Non-response to surveys is a continual problem for researchers. The problem is knowing whether the individuals who do not respond form a separate subsample of the population. A common way of encouraging survey response is to offer a prize draw. To test whether offering a prize is effective in increasing the response rate, two groups of financial planners are surveyed by mail, one in Adelaide without offering a prize, and the other in Sydney where a prize draw for survey participants was offered. The results are provided in the following table:

City

Adelaide

Sydney

Total

Response

75

98

173

Non-response

142

118

260

Total

217

216

433

Is there evidence of a significant difference between the two treatment groups in the proportion of responses to the survey at a 0.05 significance level?

Using a chi-squared test for differences between proportions state the hypotheses that you are testing, determine the critical value of the chi-squared statistic and state the decision rule.