You wish to test the following claim π1>π2 at a significance level of 0.002.
Ho:π1=π2
Ha:π1>π2
You obtain 90.6% successes in a sample of size n1=415 from the first population. You obtain 83.8% successes in a sample of size n2=414
from the second population. Use the Theory-based inference applet to conduct this test of significance.
(a) What is the z-score for this sample?
z-score = (Report answer accurate to two decimal places.)
(b) What is the p-value for this sample?
p-value = (Report answer accurate to four decimal places.)
(c) The p-value is...
- less than (or equal to) α
- greater than α
(d) This p-value leads to the following conclusion:
- we have statistically significant evidence to support the alternative hypothesis
- the null hypothesis is true
- the null hypothesis is plausible
- the alternative hypothesis is true
(e) As such, the final conclusion is that...
- We conclude that the first population proportion is equal to the second population proportion.
- We conclude that the first population proportion is greater than the second population proportion.
- We have statistically significant evidence that the first population proportion is greater than the second population proportion.
- It is plausible that the first population proportion is equal to the second population proportion.
The given hypothesis is,
Vs
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