A) D. No, it is impossible to determine if the Nearly Normal Condition is satisfied. E. No, it is impossible to determine if the Independence Assumption is satisfied.
B. (−18.93,22.81) minutes.
C. B. H₀ : μ_d = 0; H₁ : μ_d ≠ 0.
Conclusion is d. The null hypothesis would not be rejected because the 99% confidence interval contains 0.
How do we find the confidence interval?
A. We don't have enough information to assess the normality of the distribution of differences. With N=23, it's borderline for the central limit theorem to apply. We also need a histogram or a normal probability plot before we can definitively say whether this condition is met.
B. 99% Confidence Interval for the Mean Difference
Xbar =1.94 minutes
s = 35.512 minutes
n = 23
df = 22
a 99% confidence level and 22 degrees of freedom, the t-score is 2.819.
xbar ± t × s/ √n
ME = 2.819 × 35.512/√23 = 20.874
Lower Bound = 1.94 − 20.87 ≈ −18.93 minutes.
Upper Bound = 1.94 +20.87≈22.81 minutes.
The 99% confidence interval for the mean difference in finishing times between the women's wheelchair marathon winner and the men's marathon winner on foot is (−18.93,22.81) minutes.
C. . H₀ : μ_d = 0; H₁ : μ_d ≠ 0.
The conclusion that can be drawn is;
The null hypothesis would not be rejected because the 99% confidence interval contains 0. Option D
Full question
In a certain marathon, there has been a wheelchair division for the past 23 years. A researcher would like to know who is typically faster, the men's marathon winner on foot or the women's wheelchair marathon winner. Because the conditions differ from year to year, and speeds have improved over the years, it seems best to treat these as paired measurements. The summary statistics for the pairwise differences in finishing time (in minutes) are shown below. Complete parts a) through c) below. Summary of wheelchrF-runM N=23 Mean= 1.94 SD= 35.512
a) Are the appropriate assumptions and conditions satisfied? Select all that apply.
A. Yes, all the conditions are definitely satisfied.
B. No, the Nearly Normal Condition is definitely not satisfied.
C. No, the Paired Data Condition is not satisfied.
D. No, it is impossible to determine if the Nearly Normal Condition is satisfied.
E. No, it is impossible to determine if the Independence Assumption is satisfied.
F. No, the Independence Assumption is definitely not satisfied.
b) Assuming that these times are representative of such races and the differences appeared acceptable for inference, construct and interpret a 99% confidence interval for the mean difference in finishing times. The confidence interval is................ (Round to two decimal places as needed.)
c) Would a hypothesis test at a = 0.01 reject the null hypothesis of no difference? What conclusion would be drawn? What are the null and alternative hypotheses?
О А. H₀ : μ_d ≠ 0
H₁ : μ_d = 0
О B. H₀ : μ_d = 0
H₁ : μ_d ≠ 0
Ос. H₀ : μ_d = 0
H₁ : μ_d < 0
O D. H₀ : μ_d = 0
H₁ : μ_d > 0
What conclusion would be drawn?
A. The null hypothesis would be rejected because the 99% confidence interval contains 0.
B. The null hypothesis would be rejected because the 99% confidence interval does not contain 0.
C. The null hypothesis would not be rejected because the 99% confidence interval does not contain 0.
D. The null hypothesis would not be rejected because the 99% confidence interval contains 0.