Question

1.

Which of the following statements is true about a 95% confidence interval in which the population mean is contained within the interval 3.2 to 3.8? (1 point)

Select one:

a. The width of this interval is 0.016.

b. The sample mean is 3.5.

c. The margin of error is 0.6

d. The confidence interval of 95% uses 2.576.

2.

Researchers conducted a survey to examine the difference between the proportion of females who vote and the proportion of males who vote. They found that 85 of 200 males voted whereas 124 of 220 females voted. Which of the following represents the 95% confidence interval for the difference of proportions females – males in this case? (1 point)

Select one:

a. (0.225, 0.402)

b. (0.095, 0.282)

c. (0.044, 0.233)

d. (0.050, 0.147)

Answer 1

Q1) We are given the 95% confidence interval for the population mean here as: (3.2 to 3.8)

• The width of the interval here is computed as: 3.8 - 3.2 = 0.6
• The sample mean is computed using the mean of the upper and lower limits here as:
  = (3.2 + 3.8) / 2 = 3.5
  Therefore B is correct here.
• The margin of error here is computed as:
  MOE = (U - L) / 2 = (3.8 - 3.2)/ 2 = 0.3
• From standard normal tables, we have:
  P(-1.96 < Z < 1.96) = 0.95, therefore we use the critical z value as 1.96 and not 2.576.

Therefore B is the only correct answer here.

Q2) The sample proportions here are computed as:
pF = 124/220 = 0.5636
pM = 85/200 = 0.425

The pooled proportion here is computed as:

The standard error here is computed as:

From standard normal tables, we have:
PP(-1.96 < Z < 1.96) = 0.95

The confidence interval now is obtained here as:

Therefore C is the required confidence interval here.