Question

An industrial designer wants to determine the average amount of time it takes an adult to assemble an “easy to assemble” toy. A sample of 16 times yielded an average time of 19.9 minutes, with a sample standard deviation of 6 minutes. Assuming normality of assembly times, provide a 90% confidence interval for the mean assembly time.

Answer 1

Answer:

(17.42 ; 22.38)

Step-by-step explanation:

To construct a confidence interval we use the following formula:

ci = (sample mean) +- z*(sd)/[n^(1/2)]

The sample mean is 19.9 and the standard deviation is 6. The sample has a n of 16. We have to find the value of z which is the upper (1-C)/2 critical value for the standard normal distribution. Here, as we want a confidence interval at a 90% we have (1-C)/2=0.05 we have to look at the 1-0.05=0.95 value at the normal distribution table, which is 1.65 approximately. Replacing all these values:

ci: (sample mean - z*(sd)/[n^(1/2)] ; sample mean + z*(sd)/[n^(1/2)])

ci: (19.9 - 1.65*6/[16^(1/2)] ; 19.9 + 1.65*6/[16^(1/2)])

ci: (19.9 - 9.9/4] ; 19.9 + 9.9/4)

ci: (19.9 - 2.48 ; 19.9 + 2.48)

ci: (17.42 ; 22.38)