Transcript Testing a Claim about a Mean: σ Known

Hypothesis Testing for the
Mean: 𝜎 known
Testing a Claim about a Mean: 𝜎 Known
We first need to make sure we meet the requirements.
1. The sample observations are a simple random sample.
2. The value of the population standard deviation 𝜎 is known
3. Either the Population is normal, or 𝑛 > 30
Test Statistic for Testing a Claim about a Proportion
𝑥 − 𝜇𝑥
𝑧= 𝜎
𝑛
Testing a Claim about a Mean: 𝜎 Known
P-value method in 5 Steps
1. State the hypothesis and state the claim.
2. Compute the test value. (Involves find the sample
statistic).
3. Draw a picture and find the P-value.
4. Make the decision to reject 𝐻0 or not. (compare P-value
and 𝛼)
5. Summarize the results.
Testing a Claim about a Mean: 𝜎 Known
The health of the bear population in Yellowstone National Park is
monitored by periodic measurements taken from anesthetized
bears. A sample of 54 bears has a mean weight of 152.9 lb.
Assuming that 𝜎 is known to be 12.8 lb, use a 0.05 significance
level to test the claim that the population mean of all such bear
weights is greater than 150 lb.
1. 𝐻𝑎 : 𝜇 > 150 claim and 𝐻0 : 𝜇 = 150
2. 𝑧 =
𝑥−𝜇𝑥
𝜎
𝑛
=
152.9−150
12.8/ 54
= 1.665
3. P-value=0.047
4. 0.047 < 0.05 so we reject the null.
5. There is sufficient evidence to support the claim.
Or use [Stat]→ Test →ZTest
Testing a Claim about a Mean: 𝜎 Known
A simple random sample of 50 adults is obtained, and each
person’s red blood cell count (in cells per microliter) is measured.
The sample mean is 5.23. The population standard deviation for
red blood cell counts is 0.54. Use a 0.01 significance level to test
the claim that the sample is from a population with mean less
than 5.4, which is a value often used for the upper limit of the
range of normal values. What do the results suggest about the
sample group?
Testing a Claim about a Mean: 𝜎 Known
A Sample of 106 body temperatures with a mean of 98.20°𝐹 was
obtained. Assume that 𝜎 is known to be 0.0565°𝐹. Use a 0.05
significance level to test the claim that the mean body
temperature of the population is equal to 98.6 °𝐹, as is
commonly believed. Is there sufficient evidence to conclude
that the common believe is wrong?
Testing a Claim about a Mean: 𝜎 Known
Homework!!
8-4: 7-19odd