A panel of 1400 eligible voters was assembled by randomly sampling from the popu

Question

A panel of 1400 eligible voters was assembled by randomly sampling from the population of all eligible voters. When questioned last month, 494 of the panel members indicated support for the Liberal party. When questioned this month, 72 panel members had changed their mind, with 42 becoming Liberal supporters and 30 ceasing to be Liberal supporters. (a) Give a 95% confidence interval for the proportion of eligible voters supporting the Liberal party now. Report the interval endpoints to three decimal place. (b) Give a 95% confidence interval for change in support, i.e., the proportion of eligible voters supporting the Liberal party now minus the proportion who supported them last month. Report the interval endpoints to three decimal places

Explanation / Answer

a) Liberal supporters now = 494 + 42 - 30 = 506

The statistical software output for 95% confidence interval will be:

One sample proportion summary confidence interval:
p : Proportion of successes
Method: Standard-Wald

95% confidence interval results:

Hence,

95% confidence interval will be:

(0.336, 0.387)

b) The statistical software output for 95% confidence interval of difference will be:

Two sample proportion summary confidence interval:
p1 : proportion of successes for population 1
p2 : proportion of successes for population 2
p1 - p2 : Difference in proportions

95% confidence interval results:

Hence,

95% confidence interval will be:

(-0.031, 0.053)

Proportion Count Total Sample Prop. Std. Err. L. Limit U. Limit p 506 1400 0.36142857 0.012839614 0.33626339 0.38659375

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