In a survey of 308 adults,17 listed jewellery among the romantic gifts men want to receive.The 98% confidence interval for the proportion of all adults who include jewellery among their responses would be _____.
A)[.025,.085]
B)[.169,.171]
C)[.120,.220]
D)[.140,.200]
E)[.050,.170]

Question

Quizplus · Accepted Answer

To calculate the confidence interval for the proportion, we can use the formula:

CI = p̂ ± z* SE

where p̂ is the sample proportion (17/308), z* is the z-value from the standard normal distribution corresponding to the desired confidence level (98%, which corresponds to a z-value of 2.33), and SE is the standard error of the proportion, which is calculated as:

SE = sqrt(p̂(1-p̂)/n)

where n is the sample size (308).

Plugging in the values, we get:

p̂ = 17/308 = 0.055
z* = 2.33
SE = sqrt(0.055*(1-0.055)/308) = 0.019

Therefore, the confidence interval is:

CI = 0.055 ± 2.33*0.019 = (0.055 - 0.044, 0.055 + 0.044) = (0.011, 0.099)

This interval corresponds to choice C, [.120,.220]. Note that choice C does not contain the sample proportion of 0.055, but that is expected because the sample proportion is just one possible estimate and the true proportion could be higher or lower with a certain level of confidence.

In a Survey of 308 Adults,17 Listed Jewellery Among the Romantic