Question

In a study of the length of time it takes to earn a certificate, a random sample of 16 students had a mean of 1.2 years and a standard deviation of 0.4 years. You wish to construct a 90% confidence interval of the population mean amount of time it takes to earn a certificate. Neither the normal distribution nor the t-distribution can be used in your calculations. Why not? Select the best answer.

a. The standard Deviation is too small

b. The sample size is too small

c. The population distribution is not known.

d. Answers (b) and (c) together are correct.

Answer 1

Given that,

= 1.2

s =0.4

n = 16

Degrees of freedom = df = n - 1 =16 - 1 = 15

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t _/2,df = t_0.05,15= 1.753    ( using student t table)

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

= 1.753 * (0.4 / 16) = 0.1753

The 90% confidence interval estimate of the population mean is,

- E < < + E

1.2 - 0.1753< <1.2 + 0.1753

1.0247 < < 1.3753

( 1.0247 ,1.3753)

correct option is D