Wk2 Assgn1

BST 322 Week 2 Assignment 1. ( 1 pt) What is the probability of rolling a four with a six sided die? 1/6=0.167 or 16.7% What is the probability that a person can roll a four 3 times in a row? (assume that rolling the die each time does not affect the outcome of the next roll) 1/6x1/6x1/6 = 1/216 = 0.004657 or 0.4657% 2. ( 1 pt) Population A and Population B both have a mean height of 70.0 inches with an SD of 6.0. A random sample of 50 people is picked from population A, and random sample of 20 people is selected from Population B. Which sample mean will probably yield a more accurate estimate of its population mean? Population A will probably yield a more accurate estimate Why? The margin of error is smaller for larger sample sizes. 3. ( 1 pt) Suppose we obtained data on vein size after application of a nitroglycerin ointment in a sample of 50 patients. The mean vein size is found to be 4.7mm with an SD of 1.1. Using a t distribution table and/or StatCrunch, what are the confidence limits for a 95% confidence interval? One sample T summary confidence interval: μ : Mean of population 95% confidence interval results: Mean Sample Mean Std. Err. DF Critical t L. Limit U. Limit μ 4.7 0.15556349 49 2.0095752 4.3873835 5.0126165 For a 99% confidence interval? One sample T summary confidence interval: μ : Mean of population 99% confidence interval results: Mean Sample Mean Std. Err. DF Critical t L. Limit U. Limit μ 4.7 0.15556349 49 2.679952 4.2830973 5.1169027 4. ( 2 pts) In a pilot study evaluating the use of a new drug to lower resting heart rates (HR) of patients, the following data was recorded: Subject # Resting HR 001 72 002 88 003 71 004 87 005 64 006 77

007 79 008 59 009 77 010 68 011 78 012 80 013 91 014 81 015 65 016 75 017 69 Given that the average resting HR of the general population for this study is 72, use StatCrunch to perform the appropriate t test. What is the value of t ? t: 1.5653 Using an alpha of 0.05, is the t statistic significant? It is not significant Why? P-value is greater than 0.05 What are the confidence limits for a 95% confidence interval here and what do they mean for this patient group? The lower limit is 70.8122 and the upper limit is 79.8936, so I can expect to see 95% of values to fall between those limits. Copy and Paste your work from StatCrunch into your Word document submission. One sample T hypothesis test: μ : Mean of variable H 0 : μ = 72 H A : μ ≠ 72 Hypothesis test results: Variable Sample Mean Std. Err. DF T-Stat Critical t P-value Resting HR 75.352941 2.1419157 16 1.5653936 2.1199053 0.1371 One sample T confidence interval: μ : Mean of variable 95% confidence interval results: Variable Sample Mean Std. Err. DF Critical t L. Limit U. Limit Resting HR 75.352941 2.1419157 16 2.1199053 70.812283 79.8936 5. ( 1 pt) Write a few sentences that could be used to report the results obtained for the t-test in Exercise 4. The study tests a new drug’s effect on resting heart rates. As the P-value is above 0.05, the results are not significant enough to reject the null hypothesis. 6. ( 2 pts) A study by the Fellows Research Group evaluated the mental health status of 150 women in the inner city of Philadelphia. The results of the study are in an Excel file in the Week 2 assignment area. Load the data set into StatCrunch and perform a one sample t test on the mental

c. The IV is infant birth weight (grouped as low vs high); the DV is number of days absent from school in first grade. Appropriate d. The IV is marital status (single vs divorced vs married); the DV is a happiness score, based on a 50 point scale. Inappropriate; more than two groups for the independent variable. 10. ( 2 pt) For which of the following situations is the dependent groups t-test appropriate (if not appropriate, why?) a. The IV is presence or absence of conversation directed to comatose patients (same patients with and without conversation); the DV is the patients’ intracranial pressure. Appropriate b. The IV is birth type (home vs hospital); the DV is perceived functional ability of the patient on a 20 point scale 48 hours after surgery. Inappropriate; IV not dependent c. The IV is time since incarceration for a single group of ex-cons (measured at 1 months and 6 months); the DV is body weight. Appropriate d. The IV is menopausal state (pre vs during vs post) in the same women over time; the DV is attitudes toward menopause (measured in a survey score 1-20). Inappropriate; IV has three values 11. ( 1 pt) Suppose we wanted to test the idea that a control group of cancer patients (Group 1) would report higher mean pain ratings than an experimental group receiving special massage treatments (Group 2). Use the following information. Compute a t -statistic for independent groups: mean group 1 = 78.1 SD 2 1 (variance) = 49.1n 1 = 25 mean group 2 = 74.1 SD 2 2 (variance) = 59.7n 2 = 25 What are the degrees of freedom and the value of t ? DF: 48; t - 1.9174 Using α=0.05 for a two-tailed test, is this t statistic significant? Not significant; P-value is above 0.05 Two sample T summary hypothesis test: μ 1 : Mean of Population 1 μ 2 : Mean of Population 2 μ 1 - μ 2 : Difference between two means H 0 : μ 1 - μ 2 = 0 H A : μ 1 - μ 2 ≠ 0 (with pooled variances) Hypothesis test results: Difference Sample Diff. Std. Err. DF T-Stat P-value μ 1 - μ 2 4 2.0861 48 1.9174 0.0611 Show your calculations (or StatCrunch output) for full credit. 12. ( 1 pt) For each of the following t values (a-d), indicate whether the t statistic is statistically significant for a two-tailed test, at the specified alphas: a. t = 2.90, df = 25, α = 0.01 Significant b. t = 2.20, df = 25, α = 0.05 Significant c. t = 5.52, df = 10, α = 0.01 Significant d. t = 2.02, df = 20, α = 0.05 Not Significant

13. ( 3 pts) Looking again at the Fellows Research Group data used in exercise 6 above, perform another two-sample t test on the General Practitioner Assessment of Cognition ( GPCOG ) score of the married and never married subjects. Is the result significant? Not significant, P-value is greater than 0.05 What hypothesis did you test? Mental health scores between married and never married subjects, null is accepted since results are not significant. Did you try a “pooled” variances test here in StatCrunch? Why or why not? No, the sample sizes weren’t similar. Summary statistics for GPCOG: Group by: Marital Marital n Mean Std. dev. Divorced 44 8.9545455 3.9115485 Married 44 10.113636 4.3627168 Never married 62 10.032258 3.5619471 Two sample T summary hypothesis test: μ 1 : Mean of Population 1 μ 2 : Mean of Population 2 μ 1 - μ 2 : Difference between two means H 0 : μ 1 - μ 2 = 0 H A : μ 1 - μ 2 ≠ 0 (without pooled variances) Hypothesis test results: Difference Sample Diff. Std. Err. DF T-Stat P-value μ 1 - μ 2 0.081378 0.7982553 80.592828 0.10194483 0.9191 Copy and paste your StatCrunch output into your submission document for full credit.