Question

In a random sample of 100 adult Americans who did not attend college, 37 said they believe in extraterrestrials. In a random sample of 100 adult Americans who did attend college, 47 said they believe in extraterrestrials. At the 1% level of significance, does this indicate that the proportion of people who did not attend college and believe in extraterrestrials is less than the proportion of people who did attend college and believe in extraterrestrials?

State the null and alternate hypotheses

Identify the type of test (left-tailed, right-tailed, two-tailed) and state the level of significance.

Determine the p-value or the interval containing the p-value and make a decision to either reject/not reject the null hypothesis.

Interpret your decision in the context of the problem.

Answer 1

Here, we have given that,

n1= number of adult Americans who did not attend college=100

x1=number of adult Americans who did not attend college and said they believe in extraterrestrials= 37

\hat p1=Sample proportion of adult Americans who did not attend college and said they believe in extraterrestrials

=

n2= number of adult Americans who did attend college=100

x2=number of adult Americans who did attend college and said they believe in extraterrestrials= 47

\hat p2=Sample proportion of adult Americans who did attend college and said they believe in extraterrestrials

=

Claim: To check whether the population proportion of people who did not attend college and believe in extraterrestrials is less than the population proportion of people who did attend college and believe in extraterrestrials.

The null and alternative hypotheses are as follows:

Versus

Where p1 = The population proportion of people who did not attend college and believe in extraterrestrials

p2= The population proportion of people who did attend college and believe in extraterrestrials.

This is the left one-tailed test.

= level of significance =1%=0.01

Here, we are using the two-sample proportion test to test the hypothesis.

Now, we can find the test statistics

Z-statistics=

                 =

       =

= -1.44

The test statistic is -1.44.

Now, we can find the p-value

P-value = P( Z<  z-statistics) As this is left one tailed test

              = P (Z < -1.44)

              =0.0749 Using standard normal z table see the value corresponding to the z=-1.44

we get the p-value is 0.0749

Decision:

Here, P-value (0.0749) greater than (>) 0.01

Conclusion:

we do not reject the Null hypothesis Ho

Interpretation:

we conclude that there is not sufficient evidence to support the claim the population proportion of people who did not attend college and believe in extraterrestrials is less than the population proportion of people who did attend college and believe in extraterrestrials.