Week 2 Assignment BST 322 PDF

Preview

Summary

Download Week 2 Assignment BST 322 PDF

Description

BST 322 Week 2 Assignment 1. (1 pt) What is the probability of rolling a four with a six sided die? P(rolling a four)= 1/6 = 0.17 = 17% 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): p(roll a four) x p(roll a four) x p(roll a four) = (1/6)(1/6)(1/6) = 0.0046 = 0.46% 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? The sample mean from population A will yield a more accurate estimate of its population means because the sample was from 50 people, in comparison to only a sample of 20 people from population B. A larger samples size will yield a more accurate mean. The larger the sample sizes, the more likely the outliers will cancel each other out. 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. μ 4.7 0.15556349

DF 49

L. Limit 4.3873835

U. Limit 5.0126165

Lower limit: 4.4 Upper limit: 5.0 For a 99% confidence interval? One sample T summary confidence interval: μ : Mean of population 99% confidence interval results: Mean Sample Mean Std. Err. μ 4.7 0.15556349

DF 49

L. Limit 4.2830973

U. Limit 5.1169027

Lower limit: 4.3 Upper limit: 5.1

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? One sample T hypothesis test: μ : Mean of variable H0 : μ = 72 HA : μ ≠ 72 Hypothesis test results: Variable Sample Mean Resting HR 75.352941

Std. Err. 2.1419157

DF 16

T-Stat 1.5653936

P-value 0.1371

t = 1.57 Using an alpha of 0.05, is the t statistic significant? Why? It is not significance because the 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? Copy and Paste your work from StatCrunch into your Word document submission. One sample T confidence interval: μ : Mean of variable 95% confidence interval results: Variable Sample Mean Resting 75.352941 HR

Std. Err.

DF

L. Limit

U. Limit

2.1419157

16

70.812283

79.8936

The lower limit is 70.8 and the upper limit is 79.9; with 95% confidence interval, we can expect 95% of values are between the lower and upper limit.

BST 322 Week 2 Assignment 5.

(1 pt) Write a few sentences that could be used to report the results obtained for the t-test in Exercise 4. In a study evaluating the use of a new drug to lower resting heart rates in a group of patients, the average resting heart rate was 72 beats per minute (BPM). With an alpha level of 0.05, the t stat of 1.57 is less than the tabled value of 2.12. The p value of this study is 0.137, which is greater than 0.05. Based on these results, the data is insignificant and the null hypothesis is rejected.

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 MentalHlth 45.88 0.89021125149

T-Stat 0.98852941

P-value 0.3245

The result is not significant because the p value is greater than 0.05. 7.

(1 pt) Write a few sentences that could be used to report the results obtained for the t-test in Exercise 6. In a study conducted in the inner city of Philadelphia, 150 women were asked to give a mental health score. With the national mean of 45, the p value was calculated to be greater than 0.05, being 0.32. The t stat, 0.99 for this study, is less than tabled value of 1.96 at alpha significance level of 0.05.

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 H 0 : μ1 - μ2 = 0 H A : μ1 - μ2 ≠ 0 (with pooled variances) Hypothesis test results: Difference Sample Diff. Std. Err. DF μ1 - μ2 5.3409091 2.3386091 86

T-Stat 2.2837973

P-value 0.0248

The result is significant; the p value is less than 0.05. The hypothesis tested is marital status, of either married or divorced, on mental health scores.

BST 322 Week 2 Assignment 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; there are more than 2 groups for the independent variable.

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; two groups are unrelated and independent of each other. 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; there are more than 3 groups for the independent variable.

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: 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: Difference Sample Diff. Std. Err. DF T-Stat P-value μ1 - μ2 4 15.459495 48 0.25874066 0.7969 t = 0.26 P-value is greater than 0.05, therefore not significant and null hypothesis is accepted. df = 48

BST 322 Week 2 Assignment 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.

c.

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

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/MANOVA b. The IV is smoking status – smokers vs non-smokers; the DV is a health-related hardiness score, measured on a 20-item scale. Not appropriate; Less than 3 groups for independent variables 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. Not appropriate; only two groups for independent variable 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. Not appropriate; uses the same group multiples times

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 25

Smokers 31 29 22 29 28

Quitters 30 22 29 29 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. Mean of Nonsmokers: 21.8 Total SS: 348 Smokers: 27.8 df = 4 Quitters: 28.8 MS: 71.7 F-value is 4.21, so the null hypothesis is rejected. This is because the f-value is greater than the tabled value of 2.78. P-value is 0.0412, meaning it is significant because it is less than 0.05. Analysis of Variance results: Data stored in separate columns.

BST 322 Week 2 Assignment Column statistics Column Nonsmokers Smokers Recently Quit

Source Columns Error Total

15.

DF 2 12 14

n 5 5 5

Mean 21.8 27.8 28.8

SS 143.33333 204.4 347.73333

Std. Dev. 4.5497253 3.4205263 4.3243497

ANOVA table MS 71.666667 17.033333

Std. Error 2.034699 1.5297059 1.933908

F-Stat 4.2074364

P-value 0.0412

(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. Analysis of Variance results: Data stored in separate columns. Column statistics Column Divorced MentalHlth Married MentalHlth Never married MentalHlth ANOVA table Source DF Columns 2 Error 147 Total 149

SS 1095.3334 16616.507 17711.84

n Mean 44 41.727273 44 47.068182 62 47.983871

MS 547.6667 113.03746

Std. Dev. 11.998767 9.8320731 10.137565

F-Stat 4.8450018

Std. Error 1.8088821 1.4822408 1.2874721

P-value 0.0092

The result is significant because p is 0.0092, when p is less than 0.05, the null hypothesis is rejected. The hypothesis tested is the effect of marital status on mental health scores....