Convicted murderers receive a sentence of an average of 18.7 years in prison ...

  

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. In a recent poll, it was found that 43% of registered U.S. voters would vote for the incumbent president. If 100 registered voters were sampled randomly, it was found that 35% would vote of the incumbent. Test the claim that the actual proportion is 43%.
(4 points)
 

Claim:
H0:
Ha:

 

b. Convicted murderers receive a sentence of an average of 18.7 years in prison. A criminologist wants to perform a hypothesis test to determine whether the mean sentence by one particular judge differs from 18.7 years. (4 points)
 

Claim:
H0:
Ha:

 

Section 7.2: Hypothesis Testing for the Mean (Large Samples)
Use the guidelines at the end of the project.
 

2. Convicted murderers receive an average sentence of 18.7 years in prison. A criminologist wants to perform a hypothesis test to determine whether the mean sentence by one particular judge differs from 18.7 years. A random sample of 40 cases from the court files of this judge is taken. It is found that sample mean is 17.2 years. Assume that the population standard deviation is 7.4 years. Test at the 0.05 significance level.
 

a. Use the critical value z0 method to test the claim that the judge's average sentence is not 18.7 years.
 

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

1. H0:
Ha:
2. a = 0.05
3. Test statistic (z):
4. Critical z0:
5. Rejection Region:
6. Decision:
7. Interpretation:

 

b. Use the P-value method to test the claim that the judge's average sentence is not 18.7 years.
 

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

1. H0:
Ha:
2. a = 0.05
3. Test statistics (z):
4. P-value:
5. Rejection Region:
6. Decision:
7. Interpretation: