Five patients entering a hospital with a high fever were selected at random and were administered a new drug which is designed to reduce fever. The body temperature (°F) of each patient was measured before the new drug was administered and 2 hours after the administration. The data are given in the following table.Patient 1 2 3 4 5Before 103 99 102 101 103After 100 99 98 100 100 Assume the differences between before and after measurements follow a normal distribution. Let μ1 denote the mean body temperature of high fever patients before taking the new drug and let μ2 denote the mean body temperature of high fever patients after taking the new drug. Also let μD = μ1 - μ2. Suppose we want to test whether the new drug is effective in reducing fever at the 5% level of significance. What is the test statistic for this test?Question 3Select one:a.Z=X¯−μσ/n√𝑍=𝑋¯−𝜇𝜎/𝑛 b.T=X¯1−X¯2−(μ1−μ2)S21n1+S22n2‾‾‾‾‾‾‾‾√𝑇=𝑋¯1−𝑋¯2−(𝜇1−𝜇2)𝑆12𝑛1+𝑆22𝑛2 c.T=X¯1−X¯2−(μ1−μ2)S2pn1+S2pn2‾‾‾‾‾‾‾‾√𝑇=𝑋¯1−𝑋¯2−(𝜇1−𝜇2)𝑆𝑝2𝑛1+𝑆𝑝2𝑛2 d.T=D¯−μDSD/n√
Question
Five patients entering a hospital with a high fever were selected at random and were administered a new drug which is designed to reduce fever. The body temperature (°F) of each patient was measured before the new drug was administered and 2 hours after the administration. The data are given in the following table.Patient 1 2 3 4 5Before 103 99 102 101 103After 100 99 98 100 100 Assume the differences between before and after measurements follow a normal distribution. Let μ1 denote the mean body temperature of high fever patients before taking the new drug and let μ2 denote the mean body temperature of high fever patients after taking the new drug. Also let μD = μ1 - μ2. Suppose we want to test whether the new drug is effective in reducing fever at the 5% level of significance. What is the test statistic for this test?Question 3Select one:a.Z=X¯−μσ/n√𝑍=𝑋¯−𝜇𝜎/𝑛 b.T=X¯1−X¯2−(μ1−μ2)S21n1+S22n2‾‾‾‾‾‾‾‾√𝑇=𝑋¯1−𝑋¯2−(𝜇1−𝜇2)𝑆12𝑛1+𝑆22𝑛2 c.T=X¯1−X¯2−(μ1−μ2)S2pn1+S2pn2‾‾‾‾‾‾‾‾√𝑇=𝑋¯1−𝑋¯2−(𝜇1−𝜇2)𝑆𝑝2𝑛1+𝑆𝑝2𝑛2 d.T=D¯−μDSD/n√
Solution
The correct answer is d. T=D¯−μDSD/n√
This is a paired t-test problem where we are comparing the means of two dependent groups to assess the statistical significance of the difference between the means. The test statistic for a paired t-test is calculated as the difference between the sample mean (D̄) and the hypothesized mean difference (μD) divided by the standard deviation of the differences (SD) divided by the square root of the number of observations (n).
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