In a recent survey of 160 randomly selected college students

In a recent survey of 160 randomly selected college students, 107 said that they believe in the existence of extraterrestrial life. Find the sample proportion that believes that there is extraterrestrial life. (Round the answer to three decimal places.) B)The 90 % margin of error associated with this estimate is: (Round the answer to three decimal places.) The 90 % confidence interval for the true proportion of all college students who believe there is extraterrestrial life is: (Round the answers to three decimal places.) Suppose the proportion of the general US population who beleive in extraterestrial life is 0.38. Choose the appropriate null and alternative hypothesis that tests whether the proportion of college students who beleive in extraterestrial life in greater than the general population? Calculate the z test statistic and p-value. (Round the answers to three decimal places).

Solution

b = 107 / 160

= 0.66875

Margin of error = Z * sqrt ( b * (1-b) / n)

= 1.65 * sqrt ( 0.66875 * (1-0.66875) / 160)

= 0.0614

Thus, the confidence interval

= 0.66875 +/- 0.0614

= (0.6073, 0.7301)

d)

WE need to check whether b > 0.38 or not

Thus,

We check Ho : b = 0.38

Ha: b > 0.38

e)

z -stat = (0.66875 - 0.38) / 0.0614

= 4.702

p-value is very very small and hence insignificant.