01 Blood type and COVID susceptibility 5 Points A group of researchers in Wuhan, China investigated the relationship between contracting the novel coronavirus and patients' blood type. The population in Wuhan has a blood type distribution as shown in the table below. The researchers categorized 375 patients who had contracted coronavirus by blood type. Round all calculated values in this problem to 4 decimal places. Population COVID- BIOOd Type Percentage patients Type A 33% 115 Type B 24% 101 Type AB 9% Type 0 34% Total 1 00% 01.1 1 Point Suppose we'd like to use these data to conduct a X2 goodness-offit test to determine whether the population-level blood type proportions adequately describe the distribution of blood types among patients who had contracted COVID (NOTE: this question is functionally asking whether COVID is contracted 'at random' across people of various blood types, or whether some blood types are more or less susceptible to the contagion). The hypotheses to be tested are: The hypotheses to be tested are: H0: The distribution of blood type among COVlD-19 patients is the same as that of the population (i.e., the population-level parameters 'fit' well). Any observed differences are due to chance variation. Ha: The distribution of blood type among COVlD-19 patients is not the same as that of the population. The observed differences reflect the inadequacy of using population-level parameters to model blood type among COVlD-19 patients. In the original sample of 375 paitents, we witnessed 115 with Type A blood. Assuming H0 is true. what is the expected count of patients with Type A blood? Enter your answer here Save Answer 01.2 1 Point Conduct a X2 goodness of fit test using these data. How many degrees of freedom will this test have? Enter your answer here 01.3 1 Point What is the resulting test statistic? Enter your answer here Save Answer 01.4 1 Point What is its corresponding p-value? Enter your answer here Save Answer 01.5 1 Point Write a 1-2 sentence conclusion based on the results of your hypothesis test. Does the population-level distribution appear to fit the observed data well? Enter your answer here 02 Strategies to combat scoliosis 7 Points Scoliosis is a condition involving curvature of the spine. Recent researchS compared the effects of two treatments commonly prescribed to combat scoliosis symptoms from advancing (i.e., the spine increasing in curvature). The observational study followed 286 girls aged 10 to 15 who had been diagnosed with adolescent scoliosis and were either prescribed (Group 1) no treatment, (Group 2) an underarm plastic brace, or (Group 3) nighttime electrical stimulation. Six months later. the patient's 'outcome' was recorded as either a success or failure, with 'failure' representing cases where the curvature of the spine had progressed by 6 degrees or more. Treatment Underarm Brace Elec. Stimulation Control group Total 02.1 Strategies to combat scoliosis 1 Point Suppose a 12 test of independence is conducted to assess whether there is an association between the two variables Treatment and Outcome. Which of the following statements would represent the alternative hypothesis Ha of this test? Statement A: The type of treatment a patient receives does not influence whether their scoliosis progresses over a six-month period. The true success rate is the same across all treatments, because they are all equally (in)effective, and any deviation is attributable to sampling variability. Statement B: The type of treatment a patient receives does influence whether their scoliosis progresses over a six-month period. The true success rate is the not same across all treatments. because they Statement B: The type of treatment a patient receives does influence whether their scoliosis progresses over a six-month period. The true success rate is the not same across all treatments, because they are not all equally (in)effective. 