Transcript Hypothesis Testing for the Mean: * not known

Hypothesis Testing for the
Mean: 𝜎 not known
Testing a Claim about a Mean: 𝜎 not 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 not
known
3. Either the Population is normal, or 𝑛 > 30
Test Statistic for Testing a Claim about a Proportion
𝑥 − 𝜇𝑥
𝑡= 𝑠
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
A simple random sample of 40 recorded speeds is obtained from
cars traveling on a section of Highway 405 in Los Angeles. The
sample has a mean of 68.4 mi/h and a standard deviation of 5.7
mi/h Use a 0.05 significance level to test the claim that the mean
speed of all cars is greater than the posted speed limit of 65mi/h.
1. 1. 𝐻𝑎 : 𝜇 > 65 claim and 𝐻0 : 𝜇 = 65
2. 𝑡 =
𝑥−𝜇𝑥
𝑠
𝑛
=
68.4−65
5.7/ 40
= 3.77
3. P-value = 0.000537
4. 0.000537 < 0.05 so we reject the null.
5. There is sufficient evidence to support the claim that the
mean is greater than 65 mi/hr.
Or use [Stat]→ Test → TTest
Testing a Claim about a Mean: 𝜎 Known
• In an analysis investigation the usefulness of pennies, the
cents portions of 100 randomly selected credit card charges
are recorded. The sample has a mean of 47.6 cents and a
standard deviation of 33.5 cents. If the amounts from 0 cents
to 99 cents are all equally likely, the mean is expected to 49.5
cents. Use a 0.01 significance level to test the claim that the
sample is from a population with a mean equal to 49.5 cents.
What does the result suggest about the cents portions of
credit charge charges?
Testing a Claim about a Mean: 𝜎 Known
• Homework!!
8-5: 13-27 odd