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BST 322 Week 2 Assignment 1. (1 pt) What is the probability of rolling a four with a six sided die? 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) Rolling a 4 is a 1/6 (.167) chance. To roll a 4 three times in a row would be 1/6 x 1/6 x 1/6 which is .00463, or .463%. 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? Why? Population A will most likely yield a more accurate result because there is a larger amount of data collected. There is a decrease in SEM when population increases.

2. (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? For a 99% confidence interval? SEM= 1.1/ 7= .16 One sample T summary confidence interval: μ : Mean of population 95% confidence interval results:

MeanSample Mean Std. Err. DF L. Limit U. Limit μ 4.70.15556349 494.38738355.0126165 There is a 95% confidence level that the mean of the vein size after application of nitroglycerin is between 4.39 and 5.01. One sample T summary confidence interval: μ : Mean of population 99% confidence interval results:

MeanSample Mean Std. Err. DF L. Limit U. Limit μ 4.70.15556349 494.28309735.1169027 There is a 99% confidence level that the mean of the vein size after application of nitroglycerin is between 4.29 and 5.12. 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:

BST 322 Week 2 Assignment Sub j e c t# 0 0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 1 4 0 1 5 0 1 6 0 1 7

Re s t i ngHR 7 2 8 8 7 1 8 7 6 4 7 7 7 9 5 9 7 7 6 8 7 8 8 0 9 1 8 1 6 5 7 5 6 9

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? Using an alpha of 0.05, is the t statistic significant? Why? What are the confidence limits for a 95% confidence interval here and what do they mean for this patient group? Copy and Paste your work from StatCrunch into your Word document submission. One sample T hypothesis test: μ : Mean of variable H0 : μ = 72 HA : μ ≠ 72 Hypothesis test results: Variable Sample Std. Err. D T-Stat PMean F value Resting 75.352941 2.1419116 1.56539 0.137 HR 57 36 1

The value of t is 1.5653936. The t statistic is not significant because the p value is > .05. One sample T confidence interval: μ : Mean of variable 95% confidence interval results:

Variable Sample Mean Std. Err. DF L. Limit U. Limit Resting HR 75.3529412.1419157 1670.812283 79.8936

BST 322 Week 2 Assignment

5.

This means that we are 95% confident that the resting HR will be between 70.8 and 79.8. (1 pt) Write a few sentences that could be used to report the results obtained for the t-test in Exercise 4.

This study is used to test whether or not a new drug will lower resting heart rates. We cannot reject the null hypothesis because the p value is greater than .05, therefore the results are not significant enough to reject it.

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 and in the “Course Resources” area. Load the data set into StatCrunch and perform a one sample t test on the mental health score given that the national average on this test is 45. Is the result significant? Copy and paste your StatCrunch output into your submission document for full credit.

One sample T hypothesis test: μ : Mean of variable H0 : μ = 45 HA : μ ≠ 45 Hypothesis test results:

Variable Sample Mean Std. Err. DF T-Stat P-value MentalHlth 45.880.890211251490.98852941 0.3245 The result is not significant.

7.

(1 pt) Write a few sentences that could be used to report the results obtained for the t-test in Exercise 6.

We can conclude that there is not a significant difference between the mental health of the 150 women in comparison to the national average because the p value is greater than .05. We also can not reject the null hypothesis.

8.

(2 pts) Looking again at the Fellows Research Group data used in exercise 6 above, perform a two-sample t test on the mental health score of the married and divorced subjects. Is the result significant? What hypothesis did you test? Copy and paste your StatCrunch output into your submission document for full credit.

Two sample T hypothesis test: μ1 : Mean of Divorced MentalHlth μ2 : Mean of Married MentalHlth μ1 - μ2 : Difference between two means

BST 322 Week 2 Assignment H 0 : μ1 - μ2 = 0 H A : μ1 - μ2 ≠ 0 (with pooled variances) Hypothesis test results:

DifferenceSample Diff. Std. Err. DF T-Stat P-value μ 1 - μ2 5.34090912.3386091 862.2837973 0.0248

The hypothesis tested is the mental health scores between married and divorced subjects. The result is significant because the p value is less than .05.

9.

(1 pt) For which of the following situations is the independent groups t-test appropriate (if inappropriate, why?): a. The independent variable is infant birth weight at one week (normal vs high); the dependent variable is resting heart rate. Appropriate b. The independent variable is radiation treatment on throat cancer patients (one group getting a low dose and the other a high dose treatment); the dependent variable is white blood cell count. Appropriate 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 because the IV has too many groups

10.

