uestion content area top Part 1 A study was done using a treatment group and a placebo group. The results are shown in the table. 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 0.10 significance level for both parts. Treatment Placebo μ μ1 μ2 n 26 36 x 2.34 2.67 s 0.53 0.82 Question content area bottom Part 1 a. Test the claim that the two samples are from populations with the same mean. 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 Your answer is correct. Part 2 The test statistic, t, is negative 1.92−1.92. (Round to two decimal places as needed.) Part 3 The P-value is 0.0590.059. (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 the two samples are from populations with the same mean. B. Reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean. C. Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean. Your answer is correct. D. Fail to reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean. Part 5 b. Construct a confidence interval suitable for testing the claim that the two samples are from populations with the same mean. ------<μ1−μ2< ------- enter your response here

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 content area top

Part 1

A study was done using a treatment group and a placebo group. The results are shown in the table. 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 0.10 significance level for both parts.			Treatment	Placebo
μ	μ1	μ2
n	26	36
x	2.34	2.67
s	0.53	0.82

Question content area bottom

Part 1

a. Test the claim that the two samples are from populations with the same mean.

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

Your answer is correct.

Part 2

The test statistic, t, is

negative 1.92−1.92.

(Round to two decimal places as needed.)

Part 3

The P-value is

0.0590.059.

(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 the two samples are from populations with the same mean.

Reject

the null hypothesis. There

is not

sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean.

Reject

the null hypothesis. There

sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean.

Your answer is correct.

Fail to reject

the null hypothesis. There

sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean.

Part 5

b. Construct a confidence interval suitable for testing the claim that the two samples are from populations with the same mean.

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

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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