Question

1. In a sample of 50 days taken at Piece of Cake Bakery, it was found that an average of 75 cakes per

day were sold. From similar past surveys, the population standard deviation was found to be 25 cakes

per day.

(a) Determine the standard error of cakes sold per day.

(b) Determine the 90% confidence interval for the population mean number of cakes sold per day.

(c) If you wanted a wider interval, would you increase or decrease the confidence level?

2. Schadek Silkscreen Printing Inc purchases plastic cups on which to print logos for sporting events, proms, birthdays, and other special occassions. Zek Schadek, the owner, received a large shipment this morning. To ensure the quality of the shipment, he selected a random sample of 300 cups. He found 15 to be defective.

(a) What is the estimated proportion of cups that are defective for this population?

(b) Develop a 95% confidence interval for the proportion that was defective.

(c) Zek has an agreement with his supplier that he is to return lots that are 10% or more defective.

Should he return this lot? Explain your decision.

3. The data below give the lengths (in mm) of a random sample of 9 herring:

57.9       52.1      51.3       53.7       55.5      51.9       58.2      57.8       54.7

(a) Compute the mean and standard deviation of this sample

(b) Determine a 98% con_dence interval for the population mean length of herring.

(c) Would it be reasonable to conclude that the population mean is actually 52 mm? Justify your

answer.

4. Gus Gale is the owner of Gale's Gas Garage. Gus would like to estimate the mean number of litres

(L) of gasoline sold to his customers. From his records, he selects a random sample of 60 sales and

_nds the mean number of litres sold is 40 with a population standard deviation of 10 L.

(a) What is the point estimate of the population mean?

(b) Develop a 99% con_dence interval for the population mean.

(c) Interpret the meaning of part (b).

Answer 1