TABLE 9-4
A drug company is considering marketing a new local anesthetic. The effective time of the anesthetic the drug company is currently producing has a normal distribution with an mean of 7.4 minutes with a standard deviation of 1.2 minutes. The chemistry of the new anesthetic is such that the effective time should be normally distributed with the same standard deviation, but the mean effective time may be lower. If it is lower, the drug company will market the new anesthetic; otherwise, they will continue to produce the older one. A sample of size 36 results in a sample mean of 7.1. A hypothesis test will be done to help make the decision.
-Referring to Table 9-4, the null hypothesis will be rejected with a level of significance of 0.10.

Question

Quizplus · Accepted Answer

The null hypothesis (H0: μ = 7.4) is tested against the alternative hypothesis (H1: μ < 7.4). With a sample mean of 7.1, a sample size of 36, and a standard deviation of 1.2, the test statistic is calculated. At a significance level of 0.10, the critical value for a one-tailed test is approximately -1.28. The calculated test statistic is less than -1.28, leading to the rejection of the null hypothesis.

TABLE 9-4 A Drug Company Is Considering Marketing a New Local Anesthetic