Question
Asked Mar 26, 2020
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A survey of 1060 randomly selected US teens ages 13-17 found that 605 of them say they have made a new friend online.

(a) Find and interpret a 90% confidence interval for the proportion, p, of all US teens who have made a new friend online.

(b) Give the best estimate for p and give the margin of error for the estimate.

(c) Use the interval to determine whether we can be 90% confident that more than half of US teens have made a new friend online.

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Expert Answer

Step 1

Given:

Statistics homework question answer, step 1, image 1

Step 2

(a)

From the standard normal table, the z-score at 90% confidence level is 1.645.

The 90% confidence interval for the proportion of all US teens that have made a new friend online can be constructed as:

Statistics homework question answer, step 2, image 1

There is 90% probability that the proportion of US teens that have made a new friend online lies between 0.545 and 0.596.

Step 3

(b)

The point estimate is:

Statistics homework question answer, step 3, image 1

The margin of error can be calculated as:

Statistics homework question answer, step 3, image 2

...

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