12.6 Can a pretest on mathematics skills predict success in a statistics course? Assume students in...

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12.6 Can a pretest on mathematics skills predict success in a statistics course? Assume students in an introductory stats class can be considered a random sample from a larger population of statistics students. These 62 students took a pretest at the beginning of the semester, and their score from the pre-test and their score from the final exam in the course were recorded. The least squares regression line was found to be = 13.8 +0.81x, and the standard error of b was 0.43. (SE b1) (a) (10m) Would you reject this null hypothesis versus the one-sided alternative that the slope is positive? Fill in the table to find your answer. See part j) of fill in, but do a one sided test! Hypotheses Test statistic and degrees of freedom Pvalue statement and Pvalue Decision: Reject or Fail to Reject Ho and why or why not English conclusion regarding significance or non significance. Ho: = 0 Ha: > 0 t* = b/SE b1 1.(from online t calculator) df=n-2 2.(from t tables) (b) (10m) Use the hypothesis test approach to test the null hypothesis that there is no linear relationship between the pretest score and the score on the final exam against the two-sided alternative that the slope is non-zero. Use a significance level of 5%. See part j) of fill in, but do a one sided test! Hypotheses Test statistic English conclusion regarding significance or non-significance. and degrees of freedom Pvalue statement and Pvalue Decision: Reject or Fail to Reject Ho and why or why not Ho: = 0 Ha: 10 t* = b/SE 1 1.(from online t calculator) 60 2. (from t tables) PAGE 6 c) (2m) Why would you be able to use a z approximation to calculate your pvalue above? Hint: Consider the sample size. Recall that the bottom line of the t table has z values. 12.7 Excessive consumption of alcohol is associated with numerous adverse consequences. In one study, researchers analyzed binge-drinking rates from two national surveys, the Harvard School of Public Health College Alcohol Study (CAS) and the Centers for Disease Control and Prevention's Behavioral Risk Factor Surveillance System (BRFSS). The CAS survey was used to provide an estimate of the college binge-drinking rate in each state, and the BRFSS was used to determine the adult binge-drinking rate in each state. A correlation of 0.43 was reported between these two rates for their sample of n = 40 states. The college binge-drinking rate had a mean of 46.5% and standard deviation 13.5%. The adult binge-drinking rate had a mean of 14.88% and standard deviation 3.8%. (a) (3m) Find the equation of the least-squares line for predicting the college binge-drinking rate Y from the adult binge- drinking rate X. HINT: recall that slope can be written as a function of correlation. ,r= = br (Sy/Sx) (0.43)(13.5/3.8) etc =r b = y - bx= b) (10m) Test the null hypothesis that the slope is 0 versus that alternative that it is nonzero. (Hint: recall that the test statistic can be written as a function of correlation) Assume a = 0.01. Hint: Revisit Question 12.3j in the Workbook. Hypotheses Test statistic and degrees of freedom n-2 Pvalue statement and Pvalue 1.(online t calculator) Decision and why English: significant or non significant? 2.(t tables approximation) 12.6 Can a pretest on mathematics skills predict success in a statistics course? Assume students in an introductory stats class can be considered a random sample from a larger population of statistics students. These 62 students took a pretest at the beginning of the semester, and their score from the pre-test and their score from the final exam in the course were recorded. The least squares regression line was found to be = 13.8 +0.81x, and the standard error of b was 0.43. (SE b1) (a) (10m) Would you reject this null hypothesis versus the one-sided alternative that the slope is positive? Fill in the table to find your answer. See part j) of fill in, but do a one sided test! Hypotheses Test statistic and degrees of freedom Pvalue statement and Pvalue Decision: Reject or Fail to Reject Ho and why or why not English conclusion regarding significance or non significance. Ho: = 0 Ha: > 0 t* = b/SE b1 1.(from online t calculator) df=n-2 2.(from t tables) (b) (10m) Use the hypothesis test approach to test the null hypothesis that there is no linear relationship between the pretest score and the score on the final exam against the two-sided alternative that the slope is non-zero. Use a significance level of 5%. See part j) of fill in, but do a one sided test! Hypotheses Test statistic English conclusion regarding significance or non-significance. and degrees of freedom Pvalue statement and Pvalue Decision: Reject or Fail to Reject Ho and why or why not Ho: = 0 Ha: 10 t* = b/SE 1 1.(from online t calculator) 60 2. (from t tables) PAGE 6 c) (2m) Why would you be able to use a z approximation to calculate your pvalue above? Hint: Consider the sample size. Recall that the bottom line of the t table has z values. 12.7 Excessive consumption of alcohol is associated with numerous adverse consequences. In one study, researchers analyzed binge-drinking rates from two national surveys, the Harvard School of Public Health College Alcohol Study (CAS) and the Centers for Disease Control and Prevention's Behavioral Risk Factor Surveillance System (BRFSS). The CAS survey was used to provide an estimate of the college binge-drinking rate in each state, and the BRFSS was used to determine the adult binge-drinking rate in each state. A correlation of 0.43 was reported between these two rates for their sample of n = 40 states. The college binge-drinking rate had a mean of 46.5% and standard deviation 13.5%. The adult binge-drinking rate had a mean of 14.88% and standard deviation 3.8%. (a) (3m) Find the equation of the least-squares line for predicting the college binge-drinking rate Y from the adult binge- drinking rate X. HINT: recall that slope can be written as a function of correlation. ,r= = br (Sy/Sx) (0.43)(13.5/3.8) etc =r b = y - bx= b) (10m) Test the null hypothesis that the slope is 0 versus that alternative that it is nonzero. (Hint: recall that the test statistic can be written as a function of correlation) Assume a = 0.01. Hint: Revisit Question 12.3j in the Workbook. Hypotheses Test statistic and degrees of freedom n-2 Pvalue statement and Pvalue 1.(online t calculator) Decision and why English: significant or non significant? 2.(t tables approximation)