Question

Proportion Problem. A plan for an executive traveler's club has been developed by an airline on the premise that at least 5% of its current customers would qualify for membership. A random sample of 500 customers yielded 40 who would qualify. Using this proportion data, test at alpha = .01 the null hypothesis that the company's premise is correct, against the alternative that it is higher than the premise. What is the test statistic (z*)? Use three decimal places in your answer and use the proper rules of rounding.

Answer 1

Solution :

$\hat p$ = 40 / 500 = 0.08

Test statistic = z

= $\hat p$ - P₀ / [$\sqrt$P_{0 *} (1 - P₀ ) / n]

= 0.08 - 0.05 / [$\sqrt$(0.05 * 0.95) / 500]

= 3.078

Test statistic = 3.078