Estimating a Population Proportion assignment
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.
90% one sample z-interval for p (0.549, 0.744) (0.549, 0.744) who plan to attend prom
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.
95% one sample z-interval for p (0.077, 0.243) (0.077, 0.243) that contain
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.
95% one sample z-interval for p (0.504, 0.536) (0.504, 0.536) who use their cell phones
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.
99% one sample z-interval for p (0.618, 0.682) (0.618, 0.682) who have a computer
A small pilot study estimated that 34% of Americans do not like the taste of cilantro. How large would the random sample need to be to obtain a margin of error of at most 0.03 with 95%?
958
A nationwide random survey of 1,500 teens aged 13-17 found that approximately 65% have their own desktop or laptop computer. The 99% confidence interval for the true proportion of teens who have their own desktop or laptop computer is (0.618, 0.682). Based on the interval, is it reasonable to conclude that a majority of teens aged 13-17 have their own desktop or laptop computer?
Yes, because the interval of teens who have their own desktop or laptop computer is entirely above 0.5.
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 the 90% confidence interval for the proportion of seniors who plan to attend the prom is (0.549, 0.744). Is it reasonable to conclude that more than two-thirds of the seniors at Christian's school plan to attend the prom?
No, because the interval of seniors who plan to attend prom is not is entirely above 0.67.
According to a recent random survey of 3,728 US adults, 1,939 report using their cell phones to play online games. The 95% confidence interval for the proportion of US adults who use their cell phones to play online games is (0.504, 0.536). A journalist uses this information in an article and states that more than half of US adults use their cell phones to play online games. Is it reasonable to conclude that more than half of US adults use their cell phones to play online games?
Yes, because the interval of US adults who use their cell phones to play online games is entirely above 0.5.
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. The 95% confidence interval for the true proportion of popcorn bags that contain at least 10% unpopped kernels is (0.077, 0.243). If the inspector finds that the machine is underpopping the corn more than 6% of the time, then the machine needs to be recalibrated. Based on the interval, is it reasonable to conclude that the machine needs to be recalibrated?
Yes, because the interval of popcorn bags that contain at least 10% unpopped kernels is entirely above 0.06.