Answered: A study was conducted to determine the…

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 conducted to determine the proportion of people who dream in black and white instead of color. Among

305305

people over the age of 55,

6666

dream in black and white, and among

306306

people under the age of 25,

1717

dream in black and white. Use a

0.010.01

significance level to test the claim that the proportion of people over 55 who dream in black and white is greater than the proportion for those under 25. Complete parts (a) through (c) below.

a. Test the claim using a hypothesis test.

Consider the first sample to be the sample of people over the age of 55 and the second sample to be the sample of people under the age of 25. What are the null and alternative hypotheses for the hypothesis test?

Upper H 0H0:

p 1p1not equals≠p 2p2

Upper H 1H1:

p 1p1equals=p 2p2

Upper H 0H0:

p 1p1less than or equals≤p 2p2

Upper H 1H1:

p 1p1not equals≠p 2p2

Upper H 0H0:

p 1p1greater than or equals≥p 2p2

Upper H 1H1:

p 1p1not equals≠p 2p2

Upper H 0H0:

p 1p1equals=p 2p2

Upper H 1H1:

p 1p1greater than>p 2p2

Upper H 0H0:

p 1p1equals=p 2p2

Upper H 1H1:

p 1p1not equals≠p 2p2

Upper H 0H0:

p 1p1equals=p 2p2

Upper H 1H1:

p 1p1less than<p 2p2

Identify the test statistic.

zequals=

(Round to two decimal places as needed.)

Identify the P-value.

P-valueequals=

(Round to three decimal places as needed.)

What is the conclusion based on the hypothesis test?

The P-value is

the significance level of

alphaαequals=0.010.01,

......

the null hypothesis. The

re is

evidence to support the claim that the proportion of people over 55 who dream in black and white is greater than the proportion for those under 25.

b. Test the claim by constructing an appropriate confidence interval.

The

9898%

confidence interval is

nothingless than<left parenthesis p 1 minus p 2 right parenthesisp1−p2less than<nothing.

(Round to three decimal places as needed.)

What is the conclusion based on the confidence interval?

Because the confidence interval limits

▼

0, it appears that the two proportions are

▼

equal.

not equal.

Because the confidence interval limits include

▼

values, it appears that the proportion of people over 55 who dream in black and white is

▼

lesser than

greater than

not significantly different from

the proportion for those under 25.

c. An explanation for the results is that those over the age of 55 grew up exposed to media that was displayed in black and white. Can these results be used to verify that explanation?

Yes. The results can be used to verify the given explanation because the difference in proportions is practically significant.

Yes. The results can be used to verify the given explanation because the difference in proportions is statistically significant.

No. The results speak to a possible difference between the proportions of people over 55 and under 25 who dream in black and white, but the results are not statistically significant enough to verify the cause of such a difference.

No. The results speak to a possible difference between the proportions of people over 55 and under 25 who dream in black and white, but the results cannot be used to verify the cause of such a difference.

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