Dataset 1: Questions 1 to 7 are based on this dataset

Two pain-relieving drugs were compared for effectiveness on the basis of the time elapsing between administration of the drug and cessation of the pain. Thirteen patients received drug A and thirteen received drug B. The sample statistics were.

Assume normal distribution and test the null hypothesis that the two population variances are equal. Let a=0.05

  1. What is the null hypothesis? (.5)
  1. What is the alternative hypothesis? (.5)
  1. What is the test statistic used? (.5)
  1. What is the critical value of the test statistic (.5)
  1. What is the calculated test statistic (1)
  1. What is the p-value (.5)
  1. Construct a 95 % confidence interval for the ratio of the two variances (2)

Dataset 2: Questions 8 to 14 are based on this dataset

The object of a research project was to test if Type of psychological problems were independent of source of referral There were three categories of psychological problems (1) those with family problems but without mental disorders (2) those with family problems and mental disorders, and (3) those with mental disorders but without family problems. Source of referral were categorized as (1) Court referred (2) Family referred. The following table shows the study subjects cross-classified by type of problem and source of referral.

Source of referral / Type of problem / Total
1 / 2 / 3
Court / 15 / 37 / 16 / 68
Family / 25 / 25 / 17 / 67
Total / 40 / 62 / 33 / 135

Do these data provide sufficient evidence to warrant the conclusion that problem category and source of referral are related? Let a =0.05

  1. What is the null hypothesis? (.5)
  1. What is the alternative hypothesis? (.5)
  1. What is the test statistic used? (.5)
  1. What is the critical value of the test statistic? (.5)
  1. What is the calculated test statistic (2)
  1. What is the p-value (.5)
  1. What is the statistical decision? (.5)

Dataset 3: Questions 15 to 20 are based on this dataset

A study is conducted of tooth emergence in young boys. The purpose is to detect if on an average left sided teeth emerge later than right side permanent teeth. One tooth studied is the incisor. All subjects are males. The age of the subject at the time of the emergence of the left incisor and his age at the time of emergence of the right incisor are determined. Thus each subject produces a pair of observations. Summary statistics for the study are as shown, where the order of subtraction is left side age-right side age.

left side - Right side

Mean 1.5

Standard deviation 4.7

n 17

Assume normal distribution. Let a =0.05

  1. What is the null hypothesis (.5)
  1. What is the alternative hypothesis (.5)
  1. What is the test statistic used (.5)
  1. What is the critical value of the test statistic (.5)
  1. What is the calculated test statistics (1)
  1. What is the p-value (.5)

Dataset 4: Questions 21 to 27 are based on this dataset

A student is interested in comparing if there is a difference in the average number of calories in vegetarian and non-vegetarian dishes in a college dining hall. He recorded the amount of calories in 15 randomly selected vegetarian and 15 non-vegetarian entrees. Assume amount of calories in entrees are normally distributed. The results are summarized in the following table. Set a at 0.05

Vegetarian Non-Vegetarian

Number of entrees 15 15

Mean 301 352

Sample standard deviation 90 87

Population variances unknown but assumed equal

  1. What is the null hypothesis (.5)
  1. What is the alternative hypothesis (.5)
  1. What is the test statistic used (.5)
  1. What is the critical value of the test statistic (.5)
  1. What is the calculated test statistics (1)
  1. What is the p-value (.5)
  1. Give the 95% confidence interval for the difference between the two means

(2)

Dataset 5: Questions 28 to 33 are based on this dataset

A study was conducted to determine whether relaxation training aided with biofeedback and meditation could lead to a greater reduction in blood pressure. Subjects were randomly assigned to the biofeedback group or a control group. The table shows the reduction in systolic blood pressure after eight weeks

Population variances unknown but assumed unequal and reduction in blood pressure is assumed to be normally distributed. Set a=.01

  1. What is the null hypothesis? (.5)
  1. What is the alternative hypothesis? (.5)
  1. What is the test statistic used? (.5)
  1. What is the critical value of the test statistic? (1)
  1. What is the calculated test statistic (1)
  1. What is the p-value (.5)

Dataset 6: Questions 34 is based on this dataset

  1. An experiment was done to determine the effect on dairy cattle of a diet supplemented with liquid whey. While no differences were noted to milk production measurements among cattle given a standard diet (7.5 kg of grain plus hay by choice) with water and those on the standard diet and liquid whey only, a considerable difference between the groups was noted in the amount of hay ingested. Suppose prior to conducting this experiment, we wished to test the null hypothesis of no difference in mean hay consumption for the two diet groups of dairy cattle.

