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 0.01 significance level for both parts. Male BMI Female BMI μ μ1 μ2 n 41 41 x 28.0392 26.0443 s 8.698701 5.957816 Question content area bottom Part 1 a. Test the claim that males and females have the same mean body mass index (BMI). What are the null and alternative hypotheses? A. H0: μ1=μ2 H1: μ1≠μ2 B. H0: μ1≥μ2 H1: μ1<μ2 C. H0: μ1≠μ2 H1: μ1<μ2 D. H0: μ1=μ2 H1: μ1>μ2 Part 2 The test statistic, t, is enter your response here. (Round to two decimal places as needed.) Part 3 The P-value is enter your response here. (Round to three decimal places as needed.) Part 4 State the conclusion for the test. 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. B. Reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI. C. Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI. D. 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. Part 5 b. Construct a confidence interval suitable for testing the claim that males and females have the same mean BMI. enter your response here<μ1−μ2

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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 0.01 significance level for both parts.			Male BMI	Female BMI
μ	μ1	μ2
n	41	41
x	28.0392	26.0443
s	8.698701	5.957816

Question content area bottom

Part 1

a. Test the claim that males and females have the same mean body mass index (BMI).

What are the null and alternative hypotheses?

H0:

μ1=μ2

H1:

μ1≠μ2

H0:

μ1≥μ2

H1:

μ1<μ2

H0:

μ1≠μ2

H1:

μ1<μ2

H0:

μ1=μ2

H1:

μ1>μ2

Part 2

The test statistic, t, is

enter your response here.

(Round to two decimal places as needed.)

Part 3

The P-value is

enter your response here.

(Round to three decimal places as needed.)

Part 4

State the conclusion for the test.

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.

Reject

the null hypothesis. There

is not

sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI.

Reject

the null hypothesis. There

sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI.

Fail to reject

the null hypothesis. There

sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI.

Part 5

b. Construct a confidence interval suitable for testing the claim that males and females have the same mean BMI.

enter your response here<μ1−μ2<enter your response here

(Round to three decimal places as needed.)

Part 6

Does the confidence interval support the conclusion of the test?

▼

No,

Yes,

because the confidence interval contains

▼

only negative values.

zero.

only positive values.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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