# Hyplthesis Testing of Mean & Proportion

Section 7.1 : Introduction to Hypothesis Testing

1. State the claim mathematically. Then write the null and alternative hypothesis. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. (References: Definition of a statistical hypothesis on page 365, example 1 on page 366 and example 3 on page 371; end of section exercises 19 - 22 page 375, 23 - 28 page 376)

a. A candidate for mayor of a city claims to be favored by at least half the voters. Test this candidates claim. (4 points)

Answer: claim:

H0 :

Ha :

Test :

b. The mean age of bus drivers in Chicago is 50.9 years. Test the claim that the mean age differs from this. (4 points)

Answer: claim:

H0 :

Ha :

Test :

Section 7.2: Hypothesis Testing for the Mean (Large Samples)

Use the guidelines at the end of the project.

2. Use the method specified to perform the hypothesis test for the population

mean . A fast food outlet claims that the mean waiting time in line is less than 4.9 minutes. A random sample of 60 customers yield a sample mean of 4.8 minutes. From past studies it is know that the standard deviation is 0.6 minutes. At  = 0.05, test the fast food outlet's claim

a. Use the critical value z0 method from the normal distribution.

(References: example 7 though 10 pages 385 - 388, end of section exercises 39 - 44 pages 392 - 393) (6 points)

Answer: Given data

1. H0 :

Ha : c

2.  =

3. Test statistics:

4. P-value or critical z0 or t0.:

5. Rejection Region:

6. Decision:

7. Interpretation:

b. Use the P-value method.

(References: example 1 though 5 pages 379 - 383, end of section exercises 33 - 38 pages 391 - 392) (6 points)

Answer: Given data

1. H0 :

Ha :

2.  =

3. Test statistics:

4. P-value or critical z0 or t0.

5. Rejection Region:

6. Decision:

7. Interpretation:

Section 7.3: Hypothesis Testing for Mean (Small Samples)

3. The Daily Planet Transit Company claims that the mean waiting time for train during rush hour is less than 7 minutes. As random sample of 20 waiting times has a mean of 5.2 minutes with a standard deviation of 2.1 minutes. Assume the distribution is normally distributed.

a. Use the critical value t0 method from the normal distribution to test for the population mean . Test the company's claim.

(References: example 1 though 5 pages 397 - 401, end of section exercises 23 - 28 pages 404 - 405) (6 points)

Answer: Given data

1. H0 :

Ha :

2.  =

3. Test statistics:

4. P-value or critical z0 or t0.

5. Rejection Region:

6. Decision:

7. Interpretation:

b. Use the critical value t0 method from the normal distribution to test for the population mean . Test the company's claim at the level of significance  = 0.01

(References: example 1 though 5 pages 397 - 401, end of section exercises 23 - 28 pages 404 - 405) (6 points)

Answer: Given data

1. H0 :

Ha :

2.  =

3. Test statistics:

4. P-value or critical z0 or t0.

5. Rejection Region:

6. Decision:

7. Interpretation

Section 7.4: Hypothesis Testing for Proportions.

4. For a candidate to win in a congressional district, he has to have won over half of the vote. The Republican candidate takes a poll to assess his chances in a two-candidate race. He polls 1200 potential voters and find that 621 plan to vote for the Republican candidate. Does the Republican candidate have a chance to win? Use a level of significance of a = 0.05. (Round phat to 4 decimal places.)

Answer: Given data

1. H0 : Ha :

2. a =

3. Test statistics:

4. P-value or critical z0

5. Rejection Region:

6. Decision:

7. Interpretation:

Unit Projects should be uploaded to the Dropbox for the appropriate Unit.

Projects will be submitted as a Microsoft Word document with a doc file. All Projects are due by Tuesday at 11:59 PM ET of the assigned Unit.

NOTE: Project problems should not be posted to the Discussion threads. Questions on the project problems should be addressed to the instructor by sending an email or by attending office hours.

Guidelines -- Hypothesis Testing Steps:

1. State H0 and Ha.

2. Specify the level of significance alpha a.

3. Determine the test statistic, either z or t. Find the test statistic using the given data.

4. Find the P-value or the critical value(s) z0 or t0. Use the method specified in the problem statement.

5. Define the rejection region using either the P-value method or critical values from the Normal distribution.

6. Make a decision to reject or fail to reject the null hypothesis.

7. Interpret the decision in the context of the original claim.

#### Solution Summary

The solution provides step by step method for the calculation of testing of hypothesis. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.