In 1970, 59% of college freshmen thought that capital punishment should be abolished; in 2005, the percentage was 35%. The percentages are based on two independent simple random samples, each of size 1,000. Compute a 95% confidence interval for the difference in the percentages.

The 95% confidence interval for the difference in the percentages = [19.75, 28.25]

Step-by-step explanation:

The formula for confidence interval for difference in percentages =

p1 - p2 ± z x √[p1(100 - p1)/n1 + p2(100 - p2)/n2)

From the above question:

p1 = 59%

n1 = 1000

p2 = 35%

n2 = 1000

z = z score of the 95% confidence interval = 1.96

Confidence interval = p1 - p2 ± z x √[p1(100 - p1)/n1 + p2(100 - p2)/n2)

= 59 - 35 ± 1.96 × √[59(100 - 59)/1000] + [35(100 - 35)/1000]

= 24 ± 1.96 × √ [59 × 41/1000] + [35 × 65/1000]

= 24 ± 1.96 × √[2419/1000 + 2275/1000]

= 24 ± 1.96 × √2.419 + 2.275

= 24 ± 1.96 × √(4.694)

= 24 ± 1.96 × 2.1665641001

= 24 ± 4.2464656363

Confidence Interval = 24 ± 4.2464656363

24 - 4.2464656363 = 19.753534364

Approximately = 19.75

24 + 4.2464656363 = 28.2464656363

Approximately = 28.25

Therefore, the 95% confidence interval for the difference in the percentages = [19.75, 28.25]

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step-by-step explanation: