Biostatistics Assignment

Description

Part I    True-False Statements: Fill in T or F (4 points each) 1.      Significant difference in a statistical sense means that the observed, or apparent, difference is of practical importance and should not be neglected. ___   2.      For a fixed sample size, testing at the 1% level instead of the 5% level will decrease the chance of committing a Type II error. ___   3.      If random samples of size 20 are drawn from a normal population, the means of these samples will be normally distributed. ___   4.      When a 95% confidence interval around a point estimate of µ includes µo, Ho should not be rejected at the 0.05 level. ___   5.      A P-value less than 0.05 is proof that the null hypothesis is false. ___                                   Part II   Fill in the correct choice (4 points each)   1.               Part 1: As the variance decreases, the power of a significance test ___.   a)     Increases   b)     Decreases .   Part 2: As the sample size decreases, the power of a significance test ___.   a)     Increases   b)     Decreases     2.               Part 1: Fill in the correct choices:   Statistic? ___   Parameter? ___   a)     Characteristic of a population (constant) b)   Characteristic of a random sample drawn from a population (vary from sample to sample)     Part 2: Complete the following statement regarding the relationship between the Z and t distributions.                   Z is a special case of t as the number of degrees of freedom approaches ___________.     3.               What is the only way to increase power of a significance test when lowering the probability of committing a Type I error? ___   a)     Reduce the variance   b)     Increase the sample size   c)      Increase the minimum detectable difference   4.               Part 1: In what circumstance is the median superior to the mean as an indicator of central tendency? ___   a)     When dealing with skewed distributions   b)     When dealing with outliers   c)      When dealing with bimodal distributions   Part 2: To determine if a distribution is approximately normal we need to know the ___. a)     Skewness   b)     Kurtosis   c)      Variance   d)     Skewness and Kurtosis   e)     Skewness and Variance   f)       Kurtosis and Variance   g)     Skewness, Kurtosis, and Variance     5.               Part 1:  As the difference between two means increases, the power of a significance test ___.   a)     Increases   b)     Decreases .   Part 2:  In performing an ANOVA with a fixed total sample size, as the number of groups being compared increases, the power ___.   a)     Increases   b)     Decreases           6.               When comparing three means, why is ANOVA used instead of performing three separate t-tests? ___   a)     To prevent inflation of the type I error   b)     To increase power         7.               Part 1: Fill in the correct choices concerning nonparametric alternatives to the:   Independent 2-sample t-test? ___   Paired-sample t-test? ___   One-way ANOVA? ___   Randomized block ANOVA? ___     a)     Kruskal-Wallis test   b)     Mann-Whitney test   c)      Friedman’s test   d)     Wilcoxon paired-sample test     Part 2:  Under what circumstances are nonparametric tests employed? ___   a)     When there is a violation of the assumption of normality   b)     When there is a violation of the assumption of equality of variance   c)      When dealing with ordinal data d)   All of the above               8.               If the null hypothesis is not rejected in a significance test, what must be known for one to accept Ho? ___   a)     The probability of committing a type II error   b)     The probability of committing a type I error 9.               As health commissioner of city A, you have decided to implement a $ 20 million exercise program for elementary school children if there was 95% confidence that the mean resting heart rate in this population was different from 80 beats/min.  Using a random sample of 50 elementary school children, the estimated mean heart rate was found to be 86.5 beats/min with a 95% confidence interval from 80.1 to 92.9 beats/min.  What is your decision? ___   a)     Implement program   b)     Do not implement program     10.            When planning a statistical analysis, what takes precedence? ___   a)     Maximizing power   b)     Minimizing bias   a)       Part III  Problems (20 points each)   1.         The health commissioner of city B postulated that the mean diastolic blood pressure (DBP) in a population of patients diagnosed as hypertensive was 100 mm Hg. Wishing to test this null hypothesis, a random sample of 11 subjects was drawn from this target population.             The results were as follows (DBP in mm Hg):                         96, 114, 125, 105, 97, 96, 131, 117, 107, 111, 123 Assume the sample was drawn from a normally distributed population. a)     Use α = 0.05 (two-tailed) and assume 80% power. b)   State the null and alternative hypotheses.             c)  List the critical value                                     d) Perform the appropriate statistical test using the attached SAS file.   e) Report your decision based on the critical value (reject Ho and accept HA OR fail to reject Ho), P-value, and 95% confidence interval.       f) If the decision was to fail to reject Ho, can Ho be accepted?                                     2.         A study was conducted among children aged 8-10 to determine if resting heart rate differed between males and females.  Independent samples of 8 females and 8 males were selected from the two respective populations.              The results were as follows (heart rates in beats/min):                         Females           71, 80, 80, 75, 78, 77, 81, 82                         Males               71, 81, 79, 74, 73, 78, 71, 74 Assume the samples were drawn from normally distributed populations with equal variance. a)     Use α = 0.05 (two-tailed) and assume 80% power. b)   State the null and alternative hypotheses.             c)  List the critical value                                     d) Perform the appropriate statistical test using the attached SAS file.   e) Report your decision based on the critical value (reject Ho and accept HA OR fail to reject Ho), P-value, and 95% confidence interval.       f) If the decision was to fail to reject Ho, can Ho be accepted