MAT106 Statistics

Palo Verde – Spring 2024 MAT 106 Statistics Quiz 4 I. True/False Questions (circle one) (2 points each). True or False 1. When conducting a hypothesis test for paired samples, we use the t-distribution. True or False 2. In a Test of Independence, H0 is always a statement of independence. True or False 3. r = – 0.123 indicates a strong negative correlation. II. Multiple-choice Questions (circle one) (2 points each). 4. All of these are requirements for conducting a hypothesis test for two population proportions, except a. the two samples must be independent b. the two samples must be simple random c. there must be at least 5 successes and 5 failures for each sample d. the population must be at least 20 times the size of the sample e. none of the above 5. In a Goodness-of-Fit test, we have all of the followings except a. k (number of categories) b. t-distribution c. O (observed values) 6. Which of the following is not a property of the linear correlation coefficient r? a. r is inclusively between -1 and 1 b. r measures the strength of all x-y relationships c. r is not affected by the choice of x or y d. r is sensitive to outliers d. df = k – 1 Palo Verde – Spring 2024 MAT 106 Statistics III. Essay Questions (show all works for full credit). 7. Two samples are shown in the table below. Both have normal distributions. The means for the two populations are thought to be the same. Is there a difference in the means? Test at the 5% level of significance. (10 points) Sample Size Sample Mean Sample Standard Deviation Population A 25 5 1 Population B 16 4.7 1.2 Palo Verde – Spring 2024 MAT 106 Statistics 8. Do men and women select different breakfasts? The breakfasts ordered by randomly selected men and women at a popular breakfast place is shown in the table below. Conduct a test for homogeneity at a 5% level of significance. (10 points) Palo Verde – Spring 2024 MAT 106 Statistics 9. The following table shows data on average per capita coffee consumption and heart disease rate in a random sample of 10 countries. a. Enter the data into your calculator and graph a scatter plot. (2 points) b. Use your calculator’s regression function to find the equation of the least-squares regression line. Write the equation of the regression line. (2 points) c. Explain in words what the slope and y-intercept of the regression line tell us. (2 points) d. How well does the regression line fit the data? Explain your answer. (2 points) e. Which point has the largest residual? Explain what the residual means in context. Is this point an outlier? An influential point? Explain. (2 points) f. Do the data provide convincing evidence that there is a linear relationship between the amount of coffee consumed and the heart disease death rate? Carry out an appropriate test at a significance level of 0.05 to help answer this question. (8 points)