Question

A pharmaceutical company has developed a new antiviral drug to relieve Covid symptoms. The company advertises that their new antiviral drug in tablet form will significantly reduce the mean number of days an individual suffers from Covid symptoms. To test their claim, a medical researcher randomly selects 40 individuals who tested positive for Covid on the same day. The 40 individuals are then randomly divided into two equal groups: a treatment group of 20 subjects and a control group of 20 subjects. The individuals in the treatment group are administered the new antiviral drug while the control group individuals are administered a placebo tablet (that is, a pill that has no effect on reducing Covid symptoms). The researcher records the number of days it takes for each of the 40 individuals to recover from Covid symptoms. The researcher then computes the sample mean and standard deviation number of days for both the treatment and control groups. The sample test results for each group are summarized in the following table. Summary Test Results for the Treatment and Control Groups Treatment Group Control Group n1 = 20 n2 = 20 sample mean 1 = 6.5 sample mean 2 = 9.3 s1 = 2.5 s2 = 3.9 The researcher decides to perform the 5-step hypothesis testing procedure to determine if the new antiviral drug will significantly reduce the mean number of days an individual suffers from Covid symptoms at α= 1%. Assume equal population standard deviations. Let population #1 represent the treatment group and population #2 represent control group. Then, the Distribution of the Test Statistic is: Question 30 options: a) Normal Distribution b) t Distribution c) Skewed Distributi

Answer 1

The question asks which distribution should be used for the test statistic in a hypothesis test comparing a treatment and control group. As both sample sizes are large (greater than 30), and equal population standard deviations are assumed, the Normal Distribution is appropriate for this test.

Step-by-step explanation:

The student's question involves determining whether the new antiviral drug developed by a pharmaceutical company has significantly reduced the mean number of days individuals suffer from Covid symptoms. To test this claim, a hypothesis test was conducted with a treatment group given the antiviral drug and a control group given a placebo. Since we have sample sizes greater than 30 for both groups, and we are assuming equal population standard deviations, the Central Limit Theorem applies, which allows us to use a Normal Distribution for the test statistic.

For hypothesis testing involving mean differences with known population standard deviations or large sample sizes (n>30), the normal distribution is typically applied. Although the populations' standard deviations are not given, assuming equal population standard deviations and large sample sizes justifies the use of the Normal Distribution.

In a normal distribution, data are symmetrically distributed with no skew. Most values cluster around a central region, with values tapering off as they go further away from the center. The measures of central tendency (mean, mode, and median) are exactly the same in a normal distribution.