Ten years ago, 53% of American families owned stocks or stock funds. Sample data

Question

Ten years ago, 53% of American families owned stocks or stock funds. Sample data collected by the Investment Company Institute indicates that the percentage is in 2016 is 46%. Develop appropriate hypotheses such that the rejection of H_0 will support the conclusion that a smaller proportion of North American families own stocks or stock funds in 2016 than ten years ago. Assume that the Investment Company Institute samples 300 American families to estimate that the percent owning stocks or stock funds was 46% in 2016. What is the p-value for your hypothesis test? At alpha = 0.01, test your hypothesis. What is your conclusion?

Explanation / Answer

a) here null hypothesis:p>=0.56

alternate hypothesis:p<0.56

b)here std error =(p(1-p)/n)1/2=0.0287

also phat=0.46

hence test stat z=(phat-p)/std error =-2.79145

for above zstat at one tailed ; p value =0.0026

c) as p vlaue is less then 0.01 level, we reject null hypothesis, and conclude that a smaller % of families own stock in 2016

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