A random sample of Democrats and a random sample of Republicans were polled on an issue. Of 100 Republicans, 69 would vote yes on the issue; of 200 democrats, 123 would vote yes. Let pl and p2 denote respectively the proportions of all Democrats or all Republicans who would vote yes on this issue. Use the R script to finish the following questions. (a) Construct a 95% confidence interval for pl - p2
(b) Can we say that more Democrats than Republicans favor the issue at the 1% level of significance.

Step-by-step explanation:

(a)

For the two proporion confidence interval p1-p2

# by default R = 95% confidence interval

The R-code = prop.test(X = c(123,690, n=c (200, 100))

where;

x - takes favorable cases

n - sample size

(b)

Here;

The R-code = prop.test (X = c(123,690, n=c (200, 100)), alternative = "greater", conf.int = 0.99)

Now;

From the information given;

out of 200 democrats, 123 voted yes;

Since 69 voted yes out of 100 republicans, then:

For pooled proportion;

Since p = 0.64

Then; q = 1 - p

q = 1 - 0.64

q = 0.36

∴

The confidence interval for the difference in population proportion

∴

∴

Lower limit = -0.19022

upper limit = 0.04022

Thus; the 95% confidence interval lies between:

-0.19022 < p1 - p2 < 0.04022

b)

Recall that:

Null hypothesis:

Alternative hypothesis:

This is a right-tailed test.

The z test statistics can be computed as:

P-value = P(Z > -1.276)

P-value = 0.899

Decision rule: Reject the null hypothesis if P-value < level of significance at 0.01

Conclusion: We fail to reject the null hypothesis since P-value is greater than the level of significance and we conclude that there is insufficient evidence to say that more democrats favor the issue at the 1% level of significance than the republicans.

x=half

step-by-step explanation:

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step-by-step explanation: