Question

Suppose that an accounting firm does a study to determine the time needed to complete one person's tax forms. It randomly surveys 150 people. The sample mean is 23.9 hours. There is a known population standard deviation of 7.0 hours. The population distribution is assumed to be normal.

A) Which distribution should you use for this problem? (Round your answers to two decimal places.)

X ~ (_) (_,_)

B) Construct a 90% confidence interval for the population mean time to complete the tax forms.

(ii) Sketch the graph. (Round your answers to two decimal places.)

(i) State the confidence interval. (Round your answers to two decimal places.)

(iii) Calculate the error bound. (Round your answer to two decimal places.)

Answer 1

answer)

N = 150

Mean = 23.9

S.d = 7

A)

X ~ N(23.9, 7)

B)

As the population s.d is known we can use standard normal z table to estimate the interval

Critical value z from z table for 90% confidence level is 1.645

Error = z*s.d/√n = 1.645*7/√150 = 0.94019581293

Lower limit = mean - moe

Upper limit = mean + moe

We are 90% confident that true population mean lies in between 22.96 and 24.84

Error bound = 0.94

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