http://www.ck12.org Chapter 7. Sampling Distributions and Estimations
Example:
You have just taken ownership of a pizza shop. The previous owner told you that you would save money if you
bought the mozzarella cheese in a 4.5 pound slab. Each time you purchase a slab of cheese, you weigh it to ensure
that you are receiving 72 ounces of cheese. The results of 7 random measurements are 70, 69 , 73 , 68 , 71 ,69 and
71 ounces. Are these differences due to chance or is the distributor giving you less cheese than you deserve?
Solution:
Begin the problem by determining the mean of the sample and the sample standard deviation.
This can be done using the graphing calculator. ̄x≈ 70 .143 ands≈ 1 .676.
t=
x ̄−μ
s/√
n
t=70. 143 − 72
1. 676 /
√
7
t≈− 2. 9315Example:
In the example before last the test statistic for testing that the mean weight of the cheese wasn’t 72 was computed.
Find and interpret theP-value.
Solution:
The test statistic computed in the example before last was− 2 .9315. Using technology, theP−value is 0.0262. If
the mean weight of cheese is 72 ounces, the probability that the volume of 7 random measurements would give a
value oftgreater than 2.9315 or less than− 2 .9315 is about 0.0262.
Example:
In the previous example, theP-value for testing that the mean weight of cheese wasn’t 72 ounces was determined.
a) State the hypotheses.
b) Would the null hypothesis be rejected at the 10% level? The 5% level? The 1% level?
Solution:
a)H 0 : The mean weight of cheese,μis 72 ounces.
Hα:μ 6 = 72b) Because theP-value of 0.0262 is less than both 10% and 5%, the null hypothesis would be rejected at these levels.
However, theP-value is greater than 1% so the null hypothesis would not be rejected if this level of confidence was
required.
Lesson Summary
A test of significance is done when a claim is made about the value of a population mean. The test can only be
conducted if the random sample taken from the population came from a distribution that is normal or approximately
normal. When you usesto estimateσ, you must usetinstead ofzto complete the significance test for a mean.