A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 310 people over the age of 55, 77 dream in black and white, and among 298 people under the age of 25, 12 dream in black and white. Use a 0.05 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. Question content area bottom Part 1 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? A. H0: p1=p2 H1: p1p2 E. H0: p1≥p2 H1: p1≠p2 F. H0: p1=p2 H1: p1≠p2 Part 2 Identify the test statistic. z=enter your response here (Round to two decimal places as needed.) Part 3 Identify the P-value. P-value=enter your response here (Round to three decimal places as needed.) Part 4 What is the conclusion based on the hypothesis test? The P-value is ▼ greater than less than the significance level of α=0.05, so ▼ fail to reject reject the null hypothesis. There is ▼ sufficient insufficient 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. Part 5 b. Test the claim by constructing an appropriate confidence interval. The 90% confidence interval is enter your response here

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section: Chapter Questions

Problem 8CR

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Question content area bottom

Part 1

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?

H0:

p1=p2

H1:

p1<p2

H0:

p1≤p2

H1:

p1≠p2

H0:

p1≠p2

H1:

p1=p2

H0:

p1=p2

H1:

p1>p2

H0:

p1≥p2

H1:

p1≠p2

H0:

p1=p2

H1:

p1≠p2

Part 2

Identify the test statistic.

z=enter your response here

(Round to two decimal places as needed.)

Part 3

Identify the P-value.

P-value=enter your response here

(Round to three decimal places as needed.)

Part 4

What is the conclusion based on the hypothesis test?

The P-value is

▼

greater than

less than

the significance level of

α=0.05,

▼

fail to reject

reject

the null hypothesis. There is

▼

sufficient

insufficient

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.

Part 5

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

The

90%

confidence interval is

enter your response here<p1−p2<enter your response here.

(Round to three decimal places as needed.)

Part 6

What is the conclusion based on the confidence interval?

Because the confidence interval limits

▼

include

do not include

0, it appears that the two proportions are

▼

equal.

not equal.

Because the confidence interval limits include

▼

only positive

positive and negative

only negative

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

▼

greater than

lesser than

not significantly different from

the proportion for those under 25.

Part 7

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?

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.

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.

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

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

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