In 2012, 14.8% of medium-sized businesses in Canada were foreign-controlled, according to Statistics Canada Table 1790005: “Corporations Returns Act (CRA), enterprise characteristics by country of control and operating revenue size.” These data are based on corporate tax returns and are therefore a few years old when published. A financial services company wants to offer financial services to foreign-controlled medium-sized businesses in Canada and, using market projections, estimates that the percentage of such businesses has by now increased to 17.5%. In order to check this out, it plans to survey 400 medium-sized businesses selected at random.

a) State the hypotheses.

b) What is the power of this test if a 10% significance level is used in interpreting the results?

c) If the company is only able to survey a smaller number of businesses, would the power be lower?

d) If the significance level was lower, would the power be lower?

Give reasons for your answers to (c) and (d) without actually doing the calculations.