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:
-
Null Hypothesis (): The drug does not change the body's temperature. Mathematically, the mean difference in temperature () is equal to zero:
-
**Alternative
Ask a new question for Free
By Image
Drop file here or Click Here to upload
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
Related Recommendation
Paired t-test to Evaluate the Effect of a Drug on Body Temperature
Paired Sample t-Test: Drug Effect on Body Temperature
Analyzing Foot Temperatures in Diabetic Patients Using Statistical Methods
Hypothesis Testing of Mean Body Temperature with T-Test
Hypothesis Testing: t-Test for Blood Pressure Changes in 10 Patients