Question

For a hypothesis test of H0: p = 0.65 against the alternative Ha: p < 0.65, the z test statistic is found to be -2.35. What can be said about his finding?

The finding is significant at both α = 0.05 and α = 0.01.

The finding is significant at α = 0.05, but not at α = 0.01.

The finding is significant at α = 0.01, but not at α = 0.05.

The finding is not significant at α = 0.05 and α = 0.01.

The finding is inconclusive because we don't know the value of p

Answer 1

The finding is significant at both α = 0.05 and α = 0.01.

Explanation:

Given that:

Null hypothesis : H0: p = 0.65 against the Alternative Ha: p < 0.65,

The test statistic ; z test = - 2.35

From the test statistic value, we can obtain the p value of the test :

To determine if the claim is significant at both α = 0.05 and α = 0.01

We compare the Zstatistic and Zcritical values

If Zstatistic < Zcritical ; then we reject H0; if otherwise, we fail to reject H0

Zcritical at 95% one tailed = - 1.645 (left tail)

Zcritical at 95% one tailed = -2.326 (left tail)

- 2.35 < - 1.645

-2. 35 < 2.326

Since, Zstatistic < Zcritical;

The finding is significant at both α = 0.05 and α = 0.01.