In a random sample of 250 employed people,

Question

1. In a random sample of 250 employed people, 61 said they bring work home with them at least occasionally. (a) Give a point estimate of the proportion of all employed people who bring work home with them at least occasionally. (b) Construct a 99% confidence interval for that proportion.
2. . In a random sample of 1250 household moves, 822 were moves to a location within the same country as the original residence. (a) Give a point estimate of the proportion of all households moves that are to a location within the same country as the original residence. (b) Construct a 95% confidence interval for that proportion.

Answer 1

1.

sample size n = 250

point estimate = sample proportion (phat) = 61/250 = 0.244

critical z for 99% confidence level = z-score for 0.995 probability = 2.58

99% confidence interval = phat +/- z-critical * sqrt( phat *(1-phat)/n) =

0.244 +/- 2.58 * sqrt(0.244 * (1-0.244)/250)

sample size n = 1250

2.

point estimate = sample proportion (phat) = 822/1250 = 0.6576

critical z for 95% confidence level = z-score for 0.975 probability = 1.96

95% confidence interval = phat +/- z-critical * sqrt( phat *(1-phat)/n) =

0.6576 +/- 1.96 * sqrt(0.6576 * (1-0.6576)/1250)