Chapter 9.5, Problem 127E

Left-Tailed Hypothesis Tests and CIs. In Exercise 8.146 on page 362, we introduced one-sided one-mean t-intervals. The following relationship holds between hypothesis tests and confidence intervals for one-mean t-procedures: For a left-tailed hypothesis lest at the significance level α, the null hypothesis H₀: μ ₌  μ₀ will be rejected in favor of the alternative hypothesis H₀: μ <  μ₀ if and only if μ₀ is greater than or equal to the (l – α )-level upper confidence bound for μ. In each case, illustrate the preceding relationship by obtaining the appropriate upper confidence bound and comparing the result to the conclusion of the hypothesis test in the specified exercise.

1. a. Exercise 9.117
2. b. Exercise 9.118

9.117 Ankle Brachial Index. The ankle brachial index (ABI) compares the blood pressure of a patient's arm to the blood pressure of the patient's leg. The ABI can be an indicator of different diseases, including arterial diseases. A healthy (or normal) ABI is 0.9 or greater. In a study by M. McDermott et al. titled “Sex Differences in Peripheral Arterial Disease: Leg Symptoms and Physical Functioning” (Journal of the American Geriatrics Society, Vol. 51, No. 2, pp. 222–228), the researchers obtained the ABI of 187 women with peripheral arterial disease. The results were a mean ABI of 0.64 with a standard deviation of 0.15. At the 1% significance level, do the data provide sufficient evidence to conclude that, on average, women with peripheral arterial disease have an unhealthy ABI?

9.118 Dirt Bikes. Dirt bikes are simpler and lighter motorcycles that are designed for off-road events. Specifications for dirt bikes can be found through Motorcycle USA on their website www.motoreycle-usa.com. A random sample of 30 dirt bikes have a mean fuel capacity of 1.91 gallons with a standard deviation of 0.74 gallons. At the 10% significance level, do the data provide sufficient evidence to conclude that the mean fuel tank capacity of all dirt bikes is less than 2 gallons?