Question

According to a Pew Research Center, in May 2011, 35% of all American adults had a smart phone (one which the user can use to read email and surf the Internet). A communications professor at a university believes this percentage is higher among community college students.She selects 300 community college students at random and finds that 120 of them have a smart phone. In testing the hypotheses: H0: p = 0.35 versus Ha: p > 0.35, she calculates the test statistic as Z = 1.82.1. There is enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.034).2. There is enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.068).3. There is not enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.966).4. There is not enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.034)

Answer 1

Explanation:

For the null hypothesis,

p = 0.35

For the alternative hypothesis,

P > 0.35

Since the z score is given as z = 1.82, we would find the probability value by determining the area above the z score from the normal distribution table. The required probability value is

1 - 0.966 = 0.034

Assuming alpha = 0.05,

Since alpha, 0.05 > than the p value, 0.034, then we would reject the null hypothesis. Therefore, the correct option is

At significance level of 5%,

There is enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.034).