Question

A z-test with a z observed of 2.56 (two-tailed) would have a p-value of ______, which would lead a research to _______ the null hypothesis if alpha is .05.

Answer 1

Solution :

The p-value for a two-tailed z-test is given as follows :

p-value = 2.P(Z > |Z_{​​​​​​observed}|)

We have, |Z_{​​​​​​observed}| = 2.56

Hence,

p-value = 2. P(Z > 2.56)

p-value = 0.0105

The p-value is 0.0105.

Based on p-value and significance level (alpha) we make decision rule as follows :

If p-value is less than the significance level (alpha), then we reject the null hypothesis.

If p-value is greater than the significance level (alpha), then we fail to reject the null hypothesis.

We have,  

Significance level (alpha) = 0.05

p-value = 0.0105

(0.0105 < 0.05)

Since, p-value is less than the significance level of 0.05 (alpha = 0.05), therefore we shall reject the null hypothesis.

A z-test with a z observed of 2.56 (two-tailed) would have a p-value of 0.0105, which would lead a research to reject the null hypothesis if alpha is .05.

Please rate the answer. Thank you.