Question

1. A sample of 152 statistics students were surveyed concerning their future pet ownership. Of the 152 students in the sample, 82 responded that they plan on getting a dog after graduating.
   1. Construct a 95% confidence interval for the proportion of statistics students overall (i.e., the entirepopulation) that want to get a dog.
   2. Suppose we wanted to take another sample to estimate the percent of percentage of statistics studentsthat want to get a dog. Find the sample size we need to estimate the percent of percentage of statistics students that want to get a dog. Use the estimate from the sample for the sample proportion, a margin of error of 4% and a confidence level of 99%.

**by hand

Answer 1

a)

Sample proportion = 82 / 152 = 0.539

95% confidence interval for p is

- Z * sqrt( ( 1 - ) / n) < p < + Z * sqrt( ( 1 - ) / n)

0.539 - 1.96 * sqrt( 0.539 * 0.461 / 152) < p < 0.539 + 1.96 * sqrt( 0.539 * 0.461 / 152)

0.460 < p < 0.618

95% CI is ( 0.460 , 0.618)

b)

Sample size = Z²/2 * p( 1 - p) / E²

= 2.5758² * 0.539 * 0.461 / 0.04²

= 1030.37

Sample size = 1031 (Rounded up to nearest integer)