Question

According to a popular wedding magazine, the mean cost of flowers for a wedding is $750. Recently, in a random sample of 45 weddings in the US it was found that the average cost of the flowers was $734, with a standard deviation of $102. On the basis of this, a 90% confidence interval for the mean cost of flowers for a wedding is $701 to $767. Choose the statement that is the best interpretation of the confidence interval.

Select one:

a. In about 90% of all samples of size 45, the resulting confidence interval will contain the mean cost of flowers at weddings in the US.

b. The probability that the flowers at a wedding in the US will cost more than $698 is greater than 10%.

c. The probability that flowers at a wedding will cost less than $767 is nearly 100%.

d. There is a 90% chance that the mean cost of flowers at a wedding in the US is between $701 and $767.

e. We are extremely confident that the mean cost of flowers at a wedding in the US is between $701 and $767.

Answer 1

Solution:

Given: A random sample of 45 weddings in the US it was found that the average cost of the flowers was $734, with a standard deviation of $102.

On the basis of this, a 90% confidence interval for the mean cost of flowers for a wedding is $701 to $767.

We have to interpret the confidence interval:

Confidence interval is an interval estimate of population parameter ( in this case parameter is Mean).

If we obtain 100 samples of sample size n or if we repeat an experiment 100 times of sample size n, then 90% confidence interval means 90 intervals out of 100 intervals would contains true population parameter value.

90% confidence interval does not mean that probability or chance.

Thus correct answer is:

a) In about 90% of all samples of size 45, the resulting confidence interval will contain the mean cost of flowers at weddings in the US.