Question

It has been suggested that no more than a quarter of Americans who invest in stocks have even a basic knowledge of investing. To investigate, Money Magazine and the Vanguard Group conducted a study in which 1555 investors were selected from across the United States and given a simple quiz on investing (source: ifa.com). If 423 of the investors who took the quiz received a passing score, would this be sufficient sample evidence to reject a null hypothesis that no more than 25% of the population of all inves- tors would receive a passing score on the quiz? Use a significance level of 5%.

a. Show the null and alternative hypotheses.

b. Based on the sample result, should you reject the null hypothesis? Explain

Answer 1

a) As we are testing here whether no more than 25% of the population of all inves- tors would receive a passing score on the quiz, therefore this is a one tailed test for which the null and the alternative hypothesis are given as:

a) The sample proportion here is computed as:
p = x/n = 423 / 1555 = 0.2720

Therefore the test statistic here is computed as:

P-P 0.2720 – 0.25 = 2.01 P(1-P) 0.25*0.75 1555 n

As this is a one tailed test, the p-value here is obtained from the standard normal tables as:
p = P(Z > 2.01) = 0.0222

As the p-value here is 0.0222 < 0.05 which is the level of significance, therefore the test is significant here and we can reject the null hypothesis here. Therefore we have sufficient evidence here to reject the claim that no more than 25% of the population of all inves- tors would receive a passing score on the quiz