Question

Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value ta /2, (b) find the critical value Za/2, or (c) state that neither the normal distribution nor the t distribution applies. Here are summary statistics for randomly selected weights of newborn girls: n= 182, x = 32.8 hg, s = 6.2 hg. The confidence level is 90%. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. ta/2 = (Round to two decimal places as needed.) OB. Za/2= (Round to two decimal places as needed.) O C. Neither the normal distribution nor the t distribution applies.

Answer 1

Sol)

Given

n = 182

Sample mean ( xbar ) = 32.8

Sample standard deviation ( s ) = 6.2

The confidence is 90%

Population standard deviation is unknown so we use t distribution

Degreesof freedom = df = n - 1 = 182 - 1= 181

Alpha = 1 - 0.90

= 0.1

Alpha / 2 = 0.1 / 2 = 0.05

T value for df = 181 and alpha /2 = 0.05 is

T value( t alpha / 2 ) = 1.653316

Option A

T ( alpha / 2 ) = 1.653316