Question

3. Interval estimation of a population mean, population standard deviation unknown

The Business Environment and Enterprise Performance Survey (BEEPS), developed by the European Bank for Reconstruction and Development and the World Bank, is a survey of more than 4,000 firms in 22 transition countries. Conducted in 2000, BEEPS gathered information on the impediments to business growth in transition countries.

As part of BEEPS, firms that import goods answered the question, “How many days does it take from the time your goods arrive in their port of entry until the time you can claim them from customs?” For the sample of 43 importing firms in Slovakia, the sample mean x̄ was 4.8 days, and the sample standard deviation s was 8.2 days.

The standard deviation of the population distribution is unknown, but you are willing to assume that the population distribution is not highly skewed and contains no outliers.

To develop a 99% confidence interval estimate of the mean number of days it takes for imported goods to clear customs in Slovakia, use the:

a. t distribution with 42 degrees of freedom

b. t distribution with 35 degrees of freedom

c. standard normal distribution

d. t distribution with 43 degrees of freedom

Use the Distributions tool to compute a 99% confidence interval estimate for the mean number of days it takes for imported goods to clear customs in Slovakia.

You are 99% confident that the mean wait time for imported goods to clear customs in Slovakia is between:

a. 1.43

b. 4.29

c. 1.78

d. 1.58

and:

a. 8.02

b. 5.31

c. 8.17

d. 7.82

days.

The confidence interval estimate you calculated is appropriate because:

a. You are assuming the population distribution is not highly skewed nor contains outliers and the sample size is at least 30.

b. The wait time for imported goods to clear customs in Slovakia is normally distributed.

c. Using the t distribution means the sampling distribution of the mean does not need to be normal.

Answer 1

a. t distribution with 42 degrees of freedom

sample mean 'x̄=	4.800
sample size   n=	43.00
sample std deviation s=	8.20
std error 'sx=s/√n=	1.2505

for 99% CI; and 42 df, value of t=		2.6980
margin of error E=t*std error    =		3.374
lower bound=sample mean-E =		1.426
Upper bound=sample mean+E =		8.174

You are 99% confident that the mean wait time for imported goods to clear customs in Slovakia is between   1.43 and 8.17

a. You are assuming the population distribution is not highly skewed nor contains outliers and the sample size is at least 30.