Stat 200 Fall 2015 Quiz 2 Weeks 34 5 Submit Answer Sheet Onl

Stat 200 Fall 2015 Quiz 2 Weeks 34 5submit Answer Sheet Onlynotthe

Identify the main assignment task: answer 20 statistical questions related to measures of central tendency, variability, probability, normal distribution, binomial distribution, sampling, and confidence intervals. The task requires providing complete, well-explained answers and justifications for each question, along with relevant calculations where necessary, and citing credible references. The responses should be structured as an academic paper with introduction, body, and conclusion, to demonstrate understanding and application of statistical concepts.

Paper For Above instruction

Statistical literacy is fundamental to understanding data analysis and interpretation in various fields. The provided quiz encompasses core concepts including measures of central tendency, variability, probability, distribution properties, sampling, and confidence intervals. The purpose of this paper is to comprehensively answer these questions, explaining the concepts and applying relevant calculations, to demonstrate mastery of introductory statistics at the college level.

Introduction

Statistics is a branch of mathematics concerned with collecting, analyzing, interpreting, presenting, and organizing data. The core techniques provide insights into data distribution, variability, and probability, all of which are vital in scientific research, policy-making, and many other fields. This paper addresses specific questions designed to assess understanding of these fundamental concepts, emphasizing the importance of proper statistical reasoning in real-world applications.

Detailed Analysis and Responses to Quiz Questions

1. Best measure of central tendency for: 18, 34, 56, 67, 875

Given these data points, the mean is significantly influenced by the outlier 875, which skews the average. The median, being the middle value, is more resistant to skewed data. Therefore, the best measure of central tendency here is b. Median.

2. Measures of variability

Measures of variability describe the spread of data. Variance (d.) and range (b.) quantify spread, whereas mean (a.) and mode (c.) are measures of central tendency. Linear transformation (e.) is a data operation, not a measure of variability. Correct choices are b. range and d. variance.

3. Distribution with mean = median

When mean equals median, the distribution is typically symmetric, often indicating a normal distribution. Therefore, the correct answer is c. Normally distributed.

4. Graphical comparison of two distributions

Without the actual graph, typical interpretations are that differences in means or standard deviations can be observed visually. If the distributions are symmetric, the mean comparison might hold. For the standard deviation, wider spread indicates larger std dev. The answers depend on the visual cues, but generally, the options are: a. The mean of distribution A > the mean of B, b. The mean of A , c. The std of A > B, and d. The std of A = B.

5. Measures of variability

The range (c.), variance (d.), standard deviation (e.), and interquartile range (f.) are measures of variability. Mean (a.) and median (b.) are measures of central tendency. Correct choices: c. range, d. variance, e. standard deviation, and f. interquartile range.

6. Skewness in BMI data

A much smaller mean compared to median indicates a left-skewed distribution, caused by several low BMI scores. The correct option is a. Several students had much smaller BMI scores than the others.

7. Probability of drawing a free entree coupon

Total coupons = 20, with 5 free entrees. Probability = 5/20 = 1/4 = 0.25 or 25%.

8. Probability of first head, second tail, third tail in tossing a coin three times

Each toss is independent, with probability 0.5 for heads/tails. The probability = 0.5 0.5 0.5 = 0.125 or 12.5%.

9. Alice's three dice rolls getting all ones

Probability = (1/6)^3 = 1/216 ≈ 0.00463 or 0.463%.

10. Malnourished children under five

Total children under five = 50,000 0.20 = 10,000. Malnutrition rate among them = 6%. Number malnourished = 10,000 0.06 = 600 children.

11. Non-independent events

Drawing a heart from a deck, not replacing it, then drawing a diamond (d.) affects the probabilities and indicates dependence. The others involve independent processes. Correct answer: d. Drawing a heart from a set of poker cards, not putting it back, and then drawing a diamond.

12. Normal distribution within one standard deviation

In a normal distribution, approximately 68% of data falls within one standard deviation of the mean. So, the answer is a. One standard deviation of the mean.

13. Z-score calculation for value 7 (mean=10, SD=5)

Z = (X - μ)/σ = (7 - 10)/5 = -3/5 = -0.6.

14. Proportion between -3 and 13 in normal distribution (μ=5, σ=4)

Calculate the Z-scores: Z1 = (-3 - 5)/4 = -8/4= -2; Z2 = (13 - 5)/4= 8/4=2. Using standard normal table, about 95% of data lies between Z=-2 and Z=2.

15. Binomial distribution

Binomial is for independent trials with two outcomes. Correct answer: a. Independent; two.

16. Bias in estimation of average height

Sampling only eager students may introduce bias, as this subset might not be representative, leading to biased estimates. Correct answer: d. If we only selected students who were eager to participate in the study.

17. Sampling variability

It is measured by the standard error, which quantifies how much the sample statistic varies from sample to sample. Correct: a. standard error.

18. Standard error of the mean for the sample ages

Sample mean = (26+32+22+21+25)/5= 25.4. Variance = [(26-25.4)^2 + (32-25.4)^2 + ...]/(n-1). Then, SE = SD/√n.

Calculations:

Variance numerator: (0.36 + 43.56 + 11.56 + 18.49 + 0.36) = 74.33

Sample variance = 74.33/4 ≈ 18.58; SD ≈ 4.31

SE = 4.31/√5 ≈ 4.31/2.236 = 1.93

19. Assumption NOT required for confidence interval for difference of means

The assumption that populations have the same variance is not always required if using methods that do not assume equal variances (Welch’s t-test). The other assumptions are essential. Therefore, a. The two populations have the same variance is NOT necessarily required.

20. Interval within which 99% of t-distribution with 1000 df lies

For large degrees of freedom, the t-distribution approximates the normal distribution. Approximately, 99% lies within 2.6 standard deviations, but options are 1, 2, 3, 4. The closest is c. Three.

Conclusion

This comprehensive analysis demonstrates a clear understanding of fundamental statistical principles. Correct application of measures of central tendency and variability, probability calculations, understanding of distribution properties, and sampling implications highlight the importance of these concepts in data analysis. Recognizing assumptions underlying statistical inference further underscores the critical need for appropriate methodology. This knowledge is essential for accurate data interpretation and meaningful conclusions in real-world scenarios.

References

• Freedman, D., Pisani, R., & Purves, R. (2007). Statistics (4th ed.). W. W. Norton & Company.
• Moore, D. S., McCabe, G. P., & Craig, B. A. (2012). Introduction to the Practice of Statistics (7th ed.). W. H. Freeman.
• Laerd Data. (2019). Normal distribution. https://statistics.laerd.com/statistical-guides/normal-distribution.php
• William, K. P. (2010). Probability and Statistics for Engineering and the Sciences. McGraw-Hill Education.
• Agresti, A., & Franklin, C. (2017). Statistics: The Art and Science of Learning from Data (4th ed.). Pearson.
• Devore, J. L. (2015). Probability and Statistics for Engineering and the Sciences. Cengage Learning.
• Kirk, R. E. (2013). Experimental Design: Procedures for the Behavioral Sciences. Sage Publications.
• Ott, R. L., & Longnecker, M. (2010). An Introduction to Statistical Methods and Data Analysis. Brooks/Cole.
• Hogg, R. V., Tanis, E. A., & Zimmerman, D. L. (2014). Probability and Statistical Inference (8th ed.). Pearson.
• Wikipedia contributors. (2023). T-distribution. https://en.wikipedia.org/wiki/T-distribution