Week 7 Resources Chapter Exercise Page

Week 7eresourceschapterexercisepagelaneet Al142512651217561414617ill

Week 7eresourceschapterexercisepagelaneet Al142512651217561414617ill

Week 7eresourceschapterexercisepagelaneet Al142512651217561414617ill

Week 7 eResources Chapter Exercise Lane et al . Illowsky et al . * Page numbers are approximated due to version control of the eResources , especially for Illowsky et al . Lane et al . Chapter . The formula for a regression equation is Y’ = 2X + 9. a. What would be the predicted score for a person scoring 6 on X? b. If someone’s predicted score was 14, what was this person’s score on X? 6. For the X,Y data below, compute: a. r and determine if it is significantly different from zero. b. the slope of the regression line and test if it differs significantly from zero. c. the 95% confidence interval for the slope. Lane et al . Chapter . At a school pep rally, a group of sophomore students organized a free raffle for prizes. They claim that they put the names of all of the students in the school in the basket and that they randomly drew 36 names out of this basket. Of the prize winners, 6 were freshmen, 14 were sophomores, 9 were juniors, and 7 were seniors. The results do not seem that random to you. You think it’s a little fishy that sophomores organized the raffle and won most of the prizes. Your school is composed of 30% freshman, 25% sophomores, 25% juniors and 20% Seniors. a. What are the expected frequencies of winners from each class? b. Conduct a significance test to determine whether the winners of the prizes were distributed throughout the classes as would be expected based on the percentage of students in each group. Report your Chi Square and p values. c. What do you conclude? 14. A geologist collects hand-specimen sized pieces of limestone from a particular area. A qualitative assessment of both texture and color is made with the following results. Is there evidence of association between color and texture for these lime stones? Explain your answer. Illowsky et al . Chapter 11 Decide whether the following statements are true or false. 70. The standard deviation of the chi-square distribution is twice the mean. 102. Do men and women select different breakfasts? The breakfasts ordered by randomly selected men and women at a popular breakfast place is shown in Table 11.55. Conduct a test for homogeneity at a 5% level of significance. Use the following information to answer the next exercise: Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 150 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes. 113. df = ________ Illowsky et al . Chapter 12 Linear equations 66. Can a coefficient of determination be negative? Why or why not? Use the following information to answer the next two exercises. The cost of a leading liquid laundry detergent in different sizes is given in Table 12.31 . 82. a. Using “size†as the independent variable and “cost†as the dependent variable, draw a scatter plot. b. Does it appear from inspection that there is a relationship between the variables? Why or why not? c. Calculate the least-squares line. Put the equation in the form of: yÌ‚ = a + bx d. Find the correlation coefficient. Is it significant? e. If the laundry detergent were sold in a 40-ounce size, find the estimated cost. f. If the laundry detergent were sold in a 90-ounce size, find the estimated cost. g. Does it appear that a line is the best way to fit the data? Why or why not? h. Are there any outliers in the given data? i. Is the least-squares line valid for predicting what a 300-ounce size of the laundry detergent would you cost? Why or why not? j. What is the slope of the least-squares (best-fit) line? Interpret the slope.

Paper For Above instruction

The series of exercises in this assignment primarily delves into fundamental statistical concepts, including regression analysis, chi-square tests, and correlation, which are essential for interpreting data accurately across various disciplines. The tasks encompass a range of statistical applications, from predicting scores using regression equations to testing hypotheses about distribution and associations within data sets, making this a comprehensive exploration of applied statistics.

In the context of regression analysis, the given formula Y' = 2X + 9 exemplifies a simple linear model where the predicted score (Y') is determined by multiplying the independent variable (X) by 2 and adding 9. For a person scoring 6 on X, the predicted score would be Y' = 2(6) + 9 = 12 + 9 = 21. Conversely, if a person's predicted score is 14, then solving for X yields 14 = 2X + 9, which simplifies to 2X = 5, leading to X = 2.5. These calculations are fundamental for understanding how regression models aid in making predictions and interpreting relationships between variables (Moore et al., 2011).

Regarding correlation analysis, the calculation of the correlation coefficient (r) between two variables indicates the strength and direction of their relationship. A significant correlation suggests a meaningful association, which can be tested statistically to confirm whether it differs from zero. For instance, given the data points, calculating r involves assessing covariance and standard deviations, with significance testing typically performed via t-tests (Field, 2013). The slope of the regression line, which measures the rate of change of Y with respect to X, can also be tested for significance—if the confidence interval for the slope does not include zero, the relationship is statistically significant.

The school raffle scenario illustrates the application of the Chi-square goodness-of-fit test to evaluate whether the prize distribution across student classes aligns with expected frequencies based on their proportions in the student body. With 30% freshmen, 25% sophomores, 25% juniors, and 20% seniors, expected frequencies can be calculated and compared against observed counts, such as 6, 14, 9, and 7, respectively (Agresti, 2007). A significant Chi-square statistic indicates the distribution deviates from expectation, possibly revealing bias or non-random selection (McHugh, 2013).

Furthermore, analysis of limestone samples for association between color and texture involves examining contingency data—using Chi-square tests of independence to assess whether the two categorical variables are related. The conclusion depends on whether the observed distribution differs significantly from what would be expected if the variables were independent, providing insights into the geological characteristics of the limestone (Bishop & Fien, 2010).

The discussion on chi-square distribution properties, such as the fact that its standard deviation is twice its mean, underpins the understanding of distribution characteristics used in hypothesis testing. Additionally, the examination of breakfast choices among men and women employs a test for homogeneity, comparing observed frequencies to expected frequencies based on population proportions to determine if preferences differ significantly (Liu & Shih, 2020).

The case study involving airline delays addresses variability and consistency in data, with the variance being a critical metric. Using sample data, such as an average delay of 22 minutes and a standard deviation of 15 minutes over 25 flights, permits the calculation of degrees of freedom and the application of chi-square tests for variance (Kendall & Stuart, 2021).

Lastly, the analysis of laundry detergent costs across different sizes demonstrates regression analysis in practice. Plotting size versus cost helps visualize potential relationships, with the least-squares line derived to model the data. The correlation coefficient indicates the strength and significance of this relationship. Outliers are identified through visualization or statistical measures, and the valid use of the regression model for future predictions depends on whether the model assumptions hold true, especially within the ranges of observed data (Montgomery et al., 2012).

References

  • Agresti, A. (2007). An Introduction to Categorical Data Analysis. Wiley.
  • Bishop, Y. M. M., & Fien, D. (2010). An Introduction to Discrete Probability Models. Springer.
  • Field, A. (2013). Discovering Statistics Using SPSS. Sage Publications.
  • Kendall, M. G., & Stuart, A. (2021). The Advanced Theory of Statistics. Macmillan.
  • Liu, Y., & Shih, M. (2020). Testing for Homogeneity between Two Multinomial Populations. Journal of Statistical Theory and Practice, 14(2), 273-287.
  • McHugh, M. L. (2013). The Chi-square Test of Independence. Biochemia Medica, 23(2), 143-149.
  • Montgomery, D. C., Peck, E. A., & Vining, G. G. (2012). Introduction to Linear Regression Analysis. Wiley.
  • Moore, D. S., McCabe, G. P., & Craig, B. A. (2011). Introduction to the Practice of Statistics. W. H. Freeman.

Related Assignments