Econ 3788                 Practice Problems 3                   Dr. Usip
                    
Please Do The Problems First Before Studying My Solutions.                        

Chapter 7: Sampling & Sampling Distribution Problems
Part 1: Sampling                 Text #3, p. 305

Part 2: Sampling Distribution of the Sample Mean    
To estimate the mean age for a population of 4000 employees, a simple random sample of 40 employees is selected.
1. Would you use the finite population correction factor (FPCF) in calculating the standard error of the mean? Explain.

2. If the population standard deviation is σ = 8.2 years, compute the standard error (a) with the FPCF and (b) without the FPCF.

3. What is the probability that the sample mean age of the employees will be within ±2 years of the population mean age, µ?

Part 3: Sampling Distribution of the Sample Proportion  
Forty-two percent of primary care doctors think that their patients receive unnecessary medical care (Reader's digest, December 2011/January 2012). Suppose a random sample of 300 primary care doctors were taken for this study. Use this information to answer these questions.

1. In words, what is the variable of interest, X, in the context of this problem?

2. Show the sampling distribution of the proportion of doctors who think their patients receive unnecessary medical care.   

3. What is the probability that the sample proportion will be within ±.03 of the population proportion?
       
Chapter 8: Interval Estimation Problems
Part 1: Estimation for the population mean, µ.
One measure of engine performance is fuel efficiency which is usually expressed as miles per gallon (mpg). In a recent study to assess the performance of midsize hybrid cars, the following mpg values were randomly recorded while the car was set to 60 mpg by cruise control.

1. What is the point estimate of the population mean mpg?

2. What is the standard error of the estimator? Interpret its meaning. 

3. Assuming that the population of the highway readings of hybrid cars is normally distributed,
   a. what is the 95% margin of error?

   b. develop a 95% confidence interval for the population mpg.

   c. Suppose a sticker information on a midsize hybrid vehicle states a higher average mpg of 27 (manufacturer's claim), are your results consistent with the manufacturer's claim? Explain.

Part 2: Estimation for the Population proportion, P.
A congressional committee was recently charged with estimating the percentage of adult Americans without health care insurance coverage.  The committee conducted a sample survey and found that 87 out of 562 adult Americans did not have health care insurance. Use this information to answer these questions.

1. Define the variable X, the random variable of interest for this problem?

2. At 95% confidence, what is the margin of error?

3. What is the 95% confidence interval for the proportion of adult Americans without health care insurance coverage?

4. Briefly, write a report of your findings to the congressional committee that paid you for the study.

Chapter 9: Hypothesis Testing Problems
                 (Please, be sure to state H₀ and H_A) 
Part 1: Hypothesis Testing about the Population Mean, µ.
Which is cheaper: eating out or dining in? The mean cost of dining in by cooking steak, broccoli and rice bought at a grocery store is $13.04 according to Money.msn website (2012). A sample of 100 neighborhood restaurants showed a mean price of $12.75 and a standard deviation of $2 for a comparable restaurant meal.
 
1. State the appropriate null and alternative hypotheses for a test to determine whether the sample data support the conclusion that the meal cost of a restaurant meal is less than fixing comparable meal at home.   

2. Using the sample of 100 restaurants, what is the p-value?

3. Using the P-value (PV) approach at α = .05, what is your conclusion?
   
4. Repeat the preceding hypothesis test using the critical value (CV) approach. Is your conclusion the same as in part 'c'?

Part 2: Hypothesis Testing about the Population Proportion, P.                  Text  #41,  p. 415.

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Last revised: Tuesday, May 18, 2021.