Information Sheet
Sample problem
Z test with two tails
In a newspaper article it states that the average time for a full time student to complete a BA is five years. A researcher wants to test this claim for the students at her college. Using the graduates of the college for 2013-2015 as the population, the researcher randomly selected a group of 100 students. For that sample, the mean length of time it took to graduate was 4.8 years, with a population standard deviation of 0.5 years. At the 0.05 level of significance, does the newspaper’s statement seem reasonable?
Step One: Identify the claim The mean is 5
Step Two: Put the claim in symbols [pic]
Step Three: What is true if the claim is not true? [pic]
Step Four: Identify the Null and Alternative Hypotheses: [pic]
Step Five: Use the significance level to find the critical value(s) and rejection region
Two tails and 0.05 has critical values of [pic]1.96
[pic]
Step Six: Use the z test formula to determine the z score for the sample data:
[pic]
Step Seven: Make a decision to reject or fail to reject the null, based on the values in step five
and six: Since -4 exceeds -1.96 it is in the rejection region
Step Eight: Answer the question about the claim: It does not seem like the statement
that it takes five years to complete a degree is accurate.
Practice problem
Z test with two tails
In a newspaper article it states that the average time for a full time student to complete an AA is three years. A researcher wants to test this claim for the students at her community college. Using the graduates of the college for 2013-2015 as the population, the researcher randomly selected a group of 35 students. For that sample, the mean length of time it took to graduate was 3.2 years, with a standard deviation of 0.3 years. At the 0.10 level of significance, does the newspaper’s statement seem reasonable?
Step One: Identify the claim
Step Two: Put the claim in symbols
Step Three: What is true if the claim is not true?
Step Four: Identify the Null and Alternative Hypotheses:
Step Five: Use the significance level to find the critical value(s) and rejection region
[pic]
Step Six: Use the z test formula to determine the z score for the sample data:
[pic]
Step Seven: Make a decision to reject or fail to reject the null, based on the values in step five
and six:
Step Eight: Answer the question about the claim:
Practice problem
t test with one tail
A teacher claims that it takes less than 90 minutes to complete her final, on average. A sample of 20 students took an average of 85 minutes with a standard deviation of 5 minutes. With a significance level of .05, is there evidence to support her claim?
Step One: Identify the claim
Step Two: Put the claim in symbols
Step Three: What is true if the claim is not true?
Step Four: Identify the Null and Alternative Hypotheses:
Step Five: Use the significance level to find the critical value(s) and rejection region
[pic]
Step Six: Use the t test formula to determine the t score for the sample data:
[pic]
Step Seven: Make a decision to reject or fail to reject the null, based on the values in step five
and six:
Step Eight: Answer the question about the claim:
Practice problem
Proportion test with one tail
A dean claims that more than 75% of students at her college are in county. In a sample of 33 students, 27 were in county. With a significance level of .01, is there evidence to support her claim?
Step One: Identify the claim
Step Two: Put the claim in symbols
Step Three: What is true if the claim is not true?
Step Four: Identify the Null and Alternative Hypotheses:
Step Five: Use the significance level to find the critical value(s) and rejection region
[pic]
Step Six: Use the proportion test formula to determine the z score for the sample data:
[pic]
Step Seven: Make a decision to reject or fail to reject the null, based on the values in step five
and six:
Step Eight: Answer the question about the claim:
Hypothesis Testing
Practice
Null and Alternative Hypotheses
For the items below, write a null and an alternative hypothesis. Mark the claim with an *
1. The average age of a CCC student is 28.
Ho =
H1 =
2. The average SAT score for a scholarship athlete is less than 450.
Ho =
H1 =
3. They put an average of at least 12 oz of beer in the cup.
Ho =
H1 =
4. A majority (more than 50%) of people favor the tax cut.
Ho =
H1 =
5. The mean is at most 5.
Ho =
H1 =
6. 15% of the students who take the placement test don’t need any basic math classes.
Ho =
H1 =
7. The amount is at least 30%.
Ho =
H1 =
Types of Hypothesis Tests
Which test should be completed? 2: ttest, 1:ztest, 5:1propztest,
Claim about a mean n [pic] 30
Claim about a mean n < 30
Claim about a percentage, proportion, or probability
Critical Values
For the information below, find the critical value(s)
1. Claim about a mean, n = 50, two tails, [pic]= .05
2. Claim about a mean, n = 15, two tails, [pic]=.05
3. Claim about a mean, n = 100, left tail, [pic]=.05
4. Claim about a proportion, two tails, [pic]=.01
5. Claim about a proportion, right tail, [pic]= .10
Practice Problems
1. The National Center for Educational Statistics surveyed 400 college graduates about the length of time required to earn their Bachelor’s degree. The mean is 4.75 years, and the population standard deviation is 1.68 years. Test the claim that it takes less than 5 years to complete a BA. ((=.05)
2. A company claims that the average yearly salary for its employees is $41,680. A sample of 15 employees report their yearly salary. Their mean is $37,400 with a standard deviation of $2500. Test the company’s claim. ((=.05)
3. A university would like to claim that students participating in its study abroad programs will significantly improve their language skills. Researchers tested the claim by comparing a group of study abroad students to the typical results of students who take the language proficiency exam. In the study abroad group 36 of 45 students passed. Typically, 75% of students pass. Can the University tout the benefits of its study abroad program? ((=.01)
Template for a Hypothesis Test
Identify the Null and Alternative Hypotheses:
Use the significance level to find the critical value(s) on the chart and identify rejection region(s)
[pic]
Use the calculator to determine the test value for the sample data:
Make a decision to reject or fail to reject the null:
Answer the question about the claim:
-----------------------
[pic]=5
-1.96
1.96
Rejection
region
Rejection
region
Fail to reject the Null
0
[pic]=
Rejection
region
Rejection
region
Fail to reject the Null
0
[pic]=
Rejection
region
Fail to reject the Null
0
[pic]=
Rejection
region
Fail to reject the Null
0
0
................
................
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