An explanation for the results is that those over the age of 55 grew up exposed

Question

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?

A.

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.

B.

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

C.

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.

D.

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

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, 77 dream in black and white, and among 299 people under the age of 25, 20 dream in black and white. Use a 0.01 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 (Round to two decimal places as needed.) Identify the P-value. P-value = Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? The P-value is | the significance level of = 0.01, so the null hypothesis. There is evidence to support the claim that the proportion of people over 55 who dream in black and white is areater than the oroportion for those under 25. Click to select your answer(s). 2

Explanation / Answer

The statistical software output for this problem is:

Two sample proportion summary hypothesis test:
p1 : proportion of successes for population 1
p2 : proportion of successes for population 2
p1 - p2 : Difference in proportions
H0 : p1 - p2 = 0
HA : p1 - p2 > 0

Hypothesis test results:

98% confidence interval results:

Hence,

a) z = 6.19

P - value = 0.000

Less than; Reject; Sufficient

b) 98% confidence interval:

0.118 < (p1 - p2) < 0.252

Does not include; different; Only Positive; Greater

c) 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.

Option A is correct.

Difference Count1 Total1 Count2 Total2 Sample Diff. Std. Err. Z-Stat P-value p1 - p2 77 306 20 299 0.18474435 0.029836215 6.1919501 <0.0001

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