### Assignment Instructions/ Description

First drop down options: dependent, independent

Second drop down options: all these quantities are greater than 5, at least one quantity is less than 5

Third drop down options: can, cannot Image transcription textA random sample of 388 married couples found that 290 had two or more personality preferences in common. In another random sample of 550 married couples, it was found that only 26 had no preferences in common. Let p, be the population proportion of all

married couples who have two or more personality preferences in common. Let p, be the population proportion of all married couples who have no personality preferences in common.

L USE SALT

(a)

Can a normal distribution be used to approximate the p, - p, distribution? Explain.

The data constitute two -Select- samples. Calculating the following quantities np, =

, nd 1 =

, np2 =

, and np2 =

, we see that -Select-

distribution -Select- be used to approximate the p, - p, distribution.

. So, the normal

(b) Find a 99% confidence interval for P, - p2. (Enter your answer in the form: lower limit to upper limit. Include the word "to." Round your numerical values to three decimal places.)

(c) Explain the meaning of the confidence interval in part (b) in the context of this problem.

O There is a 0.99 probability that the previously found interval contains the difference between the population proportion of married couples with two or more personality preferences in common and the population proportion of married couples who have

no personality preferences in common.

O With 99% confidence we can say that the previously found interval contains the difference between the sample proportion of married couples with two or more personality preferences in common in the first sample and the sample proportion of

married couples who have no personality preferences in common in the second sample.

There is a 0.99 probability that the previously found interval contains the difference between the sample proportion of married couples with two or more personality preferences in common in the first sample and the sample proportion of married

couples who have no personality preferences in common in the second sample.

O With 99% confidence we can say that the previously found interval contains the difference between the population proportion of married couples with two or more personality preferences in common and the population proportion of married couples

who have no personality preferences in common.

Does the confidence interval contain all positive, all negative, or both positive and negative numbers?

The interval contains only positive numbers.

O The interval contains only negative numbers.

O The interval contains both positive and negative numbers.

What does this tell you (at the 99% confidence level) about the proportion of married couples with two or more personality preferences in common compared with the proportion of married couples sharing no personality preferences in common?

O At the 99% level of confidence, it appears that the proportion of married couples with two or more personality preferences in common is greater than the proportion of married couples who have no personality preferences in common.

At the 99% level of confidence, it appears that the proportion of married couples with two or more personality preferences in common is less than the proportion of married couples who have no personality preferences in common.

At the 99% level of confidence, we cannot conclude that there is a difference in the proportion of married couples with two or more personality preferences in common and the proportion of married couples who have no personality preferences in

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