The following data were obtained in a study of the relationship between the weight and chest size of infants at birth: Weight (kg): 2.75 2.15 4.41 5.52 3.21 4.32 2.31 4.30 3.71 Chest Size 29.5 26.3 32.2 36.5 27.2 27.7 28.3 30.3 28.7 (cm) Determine the equation of the regression line. Y=A + BX Y = 21.7 + 2.2X Y=2.2+ 21.7X no regression equation The heights of adults in a certain town has a mean of 65.42 inches with a standard deviation of 2.32 inches. A random sample of 144 adults living in the slum district is found to have a mean height of 64.82 inches. Does this indicate that the residents of slums are significantly retarded in growth at a 0.05 level of significance? The appropriate test is a one-tailed Z-test one-tailed t-test two-tailed Z-test two-tailed t-test A geneticist is interested in the proportion of males and females in a population that have a certain minor blood disorder. In a random sample of 100 males, 31 are found to be afflicted whereas only 24 of 100 females tested appear to have the disorder. What test statistic is appropriate for this problem? t-test for two sample means z-test for single proportion z-test for two sample means z-test for two proportions Which of the following statements is TRUE? If the level of significance is 5%, then the critical region of a two-tailed test has an area of 2.5%. If r=0, then X and Y are not linearly related. ANOVA is a test concerning several variances. Rejecting Ho in a chi-square test of independence means that the row and column classifications are independent. A pill is supposed to contain 25.4 milligrams of phenobarbital. A random sample of 30 pills yield a mean of 19.7 milligrams and a standard deviation of 0.95 milligrams. What null hypothesis is appropriate for the problem? H0: μ1 = μ2 H0: μ1 ≠ μ2 H0: μ1 = 25.4 H0: μ1 ≠ 25.4 The heights of adults in a certain town has a mean of 65.42 inches with a standard deviation of 2.32 inches. A random sample of 144 adults living in the slum district is found to have a mean height of 64.82 inches. Does this indicate that the residents of slums are significantly retarded in growth at a 0.05 level of significance? Which of the following is an appropriate null hypothesis? µ = 64.82 µ ≠ 64.82 µ = 65.42 µ ≠ 65.42 A pill is supposed to contain 25.4 milligrams of phenobarbital. A random sample of 30 pills yield a mean of 19.7 milligrams and a standard deviation of 0.95 milligrams. What test is appropriate for this? z-test t-test χ2 f-test A random variable is known to be normally distributed with mean 100 and standard deviation 10. The probability that an observed value of this random variable is less than 90 or greater than 110 is approximately 0.15 0.32 0.68 0.84 0.95 The heights of adults in a certain town has a mean of 65.42 inches with a standard deviation of 2.32 inches. A random sample of 144 adults living in the slum district is found to have a mean height of 64.82 inches. Does this indicate that the residents of slums are significantly retarded in growth at a 0.05 level of significance? Which of the following is an appropriate alternative hypothesis? µ µ µ µ ≠ 64.82 > 65.42 ≠ 65.42 < 65.42 A Municipal Health Officer and his staff aim to cover 80% of the target population for their Expanded Program for Immunization (EPI). After implementing the program, they surveyed 1500 children and found that 1000 of them were immunized. Did the MHO and his staff attain his goal? Test at a 0.05 level of significance. What test – statistic will you use to answer the question? two-tailed z-test one-tailed z-test f-test Chi-Square test A study looking at the relationship between salt intake to the blood pressure of infants was recently conducted. The study involved 15 infants with a low salt diet and 20 infants with a high salt diet. The results are: High Salt Diet Mean Systolic Blood Pressure Std Deviation Systolic Blood Pressure 90.8 10.3 Low Salt Diet 87.2 9.2 n 20 15 What can we conclude at the .05 level of significance about blood pressure and the level of salt in the diet? The appropriate test statistic is one-tailed t-test two-tailed t-test one-tailed z-test two-tailed z-test The following data represent systolic blood pressure readings on 15 females pre-selected by age ( 40-85): Participant No. Age (X) Systolic Blood Pressure (Y) 1 42 130 2 46 115 3 42 148 4 71 100 5 80 156 6 74 162 7 70 151 8 80 156 9 85 162 10 72 158 11 64 155 12 44 130 13 53 135 14 55 144 15 60 146 Test the significance of the correlation coefficient at alpha = .05. There is no linear relationship between age and systolic BP with r = .25245 There is a linear relationship between age and BP with r =0.61154 There is no linear relationship between age and systolic BP with p-value = .05629 There is no linear relationship between age and BP at pvalue =.502446 The data below is concerned with serum lowering properties of a new drug tested in 6 prisoner volunteers. The serum cholesterol values were Before treatment:217 252 229 200 209 213 After treatment 209 241 230 208 206 211 Is the new drug effective at a .01 level of significance? The appropriate alternative hypothesis is μd > 0 previously given with preventive serum. The results are given below. What is the best statistical test to check the effectivity of the new serum. Serum No Serum Recovered 18 4 Died 4 18 Point Biserial Phi-coefficient Kendall?s coefficient Pearson?s r coefficient The LD50 (lethal dose 50), ED50(effective dose 50) and ID50(infective dose 50) are example of Mean Mode Median