A- State the null and alternative hypothesisB- Identify the P Value and state the researchers conclusion if the level of significance =0.01C-What is the 95% confidence interval for the mean difference in pulse rates of men versus women A physical therapist wanted to know whether the mean step pulse of men was less than the mean step pulse of women.She randomly selected 53 men and 78 women to participate in the study. Each subject was required to step up and downa 6-inch platform. The pulse of each subject was then recorded. The following results were obtained.Two sample T for Men vs WomenMeanStDevSE MeanMenWomen99% CI for mu Men - mu Women(-11.92, - 0.08)T-Test mu Men = mu Women (vs < )T= - 2.68 P = 0.0042 DF = 12753112.911.11.578118.914.51.6(a) State the null and alternative hypotheses. Which of the following is correct?A. Ho: H1 = H2; Ha: H1> H2B. Ho: H1 = H2; Hạ: H1

a) The mean step pulse of men was less than the mean step pulse of women. Null Hypothesis: H0:μ1=μ2 Alternative Hypothesis: H0:μ1<μ2 Correct option: B B) From the output, the P value is 0.0042. Decision Rule: If p-value ≤ α, then reject the null hypothesis. Conclusion: The level of significance is α=0.01 Here, the p-value is less than the level of significance. From the decision rule, reject the null hypothesis. Conclusion: The mean step pulse of men was less than the mean step pulse of women.C) 95% confidence interval for the mean difference in pulse rates of men versus women: MINITAB Procedure: Stat > Basic Statistics > 2-Sample t>Summarized data>Sample size as 53, Mean as 112.9, Standard deviation as 11.1>In second, enter Sample size as 78, Mean as 118.9, Standard deviation as 14.5> In Confidence level, enter 95>OK. MINITAB Output: Two-Sample T-Test and CI Sample N Mean StDev SE Mean1 53 112.9 11.1 1.52 78 118.9 14.5 1.6 Difference = μ (1) - μ (2)Estimate for difference: -6.0095% CI for difference: (-10.43, -1.57)T-Test of difference = 0 (vs ≠): T-Value = -2.68 P-Value = 0.008 DF = 127 From the output, the 95% confidence interval is, 95% CI for difference: (-10.43, -1.57)

Answered: - State the null and alternative…

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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Question

A- State the null and alternative hypothesis

B- Identify the P Value and state the researchers conclusion if the level of significance =0.01

C-What is the 95% confidence interval for the mean difference in pulse rates of men versus women

A physical therapist wanted to know whether the mean step pulse of men was less than the mean step pulse of women.
She randomly selected 53 men and 78 women to participate in the study. Each subject was required to step up and down
a 6-inch platform. The pulse of each subject was then recorded. The following results were obtained.
Two sample T for Men vs Women
Mean
StDev
SE Mean
Men
Women
99% CI for mu Men - mu Women
(-11.92, - 0.08)
T-Test mu Men = mu Women (vs < )
T= - 2.68 P = 0.0042 DF = 127
53
112.9
11.1
1.5
78
118.9
14.5
1.6
(a) State the null and alternative hypotheses. Which of the following is correct?
A. Ho: H1 = H2; Ha: H1> H2
B. Ho: H1 = H2; Hạ: H1 <H2
C. Ho: H1 = H2; Ha: H1 # H2
(b) Identify the P-value and state the researcher's conclusion if the level of significance was a = 0.01. What is the P-value?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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