Question

Assume that we want to construct a confidence interval. Do one of the​ following, as​ appropriate: (a) find the critical value t Subscript alpha divided by 2tα/2​, ​(b) find the critical value z Subscript alpha divided by 2zα/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=289289​, x overbarxequals=32.632.6 ​hg, s=7.67.6 hg. The confidence level is 95​%.

Answer 1

(a)

= 0.05

ndf = n - 1 = 289 - 1 = 288

From Table, critical values of t are given by:

(b)

= 0.05

From Table, critical values of Z are given by:

(b)

Since the population standard deviation is not provided, t distribution applies.

SE = s/

= 7.6/ = 0.4471

Confidence interval:

32.6 (1.9682 X 0.4471

= 32.6 0.8799

= ( 31.7201 , 33.4799)

Confidence Interval:

31.7201 < < 33.4799