AP STATISTICS: Chapter 11
1.
Name ______________________
On a college entrance examination, the mean score is 500, while the standard deviation is 100. A high
school principal boasts better than average scores for her graduates. To support her claim, she randomly
selects 75 graduates and determines that the mean score for this sample is 515. Is her claim actually
supported by the sample data? Test the claim at the α = 0.01 significance level.
Step 1:
Step 1:
This is a …………………………………………………… test of …………………………….
Step 2:
Step 2:
…………………………………………………………………………………………………………………………………
Write the name of the test.
Identify the parameter(s) in
symbols/words.
Step 3:
…………………………………………………………………………………………………………………………………
Step 3:
Write the assumptions needed
for this test.
Step 4:
…………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………
Step 4:
Write the hypotheses.
Step 5:
Find the critical value(s). Draw
a bell curve, label critical
value(s) and shade critical
region.
…………………………………………………………………………………………………………………………………
H0: ……………………………
Ha: ……………………………
Step 5:
Critical value(s): z = …………………
–3
Step 6:
Step 6:
Find the test statistic. Show
formula and/or substitutions.
Label it on the bell curve.
Step 7:
Find the P-value associated with
this test statistic.
Step 8:
Write a mathematical conclusion
based on H0: Either “Reject” or
“Fail to reject”.
Step 9:
Write a non-mathematical
conclusion, including an
interpretation of the P-value.
–2
–1
0
1
2
3
Test Statistic:
z=
…………………………………………………………………………………………………
Step 7:
P-value = …………………
Step 8:
∴ We ………………………………………………………………… at the ……… significance
level.
Step 9:
…………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………
2. Triple X sugar is packed in boxes labeled 5 pounds. When 100 packages are randomly selected and
measured, the sample mean is found to be 4.95 pounds. At the 0.01 significance level, test the claim that
the sample comes from a population in which the mean weight is less than 5 pounds. Assume that the
population standard deviation is 0.15 pounds.
Step 1:
Step 1:
This is a …………………………………………………… test of …………………………….
Step 2:
Step 2:
…………………………………………………………………………………………………………………………………
Write the name of the test.
Identify the parameter(s) in
symbols/words.
Step 3:
…………………………………………………………………………………………………………………………………
Step 3:
Write the assumptions needed
for this test.
…………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………
Step 4:
Write the hypotheses.
Step 4:
H0: ……………………………
Ha: ……………………………
Step 5:
Find the critical value(s). Draw
a bell curve, label critical
value(s) and shade critical
region.
Step 5:
Critical value(s): z = …………………
–3
Step 6:
Find the test statistic. Show
formula and/or substitutions.
Label it on the bell curve.
Step 7:
Find the P-value associated with
this test statistic.
Step 8:
Write a mathematical conclusion
based on H0: Either “Reject” or
“Fail to reject”.
Step 9:
Write a non-mathematical
conclusion, including an
interpretation of the P-value.
Step 6:
–2
–1
1
2
3
Test Statistic:
z=
…………………………………………………………………………………………………
Step 7:
P-value = …………………
Step 8:
∴ We ………………………………………………………………… at the
Step 9:
0
…………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………
3. The engineering department of a car manufacturer claims that the fuel consumption rate of one
model is equal to 35 miles per gallon with a standard deviation of 4 miles per gallon. The advertising
department wants to test this claim to see if the announced figure should be higher or lower than 35
miles per gallon. A sample of 50 cards yields a sample mean of 33.6 mpg. Test the claim by using a
0.05 level of significance.
Step 1:
Step 1:
This is a …………………………………………………… test of …………………………….
Step 2:
Step 2:
…………………………………………………………………………………………………………………………………
Write the name of the test.
Identify the parameter(s) in
symbols/words.
Step 3:
…………………………………………………………………………………………………………………………………
Step 3:
Write the assumptions needed
for this test.
Step 4:
…………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………
Step 4:
Write the hypotheses.
Step 4a:
Find the critical value(s). Draw
a bell curve, label critical
value(s) and shade critical
region.
Step 5:
Step 4a:
Write a mathematical conclusion
based on H0: Either “Reject” or
“Fail to reject”.
Step 8:
Write a non-mathematical
conclusion, including an
interpretation of the P-value.
Critical value(s): z = …………………
–3
Step 5:
Step 6:
Step 7:
Step 8:
–2
–1
0
1
2
3
Test Statistic:
z=
Find the P-value associated with
this test statistic.
Step 7:
H0: ……………………………
Ha: ……………………………
Find the test statistic. Show
formula and substitutions.
Label it on the bell curve.
Step 6:
…………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………
P-value = …………………
∴ We ………………………………………………………………… at the ……… significance
level.
…………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………
………………………………………………………………………………