Given in the table are the BMI statistics for random samples of men and women. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.05 significance level for both parts. a. Test the claim that males and females have the same mean body mass index (BMI). What are the null and alternative hypotheses? OA. H₂:₁₂ H₁: P₁ P₂ OC. H₂H₁ H₂ H₂: P₁ P₂ The test statistic, t, is (Round to two decimal places as needed.) The P-value is (Round to three decimal places as needed.) State the conclusion for the test. OB. H₂₁ 2₂ H₁: P₁ P₂ ▼ OD. H₂H₁ H₂ H₂: P₁ P₂ O A. Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI. OB. Fail to reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI. O C. Reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI. O D. Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI. b. Construct a confidence interval suitable for testing the claim that males and females have the same mean BMI.
Given in the table are the BMI statistics for random samples of men and women. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.05 significance level for both parts. a. Test the claim that males and females have the same mean body mass index (BMI). What are the null and alternative hypotheses? OA. H₂:₁₂ H₁: P₁ P₂ OC. H₂H₁ H₂ H₂: P₁ P₂ The test statistic, t, is (Round to two decimal places as needed.) The P-value is (Round to three decimal places as needed.) State the conclusion for the test. OB. H₂₁ 2₂ H₁: P₁ P₂ ▼ OD. H₂H₁ H₂ H₂: P₁ P₂ O A. Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI. OB. Fail to reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI. O C. Reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI. O D. Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI. b. Construct a confidence interval suitable for testing the claim that males and females have the same mean BMI.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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Transcribed Image Text:Given in the table are the BMI statistics for random samples of men and women. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population
standard deviations are equal. Complete parts (a) and (b) below. Use a 0.05 significance level for both parts.
a. Test the claim that males and females have the same mean body mass index (BMI).
What are the null and alternative hypotheses?
OA. Ho: H₁ H₂
H₁:₁ <H₂
OC. Ho: H₁
H₁: H₁
The test statistic, t, is
The P-value is
H₂
H₂
(Round to two decimal places as needed.)
15
(Round to three decimal places as needed.)
State the conclusion for the test.
C
OB. Ho: ₁2₂
H₁ H₁ H₂
OD. Ho: H=H2
H₁: H₁ H₂
O A. Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI.
O B. Fail to reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI.
Reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI.
O C.
O D. Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI.
b. Construct a confidence interval suitable for testing the claim that males and females have the same mean BMI.
<H4-4₂ <
(Round to three decimal places as needed.)
Does the confidence interval support the conclusion of the test?
▼because the confidence interval contains
Male BMI Female BMI
μ
H₁
H₂
n
43
43
X 27.8501 24.0589
s 8.739478
4.939052
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