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. Male BMI Female BMI μ μ1 μ2 n 41 41 x 28.3981 26.4624 s 7.246507 5.820596 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 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. 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. 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. 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. 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) Construct a confidence interval suitable for testing the claim that males and females have the same mean BMI. <μ1−μ2<___ (Round to three decimal places as needed.) Does the confidence interval support the conclusion of the test? (yes OR No) because the confidence interval contains (zero. only positive values. only negative values.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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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 0.05 significance level for both parts.			Male BMI	Female BMI
μ	μ1	μ2
n	41	41
x	28.3981	26.4624
s	7.246507	5.820596

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

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.

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.

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 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.

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

______<μ1−μ2<_______

(Round to three decimal places as needed.)

Does the confidence interval support the conclusion of the test?

(yes OR No)

because the confidence interval contains

(zero.

only positive values.

only negative 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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