Question

3. A large corporation has a promotion where they claim that 1 in 20 of people who purchase a specific product wins a prize. You journalist decides to test this. They purchase 250 of said products and see that 8 of them were winners. Perform a hypothesis test with α= 0.05 to test whether the company’s claim is accurate.

Answer 1

Given that, n = 250 and x = 8

=> sample proportion = 8/250 = 0.032

The null and alternative hypotheses are,

H0 : p = 1/20 (0.05)

Ha : p ≠ 1/20 (0.05)

Test statistic is,

=> Test statistic = Z = -1.31

p-value = 2 * P(Z < -1.31) = 2 * 0.0951 = 0.1902

=> p-value = 0.1902

Since, p-value is greater than significance level of α= 0.05, we fail to reject the null hypothesis.

Conclusion : There is not sufficient evidence to warrant rejection of the claim that  1 in 20 of people who purchase a specific product wins a prize.

Hence, the company's claim is accurate.