Download Sec. 6.1 – Confidence intervals for the Mean (large samples)

Sec. 6.1 – Confidence intervals for the Mean (large samples)
You can use sample _____________ to estimate population _______________.
A ___________ _________________ is a single value estimate for a population
parameter. The most unbiased point estimate of the population mean _______ is
the sample mean ______.
An _____________ _____________ is an interval, or range of values, used to
estimate a population parameter.
For example,
The _____________ of ________________ ____ is the probability that the
interval estimate contains the population parameter.
Given a level of confidence c, the ___________ of ________ ______ is the
greatest possible distance between the point estimate and the value of the
parameter it is estimating.
𝐸=
In order to use this technique, it is assumed that the population standard
deviation is known. This is rarely the case, but when ____________, the sample
standard deviation ____ can be used in place of ______.
A __________________ _______________ for the population mean ______
is____________________________. The probability that the confidence interval
contains ______ is ______.
Market Researchers use the number of sentences per advertisement as a
measure of readability for magazine advertisements. The following represents a
random sample of the number of sentences found in 50 advertisements.
9
5
10
17
12
20
18
9
13
14
18
6
10
11
11
16
6
10
7
9
9
5
5
14
18
9
12
11
6
12
11
25
18
11
12
13
17
18
12
17
22
23
9
11
11
16
7
9
6
20
A. Find a point estimate of the population mean 𝜇.
B. Find the margin of error for the mean number of sentences in all magazine
advertisements for a 95% confidence level. Assume that the sample standard
deviation is about 5.0.
C. Construct a 95% confidence interval for the mean number of sentences in all
magazine advertisements.
D. Construct a 99% confidence interval for the mean number of sentences in all
magazine advertisements.
A college admissions director wishes to estimate the mean age of all students
currently enrolled. In a random sample of 20 students, the mean age is found to
be 22.9 years. From past studies, the standard deviation is known to be 1.5 years,
and the population is normally distributed. Construct a 90% confidence interval of
the population mean age.
Find a Minimum Sample Size to Estimate 𝝁
From the margin of error formula, = 𝑧𝑐
𝜎
√𝑛
, we can derive a formula to find a
minimum sample size.
Given a 𝑐-confidence level and margin of error 𝐸, the minimum sample size 𝑛
needed to estimate the population mean 𝜇 is
𝑛=
If _____ is unknown, you can estimate it using _____, provided you have a
preliminary sample with at least 30 members.
You want to estimate the mean number of sentences in a magazine
advertisement. How many magazine advertisements must be included in the
sample if you want to be 95% confident that the sample mean is within one
sentence of the population mean?
A beverage company uses a machine to fill one-liter bottles with water. Assume
that the population of volumes is normally distributed. The company wants to
estimate the mean volume of water the machine is putting in the bottles within 1
milliliter. Determine the minimum sample size required to construct a 95%
confidence interval for the population mean. Assume the population standard
deviation is 3 milliliters.
Using the information above, find the sample size for an error tolerance of 2
milliliters. Which error tolerance requires a larger sample size? Explain.