1. You are tasked with determining if there is a difference in the average number of years of education of men and women in California. You take a random sample of 1,800 men and 3,200 women. The average education in your sample of men is 13 years with a sample standard deviation of 3 years. The average education in your sample of women is 14 years with a sample standard deviation of 4 years.

   1. What is your null hypothesis?

   2. What is your alternative hypothesis?

   3. State your conclusion regarding the difference in average education,

      using 5% significance.

   4. What is the 95% confidence interval for the difference in average

      wages?

Suppose a group is interested in determining whether teenagers obtain their drivers licenses at approximately the same average age across the country. Suppose that the following data are randomly collected from five teenagers in each region of the country. The numbers represent the age at which teenagers obtained their drivers licenses. Use a level of significance of 0.10.

Northeast      South           West            Central

16.3              16.9              16.4              16.2    

16.1              16.5              16.5              16.6    

16.4              16.4              23.0              16.5    

16.5              16.2              20.2              16.4   

What test are you going to run?

Question 2

What is the null hypothesis?

Question 2 options:

Question 3

What is the alternative hypothesis?

Question 3 options:

Question 4

What is test statistic? Please answer with two decimal places.

A data set has a mean of 700 and a standard deviation of 40.

a. Using Chebyshev's theorem, what percentage of the observations fall between 540 and 860?

b. Using Chebyshev’s theorem, what percentage of the observations fall between 500 and 900?

Using the unit normal table, find the proportion under the standard normal curve that lies between the following values. (Round your answers to four decimal places.)

(a) the mean and z = 1.96

(b) the mean and z = 0

(c)    z = −1.30 and z = 1.30

(d)    z = −0.30 and z = −0.20

(e)    z = 1.00 and z = 2.00

(f)    z = −1.15

B) An insurance company believes that people can be divided into two categories; those who are accident prone and those who are not. The company’s statistics show that an accident-prone person will have a car accident within a one-year period with probability 0.4, whereas this probability decreases to 0.2 for a person who is not accident prone. The data also suggest that 30% of the population is accident prone. What is the probability that a new policyholder will have an accident within a year of purchasing the policy?

B)A spam filter is designed by looking at commonly occurring phrases in spam. Suppose that

80% of all emails sent are spam. In 10% of the spam emails, the phrase "free money" is used,

whereas this phrase is only used in 1% of non-spam emails. A new email has just arrived, which

does mention "free money". What is the probability that it is spam?

STEP BY STEP

Use R for coding

Fit a density estimate to the data set `pi2000` (**UsingR**). Compare with the appropriate histogram. Why might you want to add an argument like `breaks = 0:10-.5` to `hist()`?

I know this much code:

install.packages("UsingR")
library(UsingR)
data(pi2000)

if you put this in R a data set will appear

Tom’s Top End Motors and Fast Eddie’s Quality Cars are two local used car dealers. Tom and Eddie are comparing their sales. The mean monthly sales are similar, however, Tom Monroe (owner of Tom’s Top End Motors) thinks his sales are no more consistent than Fast Eddie’s. Below is a listing of the number of cars sold for the last eight months for Tom’s Top End Motors and for the last seven months for Fast Eddie’s Quality Cars.

Conduct a hypothesis test (using α = 0.05) to see if you agree with Tom’s view that his sales are no more consistent.

List all the steps of the hypothesis test and write a note to Tom telling him whether you agree with him or not and back up your conclusion.

A new drug for pain relief is being tested within a given palliative care population. The new drug is being compared to an already approved pain relief drug that is commonly used in providing palliative care to patients who experience chronic severe pain. Assume the patients are asked to rate the pain on a scale from 1 to 10, and the data presented below was obtained from a small study designed to compare the effectiveness of the two drugs. Set up and interpret the results of a Mann-Whitney U test with an alpha of .05.

                        Pain Rating as Reported by Patients

Old Drug           1          3          3          4          6         

New Drug         1          2          3          3          7

A) We fail to reject H₀, which states the two populations are equal at the alpha equals .05 level because the calculated U value of 10.5 is greater than the critical U value of 2.

B) We fail to reject H₀, which states the two populations are equal at the alpha equals .05 level because the calculated U value of 14.5 is greater than the critical U value of 2.

