Estimating a Population Proportion

Question 1

According to a recent random survey of 3,728 US adults, 1,939 report using their cell phones to play online games. Construct and interpret a 95% confidence interval for the proportion of US adults who use their cell phones to play online games. State: confidence interval for the true proportion of US adults who use their cell phones to play online games. Plan: ; Random: Random survey; 10%: 3,728 is less than 10% of all US adults; Large Counts: 1,939 successes and 1,789 failures ≥ 10. Do: Conclude: We are 95% confident that the interval from includes the true proportion of all US adults to play online games.

Revolt · Accepted Answer

95%; State: confidence interval for the true proportion of US adults who use their cell phones to play online games.: 95%; Plan: ; Random: Random survey; 10%: 3,728 is less than 10% of all US adults; Large Counts: 1,939 successes and 1,789 failures ≥ 10.: one-sample z-interval for p; Do:: (0.504, 0.536); Conclude: We are 95% confident that the interval from includes the true proportion of all US adults to play online games.: (0.504, 0.536); Conclude: We are 95% confident that the interval from includes the true proportion of all US adults to play online games.: who use their cell phones

Question 2

✔ one-sample z-interval for ptwo-sample z-interval for pone-sample t-interval for mutwo-sample t-interval for mu

Revolt · Accepted Answer

one-sample z-interval for p

Question 3

(0.464, 0.496)(0.499, 0.541)✔ (0.504, 0.536)(0.519, 0.520)

Revolt · Accepted Answer

(0.504, 0.536)

Question 4

(0.464, 0.496)(0.499, 0.541)✔ (0.504, 0.536)(0.519, 0.520)

Revolt · Accepted Answer

(0.504, 0.536)

Question 5

✔ who use their cell phoneswho used their cell phoneswho did use their cell phoneswho would have used their cell phones

Revolt · Accepted Answer

who use their cell phones

Question 6

Christian wants to estimate the proportion of seniors who plan to attend her school’s prom. She interviews an SRS of 65 of the 695 seniors in her school and finds that 42 plan to attend the prom. Construct and interpret a 90% confidence interval for the proportion of seniors who plan to attend the prom.

Revolt · Accepted Answer

✔ 90%; State: confidence interval for the true proportion of seniors who plan to attend the prom.: 90%; Plan: ; Random: SRS; 10%: 65 is less than 10% of all seniors; Large Counts: 42 successes and 23 failures ≥ 10.: one-sample z-interval for p; Do:: (0.549, 0.744); Conclude: We are 90% confident that the interval from includes the true proportion of all seniors .: (0.549, 0.744); Conclude: We are 90% confident that the interval from includes the true proportion of all seniors .: who plan to attend prom

Question 7

A nationwide random survey of 1,500 teens aged 13–17 found that approximately 65% have their own desktop or laptop computer. Construct and interpret a 99% confidence interval for the true proportion of teens who have their own desktop or laptop computer.

Revolt · Accepted Answer

✔ 99%; State: confidence interval for the true proportion of teens who have their own desktop or laptop computer.: 99%; Plan: ; Random: SRS; 10%: 1,500 is less than 10% of all teens; Large Counts: 975 successes and 525 failures ≥ 10.: one-sample z-interval for p; Do:: (0.618, 0.682); Conclude: We are 99% confident that the interval from includes the true proportion of all teens .: (0.618, 0.682); Conclude: We are 99% confident that the interval from includes the true proportion of all teens .: who have a computer

Question 8

An inspector at a popcorn factory selects a random sample of 75 bags of popcorn from the hundreds produced each hour and finds that 12 contain at least 10% unpopped kernels. Construct and interpret a 95% confidence interval for the true proportion of popcorn bags that contain at least 10% unpopped kernels.

Revolt · Accepted Answer

✔ 95%; State: confidence interval for the true proportion of popcorn bags that contain at least 10% unpopped kernels.: 95%; Plan: ; Random: SRS; 10%: is less than 10% of all bags of popcorn produced; Large Counts: 12 successes and 63 failures ≥ 10.: one-sample z-interval for p; Do:: (0.077, 0.243); Conclude: We are 99% confident that the interval from includes the true proportion of all bags of popcorn at least 10% unpopped kernels.: (0.077, 0.243); Conclude: We are 99% confident that the interval from includes the true proportion of all bags of popcorn at least 10% unpopped kernels.: that contain

Question 9

Is it reasonable to conclude that more than half of US adults use their cell phones to play online games?

Revolt · Accepted Answer

Yes, because the interval of US adults who use their cell phones to play online games is entirely above 0.5.

Question 10

Is it reasonable to conclude that more than two-thirds of the seniors at Christian’s school plan to attend the prom?

Revolt · Accepted Answer

No, because the interval of seniors who plan to attend prom is not is entirely above 0.67.

Estimating a Population Proportion Answers

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