Question

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

306

people over the age of​ 55,

67

dream in black and​ white, and among

287

people under the age of​ 25,

14

dream in black and white. Use a

.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.

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.

Upper H 0H0​:

p 1p1equals=p 2p2

Upper H 1H1​:

p 1p1not equals≠p 2p2

B.

Upper H 0H0​:

p 1p1greater than or equals≥p 2p2

Upper H 1H1​:

p 1p1not equals≠p 2p2

C.

Upper H 0H0​:

p 1p1equals=p 2p2

Upper H 1H1​:

p 1p1greater than>p 2p2

D.

Upper H 0H0​:

p 1p1less than or equals≤p 2p2

Upper H 1H1​:

p 1p1not equals≠p 2p2

E.

Upper H 0H0​:

p 1p1not equals≠p 2p2

Upper H 1H1​:

p 1p1equals=p 2p2

F.

Upper H 0H0​:

p 1p1equals=p 2p2

Upper H 1H1​:

p 1p1less than<p 2p2

Identify the test statistic.

zequals=nothing

​(Round to two decimal places as​ needed.)

Identify the​ P-value.

​P-valueequals=nothing

​(Round to three decimal places as​ needed.)

What is the conclusion based on the hypothesis​ test?

The​ P-value is

▼

less than

greater than

the significance level of

alphaαequals=0.050.05​,

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.

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Answer 1

A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 306 people over the age of​ 55, 67 dream in black and​ white, and among 287 people under the age of​ 25, 14 dream in black and white. Use a .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.

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?

C.

Upper H0​:p1=p2

Upper H1​:p 1>p2

Identify the test statistic.

Z =6.03

​(Round to two decimal places as​ needed.)

Identify the​ P-value.

​P-value =0.000

​(Round to three decimal places as​ needed.)

What is the conclusion based on the hypothesis​ test?

The​ P-value is less than the significance level of α=0.05​,

So reject the null hypothesis. There is sufficient 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.

Z Test for Differences in Two Proportions
Data
Hypothesized Difference	0
Level of Significance	0.05
Group 1
Number of Items of Interest	67
Sample Size	306
Group 2
Number of Items of Interest	14
Sample Size	287
Intermediate Calculations
Group 1 Proportion	0.218954248
Group 2 Proportion	0.048780488
Difference in Two Proportions	0.170173761
Average Proportion	0.1366
Z Test Statistic	6.0304
Upper-Tail Test
Upper Critical Value	1.645
p-Value	0.0000
Reject the null hypothesis