Question

Based on information from a previous study, r₁ = 40 people out of a random sample of n₁ = 105 adult Americans who did not attend college believe in extraterrestrials. However, out of a random sample of n₂ = 105 adult Americans who did attend college, r₂ = 48 claim that they believe in extraterrestrials. Does this indicate that the proportion of people who attended college and who believe in extraterrestrials is higher than the proportion who did not attend college? Use α = 0.01.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: p₁ = p₂; H₁: p₁ > p₂H₀: p₁ = p₂; H₁: p₁ ≠ p₂    H₀: p₁ = p₂; H₁: p₁ < p₂H₀: p₁ < p₂; H₁: p₁ = p₂

(b) What sampling distribution will you use? What assumptions are you making?

The Student's t. We assume the population distributions are approximately normal.The standard normal. We assume the population distributions are approximately normal.    The standard normal. The number of trials is sufficiently large.The Student's t. The number of trials is sufficiently large.

What is the value of the sample test statistic? (Test the difference p₁ − p₂. Do not use rounded values. Round your final answer to two decimal places.)


(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)


Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.    At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(e) Interpret your conclusion in the context of the application.

Reject the null hypothesis, there is sufficient evidence that the proportion of adults that attended college who believe in extraterrestrials is higher than that of adults who did not attend college.Reject the null hypothesis, there is insufficient evidence that the proportion of adults that attended college who believe in extraterrestrials is higher than that of adults who did not attend college.    Fail to reject the null hypothesis, there is sufficient evidence that the proportion of adults that attended college who believe in extraterrestrials is higher than that of adults who did not attend college.Fail to reject the null hypothesis, there is insufficient evidence that the proportion of adults that attended college who believe in extraterrestrials is higher than that of adults who did not attend college.

Answer 1

Answer:

Given Data

Here we have:

40

48

sample proportion :

  

  

a) Hypothesis :

b) The standard normal . The number of trails is sufficient large.

  

  

= 0.581

Test statistics :

Z -test

c) P - value = p(t > | -0.0681 )

= 0.473

d) At the = 0.01 level , we fail to reject the null hypothesis and conclude the data are not statistically significant.