(a) What is the sample size of the survey?
The sample size of the survey is 1167 married or engaged women.
(b) How many women said that the bending knee was essential?
50% of the women said that the bending knee was essential. To find the actual number of women, we can multiply the percentage by the sample size:
50% of 1167 = 0.5 × 1167 = 583.5
Since we cannot have half a woman, we can round to the nearest whole number:
583 women said that the bending knee was essential.
(c) What is the margin of error for this survey at a 95% confidence level?
To find the margin of error, we need to use the formula:
margin of error = critical value × standard error
The critical value for a 95% confidence level is 1.96 (assuming a large sample size). The standard error can be calculated as:
standard error = sqrt(p(1-p)/n)
where p is the proportion of women who said the bending knee was essential (0.5), and n is the sample size (1167).
standard error = sqrt(0.5(1-0.5)/1167) ≈ 0.015
Therefore, the margin of error is:
margin of error = 1.96 × 0.015 ≈ 0.029
Rounding to two decimal places, the margin of error is approximately 0.03.
(d) What is the 95% confidence interval for the proportion of women who said that the bending knee was essential?
To find the confidence interval, we can use the formula:
confidence interval = sample proportion ± margin of error
Substituting the values we have calculated, we get:
confidence interval = 0.5 ± 0.03
Therefore, the 95% confidence interval for the proportion of women who said that the bending knee was essential is:
(0.47, 0.53)
This means that we can be 95% confident that the true proportion of women who consider the bending knee essential is between 0.47 and 0.53.