Mean Deviation When the value of correlation coefficient is ?1, then it means that there is a perfect relation between the two parameters. there is a weak negative relation between the two parameters there is a strong direct relation between the two parameters there is no relation between the two parameters A drug company alleges that the average time for a cough syrup to take effect is 15 min., with a standard deviation of 3 min. In a random sample of 49 patients, the average time was 18 min. The correct null hypothesis is The random sample of 49 patients is not enough to test the effectivity of the cough syrup. There is no difference between the sample and population average time (in min.) for a cough syrup to take effect. The drug company is not capable of making cough syrup with a standard deviation of 3 min. only. The average time of 18 min. does not help the patients recover from cough. Consider the following study in which efforts to reduce the body weights of 20 moderately overweight student volunteers by interventions involving diet, increased physical activity, or both are investigated. The students are randomly assigned to four groups Group 1: controls; no change in diet or physical activity. Group 2: diet; reduction in caloric intake Group 3: physical activity Group 4: diet plus physical activity After 3 months, weight reduction is measured, with the ff results, positive values indicate weight-loss. Group1 Group 2 Group 3 Group 4 5 2 8 12 -2 8 0 6 3 4 2 15 2 12 6 8 0 4 2 10 Two lots of rats were used in testing the effectiveness of a new serum in combating a certain disease. Both were inoculated with the causative organism but only one lot was Is there a significant difference among the 4 groups? Test at .05 level of significance. There is no significant difference among the means of the 4 groups. There is a significant difference in the means of the 4 groups. The data is incomplete hence conclusion can not be determined. Post Hoc Analysis is required to answer the question. The level of serum creatinine in the blood is considered a good indicator of the presence or absence of kidney disease. Normal persons generally have low concentrations of serum creatinine while diseased persons have high concentrations. Suppose we desire to look at the relation between analgesic abuse and kidney disorder. In particular, suppose we look at 15 persons working in a factory who are known to be "analgesic abusers" (i.e., they take more than 10 pills per day) and we measure their creatinine levels. The creatinine levels are: .9 .7 1.0 1.1 1.4 1.1 1.6 1.2 1.4 2.0 1.5 2.2 .8 .8 1.4 Terbutaline is a drug that is effective in arresting labor and prolonging the duration of the pregnancy beyond 36 weeks. However, it sometimes has undesirable cardiovascular and metabolic side effects such as tremors and hyperglycemia, which limits its use for some women. Another possibility is to give terbutaline in combination with another drug (metoprolol) which would neutralize these side effects. However, before using the combination therapy we want to be sure it is as effective as terbutaline alone in prolonging labor. Suppose that a clinical trial is carried out comparing the effectiveness of the two therapies where the outcome is whether the pregnancy lasts beyond 36 weeks. We find that in 200 patients treated with terbutaline alone, 130 have a pregnancy lasting more than 36 weeks while in 200 patients treated with terbutaline and metoprolol, 120 have a pregnancy lasting more than 36 weeks. Test the hypothesis that the combination of terbutaline and metoprolol is as effective as terbutaline alone at the .05 level of significance. The appropriate type of test is If we assume that creatinine levels for normal persons are normally distributed with a mean of 1.0 and a standard deviation of .25, at the .01 level of significance what can we conclude? What appropriate test-statistic should be used to address the problem? one-tailed t-test for single mean two-tailed t-test for single mean one-tailed z-test two-tailed z-test When the alternative hypothesis is X>Xo and the computed value of the test statistics is greater than the critical value then the alternative hypothesis is accepted alternative hypothesis is rejected null hypothesis is accepted result is always accurate Kendall?s test statistics is concern with the test for difference between two parameters test for independence test for the agreement of two or more opinions test for fitting a specific curve A subject of recent research in obstetrics is the medical management of women who go into labor prematurely, which will be defined as labor occurring between 20 and 36 weeks of pregnancy. Premature labor is undesirable because infants born prematurely have a higher rate of infant mortality and morbidity. independent t-test for 2 means assuming equal variances independent t-test for 2 means assuming variances are not equal one-tailed z-test for two proportions two-tailed z-test for two proportions For Analysis of Variance (ANOVA), the statistical test is z test x2 test t test f test All the following test statistics make use of ranking, with the exception of Chi-square Kendall?s coefficient of concordance Spearman rho coefficient of correlation Wilcoxon?s test Which of the following is not an application of chi-square test? Test for association between two categorical parameters Test for multiple column proportions. Test for the mean difference between two groups Test for independence