Question

Your friend recently started a new venture. Based on one simple random sample of a few weeks of financial performance, his analyst has calculated the 95% and 90% confidence intervals for the average weekly profit of the venture in the long run (in INR million) as [-0.03, 1.03] and [0.06, 0.94] respectively. Based on this information, which of the following statements can you make?

Select one:

a. I am 99% confident that the average weekly profit will be negative.

b. He will make a negative profit in more than 5% of the weeks.

c. He will make a positive profit in more than 90% of the weeks.

d. The mean weekly profit in the sample is INR 0.5 million.

Answer 1

The following statements can make:

c. He will make a positive profit in more than 90% of the weeks.

Reason: The 90% confidence intervals for the average weekly profit of the venture in the long run does not include the value zero.

d. The mean weekly profit in the sample is INR 0.5 million.

Reason: The mean weekly profit in the sample=(Lower limit+Upper limit)/2=( -0.03+1.03)/2=(0.06+0.94)/2=0.5.

The following statements can not make:

a. I am 99% confident that the average weekly profit will be negative.

Reason: The lower limit and upper limit of the 99% confident interval will have be negative and positive values. Here, the average weekly profit will be negative or zero or positive.

b. He will make a negative profit in more than 5% of the weeks.

Reason: From 95% confidence interval, there are 2.5% chance to have the negative value of the average weekly profit less than lower limit of the 95% confidence interval.