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Chapter 8: Q. 41 (page 522)

A Pew Research Center report on gamers and gaming estimated that 49%of U.S. adults play video games on a computer, TV, game console, or portable device such as a cell phone. This estimate was based on a random sample of 2001 U.S. adults. Construct and interpret a 95% confidence interval for the proportion of all U.S. adults who play video games.

Short Answer

Expert verified

The confidence interval is(0.468,0.512).

Step by step solution

01

Step 1. Given information

Sample proportion (p^)=49%=0.49

Sample size (n)=2001

02

Step 2. Formula used

The formula to compute the confidence interval for population proportion is:

CI=p^±zα/2×p^(1-p^)n

03

Step 3. Calculation

From the standard normal table, the z-score at 95%confidence level is 1.96.

The 95%confidence interval for the proportion of adult that play video games can be calculated as:

role="math" localid="1663923507517" CI=p^±zα/2×p^(1-p^)n=0.49±1.96×0.49(1-0.49)2001=(0.468,0.512)

Thus, the confidence interval is (0.468,0.512)

There is 95% probability that the proportion of adult that play video games lies between 0.468 and0.512.

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