Answered: A study was done on proctored and…

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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A study was done on proctored and nonproctored tests. 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.		Proctored	Nonproctored
	μ	μ1	μ2
	n	35	34
	x overbar x	74.24	82.76
	s	11.58	18.62

a. Use a

0.01

0.01 significance level to test the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests.

What are the null and alternative hypotheses?

Upper H 0

H0:

mu 1

μ1

equals

mu 2

μ2

Upper H 1

H1:

mu 1

μ1

not equals

≠

mu 2

μ2

Upper H 0

H0:

mu 1

μ1

equals

mu 2

μ2

Upper H 1

H1:

mu 1

μ1

greater than

mu 2

μ2

Upper H 0

H0:

mu 1

μ1

equals

mu 2

μ2

Upper H 1

H1:

mu 1

μ1

less than

mu 2

μ2

Upper H 0

H0:

mu 1

μ1

not equals

≠

mu 2

μ2

Upper H 1

H1:

mu 1

μ1

less than

mu 2

The test statistic, t, is ___

The P-value is ____

State the conclusion for the test.

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

C.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.

D.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. 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?

_____ because the confidence interval contains____

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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