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1.      Consider this hypothesis test: H0: p1 - p2 = < 0

aHa: p1 - p2 > 0

Here p1 is the population proportion of "yes" of Population 1 and p2 is the population proportion of "yes" of Population 2. Use the statistics data from a simple random sample of each of the two populations to complete the following:                                                                                        (8 marks)


Population 1

Population 2

Sample Size (n)

500

700

Number of "yes"

400

560

Draw a diagram for the problem marking in all the relevant values.

a.                  Compute the test statistic z



Mark in the Z value based on a =0.05. Note this is a 2-tailed test. 



b.                 Should H0 be rejected?





c.                  Also, What is the p-value?



Use the p-value and a level of significance of 0.05 to justify your answer.





d.                 Use the above data to construct a 90% confidence interval for p1 - p2

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