For a two-tail test with a=0.05, determine the number of dairy cattle that should be included in each group if we want 90% power for .

(2)

Dataset 7: Questions 35 is based on this dataset

  1. A two-sample t test for the two-tailed hypothesis, . The data are human blood-clotting times in minutes for two different drugs. What would be the probability of detecting a true difference of 1.0 minute between mean blood clotting times of persons using the two drugs, if

(2)

Dataset 8: Questions 36-40 are based on this dataset

A researcher wished to see if in a Midwestern city there were racial differences in survival following cardiac arrest in 6117 cases of non-traumatic, out of hospital cardiac arrests. During a 12-month period, less than 1% of African-Americans survived an arrest to hospital discharge (24 of 2910), compared to 2.6% of Caucasians (84 of 3207). Using the normal theory method find if there is a difference in the proportion of people who survive cardiac arrest in the African-American and the Caucasian population. a=0.05.

  1. What is the null hypothesis? (.5)
  1. What is the test statistic used? (.5)
  1. What is the critical value of the test statistic (.5)
  1. What is the calculated test statistic (2)
  1. What is the p-value (.5)

Dataset 9: Questions 41 to 45 are based on this dataset

A researcher wishes to determine if length of stay in days in a hospital can be predicted by the age of the patient. 42 cardiovascular patients are measured on length of hospitalization in days and their age in years at time of admission. Analysis of the data gave the following regression equation. Assume all assumptions are met.

  1. What is the independent (predictor) variable? (.5)
  1. What is the dependent (response) variable? (.5)
  1. What is the critical value of the test statistic to test? Let a=0.05

(.5)

  1. Complete the ANOVA table to test (2)

Source / SS / df / MS / F / P-value
Regression
Error / 8.03
Total / 416.11
  1. Interpret the regression equation to predict length of hospitalization for cardiovascular patients by age (1)

Dataset 10: Questions 46 to 49 are based on this dataset

The Pearson’s correlation coefficient (r) between the variables Blood pressure and Weight is 0.65 for a sample of 25 people from New Orleans. Let a=0.05. Assume all assumptions are met.

  1. What is the test statistic to test the null hypothesis: (.5)
  1. What is the critical value of the test statistic (.5)
  1. What is the calculated test statistic to test the null hypothesis

(1)

  1. What is the calculated p-value (.5)
  1. Is there a significant linear association between Blood pressure and Weight

(.5)

  1. Explain the following assumptions for simple linear regression

(a)  Assumption of linearity (.5)

(b)  Assumption of homogeneity of variances (.5)

State whether the statements are true or false

  1. We reject the null hypothesis if the two-sided confidence interval for the difference between two means contains a zero. (1)

True False

  1. We reject the null hypothesis if the two-sided confidence interval for the ratio of the two variances contains a 1. (1)

True False

  1. The Yates correction is used for a R*C contingency table for the chi square test of independence. (1)

True False

  1. The Pearson correlation coefficient (r) ranges between -1 and +1 (1)

True False

  1. The chi square distribution is the distribution of a categorical variables (1)

True False

  1. The F-distribution is bell shaped

True False

  1. (Slope of line) gives the average change in Y for every unit change in X.

(1)

True False

  1. The correlation model has a bivariate normal distribution

True False (1)

  1. Chi square values range from negative infinity to positive infinity

(1)

True False

  1. F-values range from negative infinity to positive infinity

(1)

True False

12