Question

. Consider this hypothesis test:

H0: p1 - p2 = < 0

Ha: p1 - p2 > 0

Here p1 is the population proportion of “happy” of Population 1 and p2 is the population proportion of “happy” of Population 2. Use the statistics data from a simple random sample of each of the two populations to complete the following:​​​​​​

Population 1

Population 2

Sample Size (n)

1000

1000

Number of “yes”

600

280

a. Compute the test statistic z.

b. What is the p-value?

c. Should H0 be rejected? Use the critical value approach and a level of significance of 0.05 to justify your answer.

d. Use the above data to construct a 95% confidence interval for p1 - p2

Answer in the word only pls

Answer 1

For the given Hypotheses:

H0: p1 - p2 = < 0

Ha: p1 - p2 > 0

Sample proportions are:

a) Test Statistic:

b) P-value is computed using the Z table shown below or using Excel tool as

P-value<0.00001

c) Conclusion:

Since P-value<<<0.05 level of significance or at any of the usual level of significance the Null hypothesis rejected hence we can conclude that there is sufficient evidence to support the claim.

d) The confidence Interval is calculated as:

hence based on the data provided, the 95% CI will be (0.279,0.361).

which states that we can be 95% confident that the true difference between population proportions is within the above-calculated interval (0.279,0.361).

The Z table used for Z value calculation is :