Question

A scooter company wants to determine the average amount of time it takes an adult to assemble an “easy to assemble” scooter. A sample of 49 times yielded an average time of 18.15 minutes. Assume that the assembly times are normally distributed and the population has a standard deviation of 5.39 minutes.

a) Give a point estimate for the population mean that the sample of data is taken from.

b) Find the 96% confidence interval for the mean assembly time.

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 18.15

Population standard deviation =    =5.39

Sample size n =49

At 96% confidence level the z is

Z/2 = Z0.02 = 2.05 ( Using z table )

Margin of error = E =   Z/2    * ( /n)
= 2.05* ( 5.39 / 49 )

= 1.5785
At 96% confidence interval estimate of the population mean
is,

- E < < + E

18.15 - 1.5785 <   <18.15 + 1.5785

16.5715 <   < 19.7285
( 16.5715 <, 19.7285 )