Question

An toy designer wants to determine the average time it takes to assemble an “easy-to-assemble” toy. A sample of 12 times yielded an average time of 19.92 minutes, with a sample standard deviation of 5.73 minutes. Assuming normal assembly times, provide a 95% confidence interval for the mean assembly time.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 19.92

sample standard deviation = s = 573

sample size = n = 12

Degrees of freedom = df = n - 1 = 12-1=11

At 95% confidence level

= 1-0.95% =1-0.95 =0.05

/2 =0.05/ 2= 0.025

t/2,df = t_{0.025,11= 2.2}

t _/2,df = 2.2

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

= 2.2* (5.73 / 12)

Margin of error = E = 3.6407

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

- E < <  + E

19.92 - 3.6407 < < 19.92 + 3.6407

16.279< < 23.561

(16.279,23.561)

A 95% confidence interval for the mean assembly time is =  16.279 and 23.561