Stat 226 Supplemental Instruction
Hypothesis Testing
Using the “Decision Rule”
p-value ≤ α
p-value > α
Reject the null hypothesis
Fail to reject the null hypothesis
In the table below, fill in the missing columns. For the inequality sign, write “≤” or “>.”
P-value
Inequality Sign
0.001
0.025
0.25
0.005
0.05
Alpha
Reject/Fail to Reject H0
0.005
0.01
0.05
0.015
0.01
True/False Questions
_____ Rejecting H0 implies that HA is true.
_____ Failing to reject the null hypothesis when the null hypothesis is false is a Type II Error.
_____ Alpha is the level of statistical significance against which the p-value is compared.
_____ A T-statistic of 1.697 implies that we have obtained a sample mean 1.697 standard errors below
the value of the population mean stated in the null hypothesis.
_____ If alpha is equal to 0.01 and the p-value is equal to 0.025, and you reject the null hypothesis, you
could be committing Type I error.
_____ In order to accurately interpret the p-value obtained from a hypothesis test, we must assume the
null hypothesis is true.
_____ The inequality sign in the alternative hypothesis determines the p-value.
_____ A two-sided hypothesis using a significance level α and a 100(1-α)% confidence interval are
equivalent.
Practice Problems
A manufacturer of frontal airbags used in semi trucks claims that the true average volume of their airbag
is 140 cm3. A random sample of n = 9 airbags off the production line yielded a sample mean volume of
141.29 cm3 and a standard deviation of 1.44 cm3. We can assume that the distribution of airbag
volumes is normal. Do the data support the manufacturer’s claim at the 0.01 significance level?
1. State the null and alternative hypothesis.
2. What is the value of the test statistic?
3. What is the appropriate p-value?
Prob > |t|
Prob > t
Prob < t
t Test
0.0276
0.0138
0.9862
4. Make a conclusion about H0 based on your p-value and the given level of significance.
5. Provide an interpretation of a type I error in terms of this problem.
6. Provide an interpretation of a type II error in terms of this problem.
A random sample of 30 Iowa State business students yielded an average of 1.86 pieces of paper printed
from the Gerdin labs per day and a standard deviation of 1.28. Is there evidence that the average
number of pieces of paper printed by all business students is different from 1.5? Test this claim at the
0.05 level of significance.
1. State the null and alternative hypothesis.
2. What is the value of the test statistic?
3. Based on the alternative, what is the appropriate p-value?
t Test
Prob > |t|
0.1343
Prob > t
0.0671
Prob < t
0.9329
4. Make a decision about H0 based on your p-value and the given level of significance.