0 Statement A 0 Statement B Save Answer 02.2 1 Point If, in fact, the null hypothesis is true, what is the expected value of the X2 test statistic? Enter your answer here Save Answer 02.3 1 Point What is the expected count for the cell that represents the patients who received the Underarm Brace treatment and who successfully prevent their scoliosis from progressing more than 6 degrees? Enter your answer here Save Answer 02.4 1 Point The observed 22 test statistic was computed to be 32 = 12.6266. What was the contribution of patients who received the Underarm Brace treatment and who successfully prevent their scoliosis from progressing more than 6 degrees toward this test statistic? Enter your answer here Save Answer 02.5 1 Point The observed 12 test statistic was computed to be ){2 =12.6266. Compute the p-value for this test. Enter your answer here Save Answer 02.6 1 Point The observed 22 test statistic was computed to be 22 = 12.6266. What is the estimated effect size? Enter your answer here Save Answer 02.7 1 Point Which of the following is not an appropriate interpretation of the p-value you computed in 03.6, above? Select all that apply. It is the probability that the null hypothesis is true. If the treatments had exactly no effect on the patient's outcome, it would be very unlikely to see sample results like we did (or something more extreme) because of sampling variability alone. We have very strong evidence that the type of treatment a patient receives for their scoliosis does affect whether the scoliosis progresses beyond a 6 degree increase in curvature. It is the probability that the alternative hypothesis Ha is true. 03 Pregnancy length 6 Points The Child Health and Development Studies investigate a range of topics. One study considered all pregnancies between 1960 and 1967 among women in the Kaiser Foundation Health Plan in the San Francisco East Bay area. For each baby in the study, the baby's weight at birth in ounces (Birthweight) and the length of the pregnancy in days (Gestation) was recorded. The scatter plot and a summary of the data is given below. The correlation between Gestation and Birthweight was found to be 0.4048. Eby BMW! and Gut-lion - "m 100 140 g _279.2355 15.7618 1;,\" a 03.1 1 Point Use the summaries above to estimate the OLS regression equation that predicts the mean birthweight 9 using pregnancy length :3. What is the estimated slope of the linear model? Enter your answer here 03.2 1 Point Use the summaries above to estimate the OLS regression equation that predicts the mean birthweight 3} using pregnancy length 2:. What is the estimated intercept of the linear model? Enter your answer here Save Answer 03.3 1 Point One of the infants in the dataset had a gestation length of 300 days and a birthweight of 100 02. What is the residual for this infant? Enter your answer here Save Answer 03.4 1 Point Explain in 1-2 sentences why this model may not provide a reliable estimate of the mean birthweight of infants with a gestation length of 148 days. Enter your answer here 03.5 1 Point What is the coefcient of determination, R2, for this regression model? Enter your answer here Save Answer 03.6 1 Point Suppose a different study of the linear relationship between baby gestation time and birthweight yielded a R2 value of 0.2233. Which of the following is an appropriate interpretation of this statistic? 0 There is little evidence that the linear model is a good fit. 0 0.223396 of the variation in Gestation can be explained by the linear relationship with Birthweight. O 22.33% of the variation in Birthweight can be explained by the linear relationship with Gestation. O 22.33% of the variation in Gestation can be explained by the linear relationship with Birthweight. Save Answer Q4 Fiber and breakfast cereal 9 Points In an attempt to learn whether cereals high in fiber are also high in sugar and calories, three researchers took a random sample of 23 brands of breakfast cereal and recorded the calories, sugar (in grams), and fiber (in grams) per serving for each brand. The researchers constructed a linear model using Fiber as the explanatory variable and Calories as the response variable to answer the question, "Can the amount of fiber per serving be used predict the amount of calories per serving in a given brand of cereal?" A linear model is fitted to the data using the statistical software, R, Cereal Fiber and Calories and a summary of that model fit is given below: 160 Coefficients Estimate Std Error t value Pr(= [t[ ) 140 Intercept) 118.8 4.823 24. 638 5.58e-17 120 Fiber -4.345 0.9506 -4.57 0.000166 Calories per serving 100 Residual standard error: 17.202 on 21 degrees of freedom 80 Multiple R-squared: 0.4987, Adjusted R-squared: 0.4748 Round all calculated answers to 4 decimal places. 