In response to the belief that house prices have changed over the past year an estate agent has drawn a random sample of 100 completed house purchases and recorded the selling price in each case.
You examine the records of selling prices and find the following frequency distribution:
Table 1 Selling prices
Selling price (£)
10,000
12,000
15,000
17,000
20,000
Number of house purchases
11
25
40
17
7
a. Calculate the sample average and sample standard deviation of selling prices (round to two decimal places).
b. Assuming that the sample standard deviation is a very good approximation of the true population standard deviation, calculate a 90% confidence interval and a 99% confidence interval for selling prices. Comment on the difference between the two intervals and explain the reason for it.
c. The average price in the previous year was £13,500.
Using a significance level of 5%, test whether there has been an increase in house prices. State your conclusion clearly.