Question 7

File CT_Undergrad_Debt. On average, a college student graduates with $28,000 in debt (The Boston Globe, May 27, 2012). A researcher collects data on debt from 45 recent undergraduates from Connecticut. Assume that the population standard deviation is $7000.

a.The researcher believes that recent undergraduates from Connecticut have less debt than the national average. Specify the competing hypotheses to test this belief.

(2 Marks)

b.Find the value of the test statistics and the p-value?

(6 Marks)

c.Do the data support the researcher's claim at ?

(2 Marks)

Question 8

According to a local newspaper report, female residents in Kota Kinabalu have a higher average life expectancy to male residents. You collect the following sample data to verify the results of the report. You also use the historical (population) standard deviation of 8.2 years for females and 8.7 years for males.

female

male

a.Set up the hypothesis test to test whether the average life expectancy of female Bostonians is higher than that of male Bostonians.

(2 Marks)

b.Calculate the value of the test statistics and the p-value.

(6 Marks)

c.At the 1% significance level, can we conclude that females in Kota Kinabalu live longer than male?

(2 Marks)

Question 4

A soft drink company fills two-liter bottles on several different lines of production equipment. The fill volumes are normally distributed with a mean of 1.95 liters and a variance of 0.04 (liter)².

a. Find the probability that a randomly selected two-liter bottle would contain between 1.90 liters or less.

(2 Marks)

b. Find the probability that a randomly selected two-liter bottle would contain between 2.00 liters or less.

(2 Marks)

c. Find the probability that a randomly selected two-liter bottle would contain between 1.90 and 2.00 liters.

(2 Marks)

d. If X is the fill volume of a randomly selected two-liter bottle, find the value of x for which P(X > x) = 0.3300.

(2 Marks)

e. What is the minimum volume of soft drink required, in liters, to meet the probability of 2.12 percent.

(2 Marks)

TOTAL 10 MARKS

Question 5

A gym knows that each member, on average, spends 50 minutes at the gym per week, with a standard deviation of 10 minutes. Assume the amount of time each customer spends at the gym is normally distributed.

a. What is the probability that a randomly selected customer spends less than 45 minutes at the gym?

(2 Marks)

b. What is the probability that a randomly selected customer spends between 45 minutes to 55 minutes at the gym?

(2 Marks)

c. Suppose the gym surveys a random sample of 30 members about the amount of time they spend at the gym each week. What are the expected value and standard deviation (standard error) of the sample mean of the time spent at the gym?

(2 Marks)

d. If 30 members are randomly selected, what is the probability that the average time spent at the gym exceeds 55 minutes?

(2 Marks)

e. If 30 members are randomly selected, what is the probability that a randomly selected customer spends between 45 minutes to 55 minutes at the gym?

(2 Marks)

TOTAL 10 MARKS

Question 6

a) The rainfall (in Centimeters) during the month of January in Sabah is normally distributed with a population standard deviation of 14.25 cm. In the last 10 years, the sample average of rainfall is computed as 115.50 cm.

i.Construct a 90% confidence interval of the average rainfall in Sabah.

(2 Marks)

ii.Construct a 95% confidence interval of the average rainfall in Sabah.

(2 Marks)

iii.Comment on the width of the preceding confidence intervals. Which confidence interval is wider?

(1 Marks)

b) A sample of holiday shoppers is taken randomly from a local mall. 30 shoppers were selected and asked what their average spending on gifts would be during the entire holiday season. The point estimate of the population mean was calculated as RM500 and the sample standard deviation was calculated as RM70.

i.Construct a 95% confidence interval of the population mean spending.

(2 Marks)

ii.Construct a 95% confidence interval of the population mean spending if the sample increased to 40 shoppers.

(2 Marks)

iii.Comment on the width of the interval estimates as the sample size increases?

(1 Marks)