Question

In a survey¹ of 1000 American adults conducted in April 2012, 43% reported having gone through an entire week without paying for anything in cash. Test to see if this sample provides evidence that the proportion of all American adults going a week without paying cash is greater than 40%. Use the fact that a randomization distribution is approximately normally distributed with a standard error of SE=0.016. Show all details of the test and use a 5% significance level.


¹‘‘43% Have Gone Through a Week Without Paying Cash,” Rasmussen Reports, April 11, 2011.

Answer 1

H0: p = 0.40

Ha: p > 0.40

Test statistics

z = $\hat{p}$ - p / SE

= 0.43 - 0.40 / 0.016

= 1.88

Critical value at 0.05 level = 1.645

Since test statistics > 1.645 , reject the null hypothesis