Eco 302: Fall 20 Assignment 2 Chapters 8, 9, 10, And 13 ✓ Solved

Eco 302: Fall-20-Assignment 2: Chapters: 8, 9, 10, and 13

This assignment consists of True/False questions, Multiple Choice questions, and Essay type questions based on Chapters 8, 9, 10, and 13.

For the True/False Questions, each carries 2 points; for the Multiple Choice Questions, each carries 4 points; and for the Essay type questions, each carries 10 points. The total assignment points add up to 250.

Answer the questions as follows:

True/False Questions should address statistical principles such as sample distributions, mean values, hypothesis testing, and regression analysis.

Multiple Choice Questions cover similar topics, asking students to select correct answers based on their understanding of statistical concepts.

Essay Type Questions require students to solve problems that involve calculations and confidence interval constructions.

Paper For Above Instructions

This essay will address the key statistical concepts outlined in the prompt, providing explanations and answers to the questions posed by the assignment.

True/False Questions

1. The statement that "the sampling distribution must be a normal distribution" is False. The sampling distribution of the sample means approaches normality as the sample size increases due to the Central Limit Theorem.

2. The claim that "sample variance has a divisor of n-1 rather than n" is True. This ensures an unbiased estimate of the population variance.

3. The assertion that "the standard deviation of the sampling distribution increases as the sample size increases" is False. In fact, standard deviation decreases as sample size increases, leading to a more precise estimate of the population parameter.

4. The statement "if a population is known to be normally distributed, then the sample mean must equal the population mean" is True.

5. The assertion about the normal distribution for large samples is True. The sampling distribution follows a normal shape for large samples, regardless of the original population distribution, as per the Central Limit Theorem.

Multiple Choice Questions

1. If the population mean is 48 and standard deviation is 18, then the mean and the standard deviation for the sampling distribution of (X-bar) for n=9 are:

D. 48 and 6 (where standard deviation = population standard deviation/sqrt(n) = 18/sqrt(9) = 6).

2. Given a population mean of 90 lbs and standard deviation of 24 lbs for a sample size of 36, the probability that the average weight exceeds 94 lbs is:

C. 15.87% (using Z-scores).

3. Since the population distribution is normal, D. All of the above statements concerning sample means and standard deviations hold true.

4. For the process of manufacturing bolts, based on random selection, to determine the probability of the mean length exceeding 3.16 inches, the answer is A. 5.48%.

Essay Type Questions

Question 1

For the average weight of sugar packages, to find the probability that 16 randomly selected packages will weigh less than 15.97 ounces: Given the population mean (μ) = 16 ounces and standard deviation (σ) = 0.24 ounces:

The standard error (SE) for this sample mean can be determined using the formula SE = σ/sqrt(n) = 0.24/sqrt(16) = 0.06. The Z-score is calculated as:

Z = (X - μ) / SE = (15.97 - 16) / 0.06 = -0.5. Now, consulting the Z-table for a Z-score of -0.5 gives P(Z

Question 2

For constructing a 99% confidence interval based on sample data of 25 items with a mean of 60 grams and a standard deviation of 9 grams, we compute the margin of error (MOE):

The critical value (Z) for 99% confidence is approximately 2.576. Therefore, the MOE is: MOE = Z (σ/sqrt(n)) = 2.576 (9/sqrt(25)) = 4.629. Consequently, the confidence interval is:

(60 - 4.629, 60 + 4.629) = (55.371, 64.629) grams.

References

  • Montgomery, D.C., & Runger, G.C. (2010). Applied Statistics and Probability for Engineers. Wiley.
  • Weisberg, S. (2005). Applied Linear Regression. Wiley.
  • Casella, G., & Berger, R.L. (2002). Statistical Inference. Duxbury Press.
  • Hinton, P.R. (2004). Statistics Explained. Psychology Press.
  • Pagano, M., & Gauvreau, K. (2000). Principles of Biostatistics. Duxbury Press.
  • Moore, D.S., McCabe, G.P., & Craig, B.A. (2017). Introduction to the Practice of Statistics. W.H. Freeman.
  • George, E.I., & Foster, D.P. (2000). The Risk of Estimating a Probability. Statistics in Medicine.
  • Wackerly, D.D., Mendenhall, W., & Scott, W. (2008). Mathematical Statistics with Applications. Thomson Brooks/Cole.
  • Hogg, R.V., & Tanis, E.A. (2009). Probability and Statistical Inference. Pearson.
  • Gravetter, F.J., & Wallnau, L.B. (2016). Statistics for The Behavioral Sciences. Cengage Learning.

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