There are 3 questions but they are similar. Casey is a statistics student who is

Question

There are 3 questions but they are similar.

Casey is a statistics student who is conducting a one-sample z-test for a population proportion p using a significance level of a 0.01. Her null (Ho) and alternative (H1) hypotheses are Ho: p 0.094. Hi p 0.094 Determine the positive value z that defines the critical region for this test. That is, determine the smallest positive number z such that if the z-statistic computed from her sample data is greater than z or less than -z her null hypothesis would be rejected at a significance level of a 0.01. Give your answer precise to at least two decimal places.

Explanation / Answer

1) This is a two tailed test.

The level of significance is given as 0.01.

So,

Critical z values = value in z table corresponding to the cumulative areas 0.005 and 0.995.

z = 2.576

2) This is a left tailed test.

The level of significance is given as 0.05.

So,

Critical z values = value in z table corresponding to the cumulative area 0.05.

z = -1.645

3) This is a right tailed test.

The level of significance is given as 0.1.

So,

Critical z values = value in z table corresponding to the cumulative area 0.9.

z = 1.282

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