2 6 8 10 12 14 Fiber (grams) per serving Q4.1 1 Point Use R above to estimate the OLS regression equation that predicts the mean amount of calories y using fiber content . What is the estimated slope of the linear model? Enter your answer hereQ4.2 1 Point Use R above to estimate the OLS regression equation that predicts the mean amount of calories y using fiber content . What is the estimated intercept of the linear model? Enter your answer here Save Answer Q4.3 1 Point Which of the following is the correlation between fiber and calories? O -0.4987 O -0.7062 O 0.7062 O 0.4987 Save Answer Q4.4 1 Point In the space below, provide a 1-2 sentence interpretation of the estimated slope of the regression model you computed in Q4.1. Enter your answer hereQ4.5 1 Point Suppose you wanted to conduct a hypothesis test of the claim that X and Y are linearly-related, using the data and its corresponding model. Which of the following would be the correct set of hypotheses to test? O Ho : B1 = Ovs Ha : B1 0 O Ho : b1 = Ovs Ha : b1 + 0 O Ho : B1 = 0 vs Ha : B1 > 0 O Ho : B1 = b1 vs Ha : B1 # b1 Save Answer Q4.6 1 Point Select the test statistic and p-value associated with the test of the hypotheses from Q2.5. O t23 = 24.638 with p = 5.58 * 10-17 O t22 = 24.638 with p = 5.58 * 10-17 O t22 = -4.57 with p = 0.000166 O t21 = -4.57 with p = 0.000166 Save AnswerQ4.7 1 Point Based on the results of the hypothesis test, which of the following is the most appropriate conclusion to draw regarding the relationship between Fiber and Calorie content of breakfast cereals? There is extremely strong evidence to say that there is a linear relationship between fiber and calories in breakfast cereal. O There is little evidence to say that there is no linear relationship between fiber and calories in breakfast cereal. O There is extremely strong evidence to say that there is no linear relationship between fiber and calories in breakfast cereal. There is little evidence to say that there is a linear relationship between fiber and calories in breakfast cereal. Save Answer Q4.8 1 Point Calculate a 99% confidence interval for the true slope of B1, the regression line predicting the number of calories per serving from the number of grams of fiber per serving. What is the lower bound of this interval, rounded to 4 decimal places? Enter your answer here04.9 1 Point Calculate a 99% condence interval for the true slope of ,81, the regression line predicting the number of calories per serving from the number of grams of fiber per serving. What is the upper bound of this interval, rounded to 4 decimal places? Enter your answer here Save Answer 05 Railways & Housing Values 6 Points In the 18005, an extensive system of railroads connected towns in New England but as automobile use spread most of the train tracks were disassembled. In recent years, many cities have converted the unused railroad beds into \"rail trails\" for citizens to use for walking and biking. In one such town, researchers collected information on 104 homes and classied them as either \"Closer" or \"Farther Away" from the rail trail and then calculated the percentage change in estimated sale price for each home between the years 1998 and 2014. oser FartherAway 05.1 1 Point What are the appropriate hypotheses to test to help answer the question of whether the mean percent change in estimated sale price differed between 'Closer' and 'Farther Away' homes? Enter your answer here Save Answer 05.2 1 Point Summarize the observed summary statistics using a t-test statistic. How many standard errors did the observed data fall from the value expected by the null? Enter your answer here Save Answer 05.3 1 Point What is the p-value associated with your test statistic in 05.2? Enter your answer here 05.4 1 Point What is the estimated effect size? Enter your answer here Save Answer 05.5 1 Point In order for this test to be valid, certain conditions must be met. Which of the following is not one of these conditions? Select all the incorrect statements. The observed 104 observations must be normally distributed. The two samples must be drawn separately from two independent, approximately normal populations. The standard deviations of the two populations must be approximately equal. We must be able to expect at least 10 successes and 10 failures in each sample. Another researcher decides to replicate this study, using data from a different, but similar town. Conducting the same test with a sample size of 50 \"Closer\" and 60 \"Farther Away\" homes, the researcher calculates a p-value of 0.053 and an effect size of 0.28. Does the second researcher's study confirm or conflict with the findings of the rst researcher? Explain your rationale in 2-3 sentences. Enter your answer here