17. Determine the appropriate approach to conduct a hypothesis test for this claim: The systolic blood pressure of men who run at least five miles each week varies less than does the systolic blood pressure of all men. Sample data: n = 100 randomly selected men who run at least five miles each week, sample mean = 108.4, and s = 20.3
16. Determine the appropriate approach to conduct a hypothesis test for this claim: Fewer than 5% of patients experience negative treatment effects. Sample data: Of 500 randomly selected patients, 2.2% experience negative treatment effects (5 point).
A) Use the normal distribution.
B) Use the Student t distribution.
C) Use the chi-square distribution.
D) Use nonparametric or bootstrapping methods.
17. Determine the appropriate approach to conduct a hypothesis test for this claim: The systolic blood pressure of men who run at least five miles each week varies less than does the systolic blood pressure of all men. Sample data: n = 100 randomly selected men who run at least five miles each week, sample mean = 108.4, and s = 20.3 (5 point).
A) Use the normal distribution.
B) Use the Student t distribution.
C) Use the chi-square distribution.
D) Use nonparametric or bootstrapping methods.
18. Determine the appropriate approach to conduct a hypothesis test for this claim: The mean sodium content of a 30 g serving of snack crackers is 2,200 mg. Sample data: n = 130 snack crackers, sample mean = 3,100 mg, and s = 570. The sample data appear to come from a normally distributed population (5 point).
A) Use the normal distribution.
B) Use the Student t distribution.
C) Use the chi-square distribution.
D) Use nonparametric or bootstrapping methods.
To conduct a hypothesis test for this claim, we need to determine if the systolic blood pressure of men who run at least five miles each week varies less than the systolic blood pressure of all men.
Here is the step-by-step approach for conducting the hypothesis test:
Step 1: State the hypotheses:
- Null hypothesis (H0): The variation in the systolic blood pressure of men who run at least five miles each week is not significantly different than the variation in systolic blood pressure of all men.
- Alternative hypothesis (Ha): The variation in the systolic blood pressure of men who run at least five miles each week is significantly less than the variation in systolic blood pressure of all men.
Step 2: Select the significance level (α):
- The significance level is a predetermined threshold used to determine if there is enough evidence to reject the null hypothesis. Let's assume α = 0.05, which is a commonly used value.
Step 3: Select the test statistic:
- In this case, we will use the F-test statistic to compare the variability between the two groups.
Step 4: Formulate the decision rule:
- In order to reject the null hypothesis, the calculated test statistic value must be less than the critical value obtained from the F-distribution table at the given significance level.
Step 5: Calculate the F-test statistic:
- The F-test statistic is calculated using the formula: F = (s1^2 / s2^2), where s1 is the variance of the sample (men who run at least five miles each week) and s2 is the variance of the population (all men).
Step 6: Find the critical value:
- Look up the critical value from the F-distribution table using the degrees of freedom for numerator (n-1) and denominator (N-1), where n is the sample size and N is the total population size.
Step 7: Make a decision:
- If the calculated test statistic is less than the critical value, reject the null hypothesis and conclude that the variability in systolic blood pressure of men who run at least five miles each week is significantly less than the variability in systolic blood pressure of all men.
- If the calculated test statistic is greater than or equal to the critical value, fail to reject the null hypothesis and do not conclude that there is a significant difference in variability.
Note: The calculations for the F-test statistic and critical value require additional information such as the degrees of freedom, which are not provided in the sample data given. Please consult a statistics textbook or use statistical software to obtain accurate results.