In a recent survey of 260 randomly selected college students, 174 said that they

Question

In a recent survey of 260 randomly selected college students, 174 said that they believe In the existence of extraterrestrial life. A) Find beta, the sample proportion that believes that there Is extraterrestrial life. beta = 0.669 B) The 90 % margin of error associated with this estimate is: 0.073 C) The 90 % confidence interval for the true proportion of all college students who believe there is extraterrestrial life is: 0.073 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: 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 H_0: P = 0.38 H_0: p notequalto 0.38 H_0: mu = 0.38 H_0: mu = 0.38 E) Calculate the z test statistic and p-value. z = p-value = 0.000 F) Based on the p-value, give a conclusion in terms of the alternative. There is no evidence that the proportion of college students who believe in extraterrestrial life is greater than 0.38. There is suggestive, but inconclusive evidence that the proportion of college students who believe in extraterrestrial life is greater than 0.38. There is moderately suggestive evidence that the proportion of college students who believe in extraterrestrial life is greater than 0.38. There is convincing evidence that the proportion of college students who believe in extraterrestrial life is greater than 0.38.

Explanation / Answer

A) here phat=174/260=0.669

std error=(p(1-p)/n)1/2 =0.0292

for 90% CI, z=1.6449

B)hence margin of error =z*std error =0.048

C)90% CI=mean proportion +/- margin of error =0.621 ; 0.717

D)Ho:p=0.38

Ha:p>0.38

E)now with p=0.38

std error =0.030

hence test stat z=(p-phat)/std error =(0.669-0.38)/0.030=9.608

p value=0.000

F)theer is convincing .............

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