C) We reject H₀ in favor of H₁, which states the two populations are not equal at the alpha equals .05 level because the calculated U value of 10.5 is greater than the critical U value of 2.

D) We reject H₀ in favor of H₁, which states the two populations are not equal at the alpha equals .05 level because the calculated U value of 14.5 is greater than the critical U value of 2.

10.4.36 Determine the​ upper-tail critical values of F in each of the following​ two-tail tests.

a. alphaequals0.05​, n1equals25​, n2equals16 .

b. alphaequals0.02​, n1equals25​, n2equals16 .

c. alphaequals0.10​, n1equals25​, n2equals16

(Round to two decimal places as​ needed.)

A) Assume that 12 jurors are randomly selected from a population in which 87% of the people are Mexican-Americans. Refer to the probability distribution table below and find the indicated probabilities.

Find the probability of exactly 5 Mexican-Americans among 12 jurors.
P(x=5)=P(x=5)=

Find the probability of 5 or fewer Mexican-Americans among 12 jurors.
P(x≤5)=P(x≤5)=

Does 5 Mexican-Americans among 12 jurors suggest that the selection process discriminates against Mexican-Americans?

yes?

no?

B) A company prices its tornado insurance using the following assumptions:
• In any calendar year, there can be at most one tornado.
• In any calendar year, the probability of a tornado is 0.12.
• The number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year.
Using the company's assumptions, calculate the probability that there are fewer than 4 tornadoes in a 14-year period.

Practice Problems (Chapters 7 and 8)

Chapter 7       

1.         Which would you expect to be more variable: (a) the distribution of scores in a population or (b) the distribution of sample means based on random samples of 25 cases from this population. Explain.

2. Given a normal distribution of scores that has a mean of 50 and a standard deviation of 10, what is the probability of selecting a score that is greater than 65? If a random sample of 10 scores were selected from this population, what is the probability that the mean score for this sample would be greater than 65?

3. In a short paragraph, explain the logic of inferential statistics (The Hinkle et al. text refers to this as the chain of reasoning in inferential statistics).

4. What is the central limit theorem and what role does it play in inferential statistics?

Chapter 8       

5. Describe a study in which a one sample t-test is appropriate. Be sure to state your research question, hypotheses, significance level, critical value, etc.

6. List the steps in the hypothesis testing sequence.

7. In a short paragraph, explain Type I and Type II errors to an audience that has no previous experience with statistics.

8.         What is meant by statistical significance? Why does your author suggest that it may not always be adequate for purposes of research?

9.         Provide an example of the following: (a) A research problem appropriate for a non-directional test using the one-sample z-statistic. (b) A research problem appropriate for a directional test using the one-sample t-statistic.

10.       Consider the data in problem 11 in the text (page 199). Enter these data into SPSS and conduct a test of the null hypothesis.

Practice Problems (Chapters 9 and 11)

Chapter 9

1.         Given a sample mean of 12.5 based on 25 cases and a population variance of 10, construct a 95% confidence interval for the population mean. Interpret the resulting interval.

2.         What can be expected to happen to the length of a confidence interval as the size of the sample used to construct it increases. Explain.

3.         In a short paragraph, explain the logic of confidence intervals.

4.         Can confidence intervals be used to test hypotheses? Explain.

Chapter 11

5.         Describe a research study appropriate for an independent measures t-test.

6.         Describe a research study appropriate for a dependent samples t-test.

7.         Consider the data in problem 4 in Chapter 11 (p. 273). Enter these data into SPSS and conduct a test of the null hypothesis. Compute a measure of effect size and construct a 95% confidence interval for your study.

8.         Consider the data in problem 5 in Chapter 11 (p. 273). Enter these data into SPSS and conduct a test of the null hypothesis. Compute a measure of effect size and construct a 95% confidence interval for your study.

How much "error" is too much before you are no longer confident about your estimates or research findings? Do sampling methods have anything to do with this? Discuss.

The following relative frequency distribution was constructed from a population of 650. Calculate the population mean, the population variance, and the population standard deviation.

Population Mean -

Population Variance -

Population Standard Deviation -

Define each and provide an example.

-1 Convenience Sample

-2 Cross-sectional research design

-3 Research Ethics

-4 Randomization “ Data Collection”