Download - Hypothesis Testing-Z-Test

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Please find the critical value(s) for each situation and draw the appropriate figure, showing the critical region:

a. Two-Tailed Test α=0.05b. Right-Tailed Test α=0.02c. Left-Tailed Test α=0.01

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Speaking of Homework / Grades

• Check Edbox• Not everyone has handed in their

homework calendars for Ch. 8• Barring any discussed changes to

your grade, what you see on Edbox is an accurate reflection of what will go home with your quarter grades.

• A statistical test uses the data obtained from a sample to make a decision about whether the null hypothesis should be rejected.• The numerical value obtained from a

statistical test is called the test value.

Review

• The critical value separates the critical region from the noncritical region.• The critical region is the range of

values of the test value that indicates that there is a significant difference and that the null hypothesis should be rejected.

Review

Two Tailed v. Left/Right-Tailed Test

NonCriticalRegion

Critical Region

Critical Value

Right-Tailed

CV=1.28

α=0.10

NonCriticalRegion

Critical Region

Critical Value

Left-Tailed

CV=-1.65

α=0.05

NonCriticalRegion

Critical Region Critical Region

Critical Value Critical Value

Two-Tailed

CV=-1.65 CV=1.65

α=0.10

α/2=0.05α/2=0.05

Five Steps in Hypothesis Testing1. State the hypotheses and identify the claim.

Make sure to use proper symbols. Please include proper units when given.

2. Find the critical value(s).Include a diagram that displays all the pertinent information.

3. Compute the test value.Include the proper formula. Round properly. Locate and place test value on the diagram.

4. Make the decision to reject or not to reject the null hypothesis.Use a complete sentence.

5. Summarize the result.Use complete sentence(s) that states the final conclusion clearly in the context of the problem. Use the proper vocabulary and statistical terms. Include the proper units if they are given.

Section 9-3

Z-Test for a Mean

When to Use the z Test

• The z test is a statistical test for the mean of a population. It can be used when n> 30 or when the population is normally distributed and σ is known.

Formula for the z Test

Where:• = sample mean• µ = hypothesized population mean• σ = population standard deviation• n = sample size

Hypothesis Testing

Traditional Method

Example 9-3• A researcher reports that the average salary of assistant

professors is more than $42,000. A sample of 30 assistant professors has a mean salary of $43, 260. At = 0.05, test the claim that assistant professors earn more than $42,000 a year. The standard deviation of the population is $5230.

H0:H1:

µ≤$42,000µ>$42,000 (Claim)

NonRejectionRegion

Example 9-3• A researcher reports that the average salary of assistant professors is more than $42,000. A sample of 30 assistant

professors has a mean salary of $43, 260. At = 0.05, test the claim that assistant professors earn more than $42,000 a year. The standard deviation of the population is $5230.

NonRejectionRegion

Critical Region

Right-Tailed

CV=1.65

43,260 42,0005230

1.32z

Step 4:Do Not Reject the null hypothesis.

Step 5:There is not enough evidence to support the claim that assistant professors earn more on average than $42,000 a year

Step 3:

1.32z

• A researcher claims that the average cost of men’s athletic shoes is less than $80. He selects a random sample of 36 pairs of shoes from a catalog and finds the following cost (in dollars). (The costs have been rounded to the nearest dollar.) Is there enough evidence to support the researchers claim at = 0.10? Reference Page 351 for costs.

Example 9-4

H0:H1:

µ≥$80µ<$80 (Claim)

NonRejectionRegion

Example 9-4• A researcher claims that the average cost of men’s athletic shoes is less than $80. He selects a random sample of 36

pairs of shoes from a catalog and finds the following cost (in dollars). (The costs have been rounded to the nearest dollar.) Is there enough evidence to support the researchers claim at = 0.10?

NonRejectionRegion

Critical Region

Left-Tailed

CV=-1.28

75 8019.2

1.56z

Step 4:Reject the null hypothesis.

Step 5:There is enough evidence to support the claim that the average cost of men’s athletic shoes is less than $80

Step 3:

1.56z

• The Medical Rehabilitation Education Foundation reports that the average cost of rehabilitation for stroke victims is $24,672. To see if the average cost of rehabilitation is different at a particular hospital, a researcher selects a random sample of 35 stroke victims at the hospital and finds that the average cost of their rehabilitation is $25,226. At = 0.01, can it be concluded that the average cost of stroke rehabilitation at a particular hospital is different from $24,672? Assume SD is 3251.

Example 9-5

Example 9-5• The Medical Rehabilitation Education Foundation reports that the average cost of rehabilitation for stroke victims is $24,672. To see if the average cost

of rehabilitation is different at a particular hospital, a researcher selects a random sample of 35 stroke victims at the hospital and finds that the average cost of their rehabilitation is $25,226. At = 0.01, can it be concluded that the average cost of stroke rehabilitation at a particular hospital is different from $24,672? Assume SD is 3251.

NonRejectionRegion

Critical Region

Two-Tailed

CV=-2.58 CV=2.58

25,226 24,6723251

1.01z

Step 4:Do Not Reject the null hypothesis.

Step 5:There is not enough evidence to support the claim that the average cost of rehabilitation at the particular hospital is different from $24,672

Step 3:

1.01z

Five Steps in Hypothesis Testing1. State the hypotheses and identify the claim.

Make sure to use proper symbols. Please include proper units when given.

2. Find the critical value(s).Include a diagram that displays all the pertinent information.

3. Compute the test value.Include the proper formula. Round properly. Locate and place test value on the diagram.

4. Make the decision to reject or not to reject the null hypothesis.Use a complete sentence.

Your Moment of Zen

Read Section 9-3

Pg. 358: 14-20all

Assigned: 2012.04.11

Due: 2012.04.16

HOMEWORK

Please write this on your Calendar

In the population, the average IQ is 100 with a standard deviation of 15. A team of scientists wants to test a new medication to see if it has an effect on intelligence (as measured by IQ). A sample of 40 participants who have taken the medication has a mean of 140. Did the medication affect intelligence? Use α=0.05.

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