You wish to test the following claim that π1<π2 .  You use a significance level of 0.005.       Ho:π1=π2       Ha:π1<π2 You obtain 50 successes in a sample of size n1=713 from the first population. You obtain 37 successes in a sample of size n2=313 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 less than the second population proportion. We have statistically significant evidence that the first population proportion is less than the second population proportion. It is plausible that the first population proportion is equal to the second population proportion.

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Author:Amos Gilat
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You wish to test the following claim that π1<π2 .  You use a significance level of 0.005.

      Ho:π1=π2
      Ha:π1<π2

You obtain 50 successes in a sample of size n1=713 from the first population. You obtain 37 successes in a sample of size n2=313

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 less than the second population proportion.
  • We have statistically significant evidence that the first population proportion is less than the second population proportion.
  • It is plausible that the first population proportion is equal to the second population proportion.
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