Question

Use the given degree of confidence and sample data to construct a confidence interval for the population mean mu.

Assume that the population has a normal distribution. Round to two decimal places. nequals​10, x overbarequals14.5​, sequals4.7​, ​95% confidence

A. 11.78less thanmuless than17.23

B. 11.14less thanmuless than17.86

C. 11.19less thanmuless than17.81

D. 11.15less thanmuless than17.85

Answer 1

Solution :

Given that,

= 14.5

s = 4.7

n = 10

Degrees of freedom = df = n - 1 = 10 - 1 = 9

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,9 =2.262

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

= 2.262 * (4.7 / 10) = 3.36

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

- E < < + E

14.5 - 3.36 < < 14.5 + 3.36

11.14 < < 17.86

(11.14 , 17.86 )

correct option is B.