Constructing a Confidence Interval

A political pollster wants to know what proportion of voters are planning to vote for the incumbent candidate in an upcoming election. A poll of 150 randomly selected voters is taken from the more than 2,000 voters in the population, and 60% of those selected plan to vote for the incumbent candidate. The pollster wants to use this data to construct a one-sample z interval for a proportion. Which conditions for constructing this confidence interval did their sample meet?

Choose all answers that apply:

• Random Sample

• Independent (10% Rule)

Nkechi wants to use a one-sample z interval to estimate what proportion of candies in a bag are red. She takes a random sample of 24 of the 80 total candies and finds that 18 of the candies in the sample are red. Which conditions for constructing this confidence interval did their sample meet?

Choose all answers that apply:

• Random

• Normal

• Independent

A certain flight transports over 1,000 passengers daily, and the airline is curious what proportion of passengers on this flight don't use overhead bin space. They take an SRS of 40 of these passengers and find that 6 of them don't use overhead bin space. The airline wants to use this data to create a one-sample z interval to estimate the proportion of passengers on this flight don't use overhead bin space. Which conditions for constructing this confidence interval did their sample meet?

Choose all answers that apply:

• Random

• Normal

• Independent

A development expert wants to use a one-sample z interval to estimate the proportion of women aged 16 and over that are literate in Albania. They take an SRS of 50 women from this population and finds that 48 are literate. Which conditions for constructing this confidence interval did their sample meet?

Choose all answers that apply:

• Random

• Normal

• Independent

• (0.001, 0.005)

• (0.566, 0.693)

• (0.148, 0.252)

• (0.023, 0.045)

Answer explanation

Point estimate: 80/400 = 0.20, Margin of Error = 0.052

Lower bound: 0.2 - 0.052 = 0.148
Upper bound: 0.2 + 0.052 = 0.252

(0.148, 0.525)

• 0.321 < p < 0.379

• 0.316 < p < 0.384

• 0.309 < p < 0.391

• 0.305 < p < 0.395

Answer explanation

Point estimate = 0.35, Margin of error = 0.034.

Lower bound: 0.35 - 0.034 = 0.316

Upper bound: 0.35 + 0.034 = 0.384

0.315 < p < 0.384

• 89.08 < μ < 94.92

• 87.27 < μ < 96.73

• 87.29 < μ < 96.71

• 87.77 < μ < 96.23

Answer explanation

point estimate = 92, margin of error = 4.73

Lower bound: 92 - 4.73 = 87.27
Upper bound: 92 + 4.73 = 96.73

 $87.27<\mu<96.73$  

True or False: The more confident you want to be, the smaller your confidence interval will be.

• True

• False

Answer explanation

If I want to be more confident, the interval will have to be wider, leaving more room to be "wrong."

Margin of Error is equal to:

• Standard Deviation

• critical value * Standard Deviation

• Critical Value

• Point Estimate

Which of the following is the definition of a "point estimate?"

• The average of a population.

• The margin of error of a sample.

• An approximate value used to best represent the true value.

• The confidence interval.

Answer explanation

The point estimate is our "best guess" at the unknown true value.