Question 11

A stratified random sample is characterised by

(a) random selection of strata included

(b) all strata being represented in the sample in proportion to their representation in the population

(c) all members of selected strata being included in the sample

(d) the same number of members selected from each strata

(e) all the above

Question 12

Which of the following is a correct statement about the sampling distribution of X ?

(a) The mean of the sampling distribution is always equal to the population mean. (b) The means of all the samples are equal.

(c) The standard deviation of the sampling distributions is always equal to the population standard deviation divided by the square root of n.

(d) The shape of the sampling distribution is always approximately normal.

(e) None of the above are correct statements.

Question 13

An investor wants to buy a chain of supermarkets. Before the deal is finalised the investor wants to have some assurance that the chain of supermarkets will be a consistent money maker. The management of the chain of supermarkets claims that each store's profits have an approximately normal distribution with both a mean and standard deviation of $12 000. If the management of the chain of supermarkets is correct, what is the probability that in a sample of nine supermarkets, the average profit will fall within $2000 of the actual mean?

(a) 0.3830

(b) 0.4772

(c) 0.0456

(d) 0.0912

(e) Unknown, since n < 30.

Question 14

The auditor for a large bank in Australia knows that the monthly balance of any given customer is $112 on average and the standard deviation is $56. If the bank selects 49 accounts, what is the probability that the sample average monthly balance is between $100 and $130?

(a) 0.079

(b) 0.9878

(c) 0.921

(d) 0.9332

(e) Cannot be determined unless the monthly balance of any given customer account is normally distributed

Question 15

The auditor for a large bank in Australia knows that the monthly balance of any given customer account is $112 on average and the standard deviation is $56. If the bank selects nine (9) accounts, what is the probability that the sample average monthly balance is below $100?

(a) 0.6428

(b) 0.7611

(c) 0.2611

(d) 0.7389

(e) Cannot be determined unless the monthly balance of any given customer account is normally distributed