Question

16) A national tabloid newspaper reported that 30% of adults in the general population believe that life exists elsewhere in the universe. A TV news station surveyed a random sample of adults from the general population and reported that 36 out of 100 sampled hold this belief. A right-tail hypothesis test is performed. What is the conclusion at a level of significance of 10%? 5%? 1%?

(A) P -value = .0952, and so the 30% claim should be disputed at all three of these levels

(B) P -value = .0952, and so the 30% claim should be disputed at the 10% and 5% level but not at the 1% level

(C) P -value = .0952, and so the 30% claim should be disputed at the 10% level, but not at the 5% and 1% levels

(D) P -value = .0952, and so the 30% claim should be disputed at the 1% level, but not the 10% and 5% levels

(E) P -value = .0952, and so there is not enough evidence to dispute the 30% claim at any of the three levels

Answer 1

H0: p = 0.30

Ha: p > 0.30

Sample proportion = 36 / 100 = 0.36

Test statistics

z = ( - p) / sqrt [ p( 1 - p) / n ]

= ( 0.36 - 0.30) / sqrt [ 0.30 * ( 1 - 0.30) / 100]

= 1.309

p-value = P(Z > z)

= P(Z > 1.309)

= 0.0952 (From Z tabe)

Decision rule = If p-value < significance level then reject H0.

Conclusion -

P -value = .0952, and so the 30% claim should be disputed at the 10% level, but not at the 5% and 1% levels