Chapter 10: Q. 10.109 (page 440)
State the two conditions required for performing a paired r-procedure. How important are those conditions?
A simple random paired sample with normal differences or a large sample size are required conditions for performing a paired t-procedure. A simple random sample assumption is required.
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In each of Exercises 10.75-10.80, we have provided summary statistics for independent simple random samples from non populations. In each case, use the non pooled test and the non pooled interval procedure to conduct the required hypothesis test and obtain the specified confidence interval.
a. Two-tailed test,
b. confidence interval.
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.
Independent:
V. Tangpricha et al. did a study to determine whether fortifying orange juice with Vitamin D would result in changes in the blood levels of five biochemical variables. One of those variables was the concentration of parathyroid hormone (PTH), measured in picograms/milliliter ( pg/ml ). The researchers published their results in the paper "Fortification of Orange Juice with Vitamin D: A Novel Approach for Enhancing Vitamin D Nutritional Health" (American Journal of Clinical Nutrition, Vol. 77, pp. 1478-1483). Concentration levels were recorded at the beginning of the experiment and again at the end of weeks. The following data, based on the results of the study, provide the decrease (negative values indicate an increase) in PTH levels, in pg/ml, for those drinking the fortified juice and for those drinking the unfortified juice.
At the significance level, do the data provide sufficient evidence to conclude that drinking fortified orange juice reduces PTH level more than drinking unfortified orange juice? (Note: The mean and standard deviation for the data on fortified juice are and , respectively, and for the data on unfortified juice, they are and, respectively.)
Two-Tailed Hypothesis Tests and CIs. As we mentioned on page , the following relationship holds between hypothesis tests and confidence intervals: For a two-tailed hypothesis test at the significance level , the null hypothesis will be rejected in favor of the alternative hypothesis if and only if the -level confidence interval for 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 and
b. Excrcises and
What constitutes each pair in a paired sample?
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