Download Math 140 Confidence Intervals #7 Constructing Confidence Intervals

Math 140 Confidence Intervals #7
Constructing Confidence Intervals for 1 population mean
and 1 population proportion (percentage)
Confidence intervals give two values that we think the population value is in between. To
construct a confidence interval, we start with the sample value (point estimate) and then add and
subtract a certain number of standard deviations from the sample value. These standard
deviations are also called standard errors. The number of standard errors is the critical zscores corresponding to a certain confidence level. Later, we will see that we can also use the tdistribution to calculate the number of standard errors, but for now we will just use the standard
normal distribution (z-scores).
s
and your calculator to calculate
n
the confidence interval estimate of the population mean  .
Directions: For numbers 1-3, use the formula x  Z c
1. A random sample of 650 high school students has a normal distribution. The sample
mean average ACT exam score was 21 with a 3.2 sample standard deviation. Construct
a 99% confidence interval estimate of the population mean average ACT exam.
2. A random sample of 200 adults found that they had a sample mean temperature of 98.2
degrees and a standard deviation of 1.8 degrees. Construct a 95% confidence interval
estimate of the population mean body temperature of adults. Does the confidence
interval indicate that normal body temperature could be 98.6 degrees?
3. A random sample of 315 adults found that the sample mean amount or credit card debt was
$435 with a standard deviation of $106. Construct a 90% confidence interval estimate of the
population mean amount of credit card debt.
pˆ 1  pˆ 
and your calculator to
n
calculate the confidence interval estimate of the population percent p. You may have to
x
use the formula pˆ  to calculate the sample percent p̂ . Also remember to write the
n
sample proportion p̂ as a decimal before plugging into the formula.
Directions: For numbers 4-6, use the formula pˆ  Z c
4. In a random sample of 72 adults in Santa Clarita, CA, each person was asked if they
support the death penalty. 31 adults in the sample said that they do support the death
penalty. What was the sample proportion of adults in Santa Clarita that support the death
penalty? Now calculate a 95% confidence interval population estimate of people in Santa
Clarita that support the death penalty. Remember to use the appropriate critical value Zscore for each.
5. In a random sample of 400 Americans, each person was asked if they are satisfied with
the amount of vacation time they given by their employers. 84% of them said that they
were not satisfied with their vacation time. Calculate the following. What was the
sample proportion of Americans that were not satisfied with their vacation time? Now
construct a 99% confidence interval in order to estimate the percent of Americans that are
not satisfied with their vacation time.
6. What percent of eligible Americans vote? In 2008, a random sample of 3000 American
adults that were eligible to vote was taken and we found that 2040 of them voted.
Construct a 90% confidence interval estimate of the population percent of Americans that
vote. Now construct another confidence interval. This time construct a 90% confidence
interval estimate of the population percent of Americans that do not vote. Hint: For the
“do not vote” group, the sample percent will change.