Question

Assume that we want to construct a confidence interval. Do one of the​ following, as​ appropriate: (a) find the critical value tα/2​, ​(b) find the critical value zα/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=151 x = 29.1 hg S =7.6 hg The confidence level is 95​%. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice. A. t Subscript alpha divided by 2 tα/2 = ​(Round to two decimal places as​ needed.) B. z Subscript alpha divided by 2 zα/2 = ​(Round to two decimal places as​ needed.) C. Neither the normal distribution nor the t distribution applies.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 29.1

sample standard deviation = s = 7.6

sample size = n = 151

Degrees of freedom = df = n - 1 = 151-1= 150

At 95% confidence level

= 1-0.95% =1-0.95 =0.05

/2 =0.05/ 2= 0.025

t/2,df = t_{0.025,150 = 1.98}

A) t _/2,df = 1.98

Margin of error = E = t_/2,df * (s /n)

= 1.98 * ( 7.6/ 151)

Margin of error = E = 1.222

The 95% confidence interval estimate of the population mean is,

- E < <  + E

29.1-1.222 < < 29.1+1.222

27.878 < < 30.222

(27.878,30.222)