Question

Which of the following statements are TRUE or FALSE? Justify your responses. (a) The true value is guaranteed by the point estimator rather than interval estimator. (b) For level α test, P( Reject H

o
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∣θ∈Θ
o
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)≤α and P( Accept H
o
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∣θ∈Θ
o
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)≥1−α provides a basis for to determine the α level region parameter estimation. (c) For a

Answer 1

With a 95% confidence level, the researchers are confident that the difference between the two population proportions, p1 - p2, is between -0.040 and 0.160.

To construct the confidence interval for the difference between two population proportions, we use the formula:

Difference in Proportions = (p1 - p2) ± Z * sqrt[(p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)]

where p1 and p2 are the sample proportions, and n1 and n2 are the sample sizes. Z is the critical value corresponding to the desired confidence level (95% in this case).

Given x1 = 35, n1 = 240, x2 = 31, and n2 = 293, we can calculate the sample proportions as p1 = 35/240 ≈ 0.146 and p2 = 31/293 ≈ 0.106.

Next, we need the critical value from the standard normal distribution corresponding to a 95% confidence level. This value is approximately 1.96.

Substituting all the values into the formula, we calculate the difference in proportions as 0.040. To find the confidence interval, we need the standard error, which is obtained by taking the square root of the sum of the variances of the two proportions.

Finally, by substituting all the values into the formula, the 95% confidence interval for the difference in proportions is calculated as (-0.040, 0.160).

Therefore, we can conclude with 95% confidence that the difference between the two population proportions, p1 - p2, falls between -0.040 and 0.160.