Question

In a Gallop poll of 1012 randomly selected adults, 9% said that cloning of humans should be allowed. We are going to use a .05 significance level to test the claim that less than 10% of all adults say that cloning of humans should be allowed. The test statistic for this test is -1.06. What is the p-value for this test statistic?A. .1446B. .2829C. .3544D. .0548

Answer 1

The answer is A, 0.1446. The hypothesis is a left-tailed test

Explanation:

The question narrates and claim that p < 0.10. This does not contain any form of equality sign to H1, so the alternate hypothesis is equals to the claim. H1: p < 0.10.

Also recall that we always test the null hypothesis

So therefore,

H₀: p = 0.10

H₁: p < 0.10

It is observed that from the hypothesis, this problem will be left tail (note that in H₁ the relation symbol points to the left) (also, since it is left tail, α is not split).

Now, for us to confirm the given critical z-value: Zα and test statistics,

Using the z-table on the left we see that Zα = -1.645.

and for the test statistics, we calculate thus:

Z = P⁰ - P/ √pq÷n = 0.09 - 0.10/ √0.10 x 0.90÷1012

= -1.06

Therefore, P - value = P( z < -1.06) = 0.1446

This confirms that the hypothesis is a left-tailed test,

However, There is not sufficient evidence to support the claim that less than 10% of all adults are opposed to duplication of humans”