores in the population are not normally distributed.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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Recall that the researchers reported the mean and the standard deviation of the anxiety scale for the sample (M = 33.56, SD = 19.40) as well as for the population (µ = 14.20, o = 9.70), and that the sample size was N= 92. As mentioned on a previous screen, the researchers reported, “A single sample z test revealed that the average score on the SCAS-P for the sample of children with AS significantly differed from the mean of the normative sample, z = 19.15, p< .05" (pp. 364–365). One assumption when performing a z test is that scores in the underlying population from which the sample is drawn are approximately normally distributed. These researchers did not report any tests of this assumption. Let's assume the worst-case scenario-that the anxiety scores in the population are not normally distributed.
Transcribed Image Text:Recall that the researchers reported the mean and the standard deviation of the anxiety scale for the sample (M = 33.56, SD = 19.40) as well as for the population (µ = 14.20, o = 9.70), and that the sample size was N= 92. As mentioned on a previous screen, the researchers reported, “A single sample z test revealed that the average score on the SCAS-P for the sample of children with AS significantly differed from the mean of the normative sample, z = 19.15, p< .05" (pp. 364–365). One assumption when performing a z test is that scores in the underlying population from which the sample is drawn are approximately normally distributed. These researchers did not report any tests of this assumption. Let's assume the worst-case scenario-that the anxiety scores in the population are not normally distributed.
What should we conclude about this z test? (Hint: Think of the central limit theorem.) O A. The results of the z test are not at all valid because the researchers failed to meet the assumption of having normally distributed scores in the population. O B. The central limit theorem tells us that the distribution of sample means will approach normality when the sample size is greater than 30, even if the underlying distribution of scores in the population is non-normal. Given that the sample size in this study is 92, the researchers are okay with using the z test. O C. We will need to penalize the p value for the z test because the data failed to meet the normality assumption. The new, penalized p value is likely to be larger than 0.05. O D. The central limit theorem tells us that the distribution of sample means will approach normality when the sample size is greater than 80, even if the underlying distribution of scores in the population is non-normal. Given that the sample size in this study is 92, the researchers are okay with using the z test.
Transcribed Image Text:What should we conclude about this z test? (Hint: Think of the central limit theorem.) O A. The results of the z test are not at all valid because the researchers failed to meet the assumption of having normally distributed scores in the population. O B. The central limit theorem tells us that the distribution of sample means will approach normality when the sample size is greater than 30, even if the underlying distribution of scores in the population is non-normal. Given that the sample size in this study is 92, the researchers are okay with using the z test. O C. We will need to penalize the p value for the z test because the data failed to meet the normality assumption. The new, penalized p value is likely to be larger than 0.05. O D. The central limit theorem tells us that the distribution of sample means will approach normality when the sample size is greater than 80, even if the underlying distribution of scores in the population is non-normal. Given that the sample size in this study is 92, the researchers are okay with using the z test.
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