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# You wish to test the following claim (Ha) at a significance level of α=0.10.       Ho:p1=p2 &n...

You wish to test the following claim (Ha) at a significance level of α=0.10.

Ho:p1=p2
Ha:p1<p2

You obtain 13.3% successes in a sample of size n1=226 from the first population. You obtain 21.4% successes in a sample of size n2=541 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 test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic = _________________

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value = _________________

The p-value is...

• _____less than (or equal to) αα
• _____greater than αα

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 less than the second population proportion.
• ___There is not sufficient evidence to warrant rejection of the claim that the first population proportion is less than the second population proportion.
• ____The sample data support the claim that the first population proportion is less than the second population proportion.
• ____There is not sufficient sample evidence to support the claim that the first population proportion is less than the second population proportion.

The statistic software output for this problem is: test statistic = -2.606

P-value = 0.0046

P-value < 0.10

less than (or equal to) α

Reject the null hypothesis

There is sufficient evidence to warrant rejection of the claim that the first population proportion is less than the second population proportion

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