Math Problem Statement

A medical researcher believes that a drug changes the body's temperature. Seven test subjects are randomly selected and the body temperature of each is measured. The subjects are then given the drug, and after 30 minutes, the body temperature of each is measured again. The results are listed in the table below. Is there enough evidence to conclude that the drug changes the body's temperature?

Let d=(body temperature after taking drug)−(body temperature before taking drug) . Use a significance level of α=0.05 for the test. Assume that the body temperatures are normally distributed for the population of people both before and after taking the drug.
Subject Temperature (before) Temperature (after) 1 99.7 99.1 2 100.6 99.8 3 98.8 99.7 4 99.2 99 5 99.4 98.7 6 99.1 98.3 7 99 98.5 Step 1 of 5 : State the null and alternative hypotheses for the test.

Solution

Step 1: State the Null and Alternative Hypotheses

To test whether the drug changes the body temperature, we formulate the hypotheses as follows:

  1. Null Hypothesis (H0H_0): The drug does not change the body's temperature. Mathematically, the mean difference in temperature (dd) is equal to zero: H0:μd=0H_0: \mu_d = 0

  2. **Alternative

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Math Problem Analysis

Mathematical Concepts

Hypothesis Testing
Paired Sample t-test
Statistics

Formulas

t = (mean difference - hypothesized difference) / (standard deviation of differences / sqrt(n))
Degrees of freedom (df) = n - 1

Theorems

Central Limit Theorem
Student's t-distribution

Suitable Grade Level

Undergraduate Statistics or Advanced High School