(1 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 group is 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 bc the IV has 3 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 mean group 2 = 74.1

SD21 (variance) = 49.1n1 = 25 SD22 (variance) = 59.7n2 = 25

What are the degrees of freedom and the value of t ? Using α=0.05 for a two-tailed test, is this t statistic significant? Show your calculations (or StatCrunch output) for full credit. Two sample T summary hypothesis test:

BST 322 Week 2 Assignment μ1 : Mean of Population 1 μ2 : Mean of Population 2 μ1 - μ2 : Difference between two means H 0 : μ1 - μ2 = 0 H A : μ1 - μ2 ≠ 0 (with pooled variances) Hypothesis test results: Differen Sample Std. Err. D T-Stat Pce Diff. F value μ1 - μ2 4 2.08703 48 1.91659 0.061 62 35 3

Degrees of freedom is 48 and the value of t is 1.92. The results are not significant because the p value is greater than .05. 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. b.

t = 2.90, df = 25, α = 0.01 Significant t = 2.20, df = 25, α = 0.05 Significant

c. d.

t = 5.52, df = 10, α = 0.01 Significant t = 2.02, df = 20, α = 0.05 Not significant

13.

(1 pt) For each of the following situations, indicate whether ANOVA is appropriate; if not appropriate, the reason why not; and, if appropriate, the type of ANOVA that would be used (i.e., one-way, repeated measures, etc.) a. The IVs are ethnicity (Asian, White, African American, Hispanic) and gender (male vs female); the DV is serum cholesterol levels. Appropriate. Two way ANOVA b. The IV is smoking status – smokers vs non-smokers; the DV is a health-related hardiness score, measured on a 20-item scale. Inappropriate. IV has only 2 options c. The IV is maternal breast feeding status (breastfeeds daily vs doesn’t breastfeed); the DV is a maternal bonding with infant score, measured on a 20-item scale. Inappropriate. IV has only 2 options d. The IV is length of gestation (preterm vs term vs postterm) using the same multiple birth mothers over time; the DV is blood pressure 10 minutes post delivery. Inappropriate. DV is nominal

14.

(2 pts) Suppose we wanted to compare the somatic complaints (as measured on a scale known as the Physical Symptom Scale or PSS) of three groups of people: non-smokers, smokers, and people who recently quit smoking. Using the following data for the PSS score, do a one-way ANOVA to evaluate smoking and PSS scores: Nonsmokers 19 28 17 20

Smokers 31 29 22 29

Quitters 30 22 29 29

25

BST 322 Week 2 Assignment 28 34

Using StatCrunch, determine the means for the three groups and compute the sums of squares, degrees of freedom, and mean squares for these data. What is the value of F? Using an alpha of 0.05, is the F statistic significant? Why? What hypothesis did you test? Did you accept or reject your hypothesis and why? Copy and Paste your work from StatCrunch into your Word document submission. The value of F is 4.2074364. It is significant because the p value is less than .05. I tested if there was a difference in the somatic complaints of 3 groups of people (non-smokers, smokers, and quitters). There is a difference so I rejected the null hypothesis. Analysis of Variance results: Responses: PSS Score Factors: Subjects

Response statistics by factor Subjects nMea Std. Std. n Dev. Error Nonsmok 5 21.8 4.54972 2.03469 er 53 9 Quitters 5 28.8 4.32434 1.93390 97 8 Smoker 5 27.8 3.42052 1.52970 63 59

ANOVA table Sourc D SS MS F-Stat Pe F value Subjec 2 143.333 71.6666 4.20743 0.041 ts 33 67 64 2 Error 12 204.4 17.0333 33 Total 14 347.733 33

15.

(2 pts) Looking again at the Fellows Research Group data used in exercise 6 above, perform a one-way ANOVA to examine the mental health scores of the married and divorced and never married subjects. Is the result significant? What hypothesis did you test? Did you accept or reject your hypothesis and why? Copy and paste your StatCrunch output into your submission document for full credit.

The result is significant because the p value is less than .05; therefore, you can reject the null hypothesis. I tested to see if there was a difference in the mental health scores of the married, divorced, and never married subjects.

BST 322 Week 2 Assignment Analysis of Variance results: Data stored in separate columns.

Column statistics Column Divorced MentalHlth Married MentalHlth Never married MentalHlth

n

Mean

4 41.7272 4 73 4 47.0681 4 82 6 47.9838 2 71

Std. Dev. 11.9987 67 9.83207 31 10.1375 65

Std. Error 1.80888 21 1.48224 08 1.28747 21

ANOVA table Sourc DF SS MS F-Stat Pe value Colum 2 1095.33 547.666 4.84500 0.009 ns 34 7 18 2 Error 14 16616.5 113.037 7 07 46 Total 14 17711.8 9 4...