Question

You wish to test the following claim (Ha) at a significance level of α=0.02

      Ho:p1=p2
      Ha:p1>p2

You obtain 118 successes in a sample of size n1=249 from the first population. You obtain 76 successes in a sample of size n2=242 from the second population. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution.

What is the critical value for this test? (Report answer accurate to three decimal places.)
critical value =

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

The test statistic is...

• in the critical region
• not in the critical region

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the first population proportion is greater than the second population proportion.
• There is not sufficient evidence to warrant rejection of the claim that the first population proportion is greater than the second population proportion.
• The sample data support the claim that the first population proportion is greater than the second population proportion.
• There is not sufficient sample evidence to support the claim that the first population proportion is greater than the second population proportion.

Please show all work and use ti84

Answer 1

Here we have to test that

Using TI-84 calculator:

Press STAT>Highlight Tests>Select 6 : 2-propZTest>Press Enter>

x1:118

n1:249

x2:76

n2:242

Highlight >p2

Calculate

Press enter.

Test statistic = z = 3.622                     (Round to 2 decimal)

P value = 0.000146

Critical value:

Test is right tailed test.

alpha = right area = 0.05

left area = 1 - alpha = 1 - 0.05 = 0.95

Using TI-84:

Press 2nd VARS> Select 3:invnorm>Press enter>

area: 0.95

Press enter two times.

Critical value = 1.645                             (Round to 3 decimal)

Here critical region is greater than or equal to 1.645

Test statistic = z = 3.622

Since z > critical value.

The test statistic is in critical region.

The test statistic leads to a decision to reject null hypothesis.

Conclusion: The sample data support the claim that the first population proportion is greater than the second population proportion.