Question

1.The sample mean is an unbiased estimator for the population mean. This means:

1. The sample mean always equals the population mean.
2. The average sample mean, over all possible samples, equals the population mean.
3. The sample mean will only vary a little from the population mean.
4. The sample mean has a normal distribution.

2.Which of the following statements is CORRECTabout the sampling distribution of the sample mean:

1. The standard error of the sample mean will decrease as the sample size increases.
2. The standard error of the sample mean is a measure of the frequency among repeated samples.
3. The sampling distribution does not always follow a normal distribution even when n (the sample size) is large.  
4. The standard error of the sample mean will increase as the sample size increases.

3.A simple random sample (SRS) is taken from a population. Which statement is CORRECT?

1. µ is an estimate of x-bar; σ is an estimate of s.
2. x-bar is an estimate of µ; s is an estimate of σ.
3. µ is an estimate of x-bar; s is an estimate of the standard deviation of the sample mean.
4. µ is an estimate of s; σ is an estimate of x-bar

4Which of the following statements about confidence intervals is CORRECT?  A confidence interval is:

1. The estimate plus or minus the t-score.
2. The parameter plus or minus the t-score times the standard error.
3. The estimate plus or minus the margin of error.
4. None of the above.

5.Which of the following statements about confidence intervals is WRONG?

5. If we keep the sample size fixed, the confidence interval gets wider as we increase the confidence coefficient.
6. A confidence interval for a mean always contains the sample mean.
7. If we keep the confidence coefficient fixed, the confidence interval gets narrower as we increase the sample size.
8. If the standard error increases, the confidence interval decreases in width.

6.Which of the following statements is CORRECT?

1. An extremely small p-value indicates that the actual data differs markedly from that expected if the null hypothesis were true.
2. The p-value measures the probability that the hypothesis is true.
3. The larger the p-value, the stronger the evidence against the null hypothesis
4. The p-value measures the probability that the sample mean is more than the population mean.

7.The average time it takes for a person to experience pain relief from aspirin is 25 minutes. A new ingredient is added to help speed up relief. Let µ denote the average time to obtain pain relief with the new product. An experiment is conducted to verify if the new product is better. What are the null and alternative hypotheses?

1. H₀: µ = 25

H_A: µ = 25

2. H₀: µ = 25

       H_A: µ < 25

3. H₀: µ < 25

       H_A: µ = 25

d.    All of the above is correct since both the null and alternative hypotheses can be set up arbitrarily.

8.Suppose you are conducting a two sample significance testing. The null hypothesis states that

1. The samples come from populations with different means
2. The samples have the same sample mean
3. The samples have very different sample means
4. The samples come from populations with the same mean

9.In a random sample of 100 individuals, 12 are left-handed. Which of the following is a plausible 95% confidence interval for the proportion of left-handed people in the population?

1. 0.056 to 0.184
2. 0.037 to 0.103
3. 0.056 to 0.084
4. 0.120 to 0.240  

DEFINITION:5 points each: write a one or two sentence definition of each term.

1000. of Error

150447976774. Error

13031. Alternative Hypothesis

2644323590070148. Significance

SHORT ANSWER:6 points each: write your answer in the space following each question.

3270399981102. Bush believed that “No Child Left Behind” improves test scores of school children. You have data before and after the implementation of the program. Using simple regression analysis, how would you test for the effect of the policy? Identify the dependent variable and the independent variable. Define the null and alternative hypotheses in words and in statistical notation.

13031. government’s Current Population Survey interviewed more than 131,000 people aged between 25 and 65, who are in the labor force, in March 2002. The mean income of this group was $44,776. median income for the same group was $35,680. Is each of the bold numbers a parameter or a statistic? Explain.

1. Gallup Poll in November 2002 found that 51% of the people in its sample said “Yes” when asked, “Would you like to lose weight?” Gallup announced: For results based on the total sample of national adults, one can say with 95% confidence that the margin of sampling error is +3 percentage points.”

1. What does it mean to say that we have “95% confidence” in this interval?

2. What is the 95% confidence interval for the percent of all adults who want to loose weight?

391522. asked why statistical significance appears so often in research reports, a student says, “Because saying that results are significant tells us that they cannot easily be explained by chance variation alone.” Do you think this statement is essentially correct? Explain your answer.

0. 13031. time taken for Leslie to travel home to school is distributed normally with a mean of 70 minutes and a standard deviation of 10 minutes.
1. What percentage of the time will the trip take less than 60 minutes?

2. Is 100 minutes an unusually long commuting trip?  What percentage of the time will this occur?

INTERPRETATION OF COMPUTER OUTPUT (10 points each).

1. The following gives the results of the regression output from Stata.

Dependent variable: travel time to work in minutes.

Independent variable: a disability affecting work indicator

--------------------------------------------------------------------------------------------------

    TRAVELTIME          |     Coef.     Std. Err.        t      P>|t|                Beta

-------------+------------------------------------------------------------------------------------

      Work Disability        |     1.595        2.299       0.694   0.488                0.023  

                      _cons          |  21.754          .727     29.904   0.000        

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For the following questions, please use 3 places of decimal.

1. What value does the work disability variable take if you are not disabled?

2. What is the average travel time to work for a person without a disability?

3. What is the difference between the time traveled by disabled persons and those who are not disabled?

4. What is the average travel time to work for disabled persons?

5. Are disabled people significantly different from non-disabled people in the time taken to reach work? Explain.

2. The following gives the results of the regression output from STATA.

Dependent variable: Wage and Salary Income.

Independent variable: a disability affecting work indicator

--------------------------------------------------------------------------------------------------

    INCWS                      |   Coef.            Std. Err.        t           P>|t|            Beta

-------------+------------------------------------------------------------------------------------

               Work Disability|    -9303.723    4475.500    -2.079    0.038         -0.070                  

                              _cons |   37931.813    1416.073    26.787    0.000                

--------------------------------------------------------------------------------------------------

1. Write the regression equation for the above output.

2. What information does the constant give you?

3. What information does the slope give you?

4. Write the null and alternative hypotheses to test whether or not disabled people earn less than non-disabled people.

5. At the 5% significance level, do disabled people earn less than non-disabled people?

6. At the 1% significance level, do disabled people earn less than non-disabled people?

Answer 1

1. The expected value of the sample mean is equal to the population mean µ. Therefore the correct answer is

b)The average sample mean, over all possible samples, equals the population mean

2. Standard error of sample mean and sample size are inversely related. Therefore the correct answer is

a)The standard error of the sample mean will decrease as the sample size increases

3. Answer for this is

b) x-bar is an estimate of µ; s is an estimate of σ.

4. We don't know what the sample size is. Depending on the sample size we use a t score or a z score. Without information on the sample size we cannot use a random statistic. Hence the correct answer would be d) None of the above

However if the sample size is sufficiently less, then the correct answer would be

a)The estimate plus or minus the t-score.