Question

An article reported that patients under care for HIV have CD4 tests every 3 months, on average. A concern at Boston Medical Center is that there is a longer lag between tests. To test the concern, a random sample of 15 patients currently under care for HIV is selected and the time between their two most recent CD4 tests is recorded. The mean time between tests is 3.9 months with a standard deviation of 0.4 month. Run the appropriate test at a 5% level of significance.

Answer 1

A hypothesis test can be conducted using the given sample mean and standard deviation to determine if there is a longer lag between CD4 tests at Boston Medical Center. The test statistic is compared to the critical value, and based on the result, the null hypothesis is rejected or not.

Step-by-step explanation:

To test the concern at Boston Medical Center, a hypothesis test can be conducted with a significance level of 5%. The null hypothesis (H0) is that there is no difference in the mean time between tests, while the alternative hypothesis (Ha) is that the mean time between tests is longer than 3.9 months.

Based on the given sample mean of 3.9 months and the standard deviation of 0.4 month, the test statistic can be calculated as Z = (sample mean - population mean) / (standard deviation / sqrt(sample size)). Using this formula, the test statistic is Z = (3.9 - 3) / (0.4 / sqrt(15)) = 3.5.

With a 5% significance level, the critical Z value is approximately 1.96. Since the test statistic (Z = 3.5) is greater than the critical Z value, we reject the null hypothesis and conclude that there is sufficient evidence to support the concern that there is a longer lag between CD4 tests at Boston Medical Center.