Question

A study is conducted to test a claim that fewer than 65% of adults believe there is intelligent life elsewhere in the galaxy. In a survey of 80 adults, 48 indicated they believe there is intelligent life elsewhere in the galaxy. Test the claim at the 0.10 level of significance. Select the correct P-value and conclusion.

Group of answer choices

P = 0.3484, Do not reject H₀

P = 0.1742, Do not reject H₀

P = 0.1742, Reject H₀

P = 0.3484, Reject H₀

Answer 1

Here we have to test that

Null hypothesis :

Alternative hypothesis :

where

n = number of adults in a survey = 80

x = number of adults who believe there is intelligent life elsewhere in the galaxy = 48

Sample proportion :

Test statistic :

z = -0.9376 (Round to 4 decimal)

Test statistic = z = -0.9376

Test is left tailed test.

P value = P(z < -0.9376)

P value from excel using function:

=NORMSDIST(-0.9376)

=0.1742 (Round to 4 decimal)

P value = 0.1742

Level of significance = = 0.10

Here p value >

So we do not reject the null hypothesis H0.

P = 0.1742, Do not reject H₀

Conclusion : There is not sufficient evidence to to test a claim that fewer than 65% of adults believe there is intelligent life elsewhere in the galaxy.