Question

Assume a 2015 Gallup Poll asked a national random sample of 482 adult women to state their current weight. Assume the mean weight in the sample was ?¯=164. We will treat these data as an SRS from a normally distributed population with standard deviation ?=36 pounds. Give a 90% confidence interval for the mean weight of adult women based on these data. Enter the upper and lower values of your confidence interval into the spaces provided rounded to two decimal places. lower value = pounds upper value = pounds

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 164

Population standard deviation = = 36

Sample size = n = 482

Z_/2 = 1.645

Margin of error = E = Z_/2* ( /n)

= 1.645 * (36 / 482)

= 2.70

At 90% confidence interval estimate of the population mean is,

- E < < + E

164 - 2.70 < < 160 + 2.70

161.3 < < 162.70

Lower value = 161.3

Upper value = 162.70