Interpreting and Constructing Confidence Interval

Find the appropriate critical value and standard error of the sample proportion.

• z* = 1.645, SE = 0.0357

• z* = 1.96, SE = 0.0114

• z* = 1.282, SE = 0.0598

• z* = 1.96, SE = 0.1784

Suppose you wanted to estimate the proportion of people who feel that unemployment compensation should be expanded with 95% confidence to within ±1.5%. Calculate how large a sample you would need.

• n = 1,793

• n = 3,443

• n = 2,078

• n = 6,540

Find the critical t* value for a 95% confidence interval with 8 degrees of freedom.

• 1.860

• 2.306

• 2.262

• 2.449

Find the critical t* value for an 80% confidence interval when n = 20.

• 1.729

• 1.066

• 0.860

• 1.328

You want to estimate the mean fuel efficiency of Ford Focus automobiles with 99% confidence and a margin of error of no more than 1 mile per gallon. Preliminary data suggest that σ = 2.4 miles per gallon is a reasonable estimate of the standard deviation for all cars of this make and model. How large a sample do you need?

• n = 30

• n = 34

• n = 39

• n = 48

(a)   gives an interval of plausible values for a parameter based on sample data.

The margin of error of an estimate describes how far, at most, we expect the estimate to vary from the true population value. That is, in a C% confidence interval, the distance between the point estimate and the true parameter value will be less than the margin of error in C% of all sample.

• False

• True

How do we interpret a confidence level?

• "If we were to select random samples from a population and construct a C% confidence interval using each sample, about C% of the intervals wouldn't capture the [parameter in context]."

• "If we were to select random samples from a population and construct a C% confidence interval using each sample, about C% of the intervals would capture the [parameter in context]."

Mr. Buckley's class wants to construct a confidence interval for p= the true proportion of red beads in the container, which includes over 3000 beads. Recall that the class's sample of 251 beads had 107 red beads and 144 other beads. Check if the conditions for constructing a confidence interval for p are met.

• Yes all conditions are met

• No, not all conditions are met

The confidence level C gives the overall success rate of the method used to calculate the confidence interval. That is, in C% of all possible samples, the interval computed from the sample data will capture the true parameter value.

• True

• False