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STAT 1350: Elementary Statistics
Lab Activity #18
Confidence Intervals
Name(s)_________________________
Date ___________________________
Let’s use our TI calculator to find confidence intervals for a population mean and a population proportion!
Example of a Confidence Interval for the mean, µ, of a population:
Suppose a random sample of 250 credit card bills showed an average balance of $1200. Also assume
that the population standard deviation is $350. Find a 95% confidence interval for the population mean
credit card balance.
To access the confidence interval choices, press STAT and select TESTS. The confidence interval choices are found in
items 7 through B. Select 7:ZInterval because the population standard deviation, σ, is known. In this example, we have
summary statistics, so we will select the STATS option for input. We enter the value of σ, the value of and the sample size
n. Use 0.95 for the C-Level. Highlight Calculate and press ENTER.
Your Turn:
1. Suppose a random sample of 50 basketball players showed the average height to be 78 inches. Also
assume that the population standard deviation is 1.5 inches.
(a) Find a 99% confidence interval for the population mean height.
(b) Find a 95% confidence interval for the population mean height.
(c) Find a 90% confidence interval for the population mean height.
(d) Find an 85% confidence interval for the population mean height.
(e) What do you notice about the length of the confidence interval as the confidence level goes down? If
you used a confidence level of 80%, would you expect the confidence interval to be longer or shorter
than that of 85%? Run the program again to verify your answer.
̂:
Example of a Confidence Interval for a population proportion, 𝒑
The public television station BPBS wants to find the percent of its viewing population that gives
donations to the station. 300 randomly selected viewers were surveyed, and it was found that 123
viewers made contributions to the station. Find a 95% confidence interval for the probability that a
viewer of BPBS selected at random contributes to the station.
To find a confidence interval for a proportion, press the STAT key and use option A:1-PropZlnt under TESTS.
Notice that the normal distribution will be used.
The letter x is used to count the number of successes. Enter 123 for x and 300 for n. Use 0.95 for the C-leve
Highlight Calculate and press ENTER.
Your Turn:
2.
Many types of error will cause a computer program to terminate or give incorrect results. One type of
error is punctuation. For instance, if a comma is inserted in the wrong place, the program might not run.
A study of programs written by students in an introductory programming course showed that 75 out of
300 errors selected at random were punctuation errors.
(a) Find a 99% confidence interval for the proportion of errors made by beginning programming
students that are punctuation errors. Interpret the results in a clear sentence.
(b) Find a 95% confidence interval. Is this interval longer or shorter?
(c) Find the margin of error for each confidence interval. (Hint: you do have enough information
from the calculator output!)
(d) Compare the margin of error from part (b) with the quick method we learned early in the
semester. Is it the same? Why or why not?