In a recent survey of 220 randomly selected college students, 114 said that they

Question

In a recent survey of 220 randomly selected college students, 114 said that they believe in the existence of extraterrestrial life. A) Find p, the sample proportion that believes that there is extraterrestrial life. (Round the answer to three decimal places.) p = 6545 B) The 95% margin of error associated with is: (Round the answer to three decimal places.) .0827 c) The 95% confidence interval for the true proportion of all college students who believe there is extraterrestrial life is: (Round the answers to three decimal places.) .0827 to .7372 D) Suppose the proportion of the general US population who believe in extraterrestrial life is 0.38. Choose the appropriate null and alternative hypothesis that tests whether the proportion of college students who believe in extraterrestrial life in greater than the general population? H_0: mu = 0.38 H_a: mu notequalto 0.38 H_0: p = 0.38 H_a: p > 0.38 H_0: p = 0.38 H_a: p > 0.38 H_0: p = 0.38 H_a: p notequalto 0.38 H_0: x = 0.38 H_a: x > 0.38 E) Calculate the z test statistic and p-value. (Round the answers to three decimal places). z = 8.388 p-value = F) Based on the p-value, give a conclusion in terms of the alternative.

Explanation / Answer

The statistical software output for this problem is:

One sample proportion confidence interval:
p : Proportion of successes
Method: Standard-Wald

95% confidence interval results:

One sample proportion hypothesis test:
p : Proportion of successes
H0 : p = 0.38
HA : p > 0.38

Hypothesis test results:

Hence,

A) 0.518

B) 0.066

C) 95% confidence interval:

0.452 to 0.584

D) Option C

E) z = 4.223

p - Value = 0

F) Reject Ho

Proportion Count Total Sample Prop. Std. Err. L. Limit U. Limit p 114 220 0.51818182 0.033687698 0.45215514 0.58420849

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