Suppose the time that it takes for a certain infection to be cured with a drug is Normally distributed, with mean (in days) μ and standard deviation σ= 1 day. The drug manufacturer advertises that its medication works in 5 days, on average, but measurements on a random sample of 400 patients gave a mean infection time of x̄= 5.2 days. Is this evidence that the mean time to be cured is actually more than advertised? To answer this, test the following hypotheses at significance level α= 0.01:
H₀: μ= 5 versus H_a: μ> 5
What should you conclude?

Question

Quizplus · Accepted Answer

Given the sample size (n=400) and the sample mean (x̄=5.2 days), with a standard deviation (σ=1 day) and a significance level (α=0.01), we can conduct a hypothesis test to determine if the mean time to be cured is actually more than advertised (μ>5). The evidence (x̄=5.2) suggests that the mean time is greater than the advertised 5 days. Since the sample size is large, we can use the Z-test to compare the sample mean to the population mean. The calculation of the Z-score and comparison to the critical value at α=0.01 would likely show that the difference is statistically significant, leading to the rejection of the null hypothesis (μ=5) in favor of the alternative hypothesis (μ>5).

Suppose the Time That It Takes for a Certain Infection