Section 5-1 and 5-2 Notes
The unknown population parameter (e.g., mean or proportion) that we are ______________ in estimating is called the ___________________________.
A _____________________________ of a population parameter is a rule or formula that tells us how to use the sample data to calculate a ________________ number that can be used as an
____________________________ of the target parameter.
An ______________________________ (or ________________________________) is a formula that tells us how to use the sample data to calculate an _________________ that
_______________________ the target parameter.
5-2: Confidence Interval for a Population Mean: Normal (z) Statistic
Example 5.1:
Consider the large hospital that wants to estimate the average length of stay of its patients, 𝜇 . The hospital randomly samples n = 100 of its patients and finds that the sample mean length of stay is 𝑥̅ = 4.5
days. Also, suppose it is known that the standard deviation of the length of stay for all hospital patients is 𝜎 = 4 days. Use the interval estimator 𝑥̅ ± 1.96 𝜎 𝑥̅ interval for the target parameter, 𝜇 . to calculate a confidence

The ____________________________ is the probability that an interval estimator ___________ the population parameter – that is, the relative frequency with which the interval estimator encloses the population parameter when the estimator is used repeatedly a very large number of times. The _______________________ is the confidence coefficient expressed as a percentage. 𝑥̅ ± 𝑧 𝛼/2 𝜎 𝑥̅
The value _____________ is defined as the value of the standard normal random variable z such that the ________________ 𝛼 will lie to its right. In other words,
Example 5-2:
Find 𝑧 𝛼/2
for 𝛼 = .80.

Example 5-3
Unoccupied seats on flights cause airlines to lose revenue. Suppose a large airline wants to estimate its average number of unoccupied seats per flight over the past year. To accomplish this, the records of 225 flights are randomly selected, and the number of unoccupied seats is noted for each of the sampled flights. Descriptive statistics for the data are displayed in the MINITAB printout below.
Estimate 𝜇 , the mean number of unoccupied seats per flight during the past year, using 90% confidence interval.

Example 5-4
Many middle schools have initiated a program that provides every student with a free laptop
(notebook) computer. Student usage of laptops at a middle school that participates in the initiative was investigated in American Secondary Education (fall 2009). In a sample of 106 students, the researchers reported the following statistics on how many minutes per day each student used his or her laptop for taking notes: 𝑥̅ = 13.2 and s = 19.5. Now the researchers want to estimate the average amount of time per day laptops are used for taking notes for all middle school students across the country. a.
Calculate a 90% confidence interval for the target parameter. Interpret the results. b.
Explain what the phrase “90% confidence” implies in part a.