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Week 2 Assignment

week 2 assignment biomedical statistics national university
Course

Intro to Biomedical Statistics (BST 322)

327 Documents
Students shared 327 documents in this course
Academic year: 2020/2021
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KM
Kimberly McGregor
National University (US)
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  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%.

  1. (1 pt) Population A and Population B both have a mean height of 70 inches with an SD of 6. 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.

  1. (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 with an SD of 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/ 7=.

One sample T summary confidence interval:

μ : Mean of population

95% confidence interval results: MeanSample Mean Std. Err. DF L. Limit U. Limit μ 4.70 494.

There is a 95% confidence level that the mean of the vein size after application of nitroglycerin is between 4 and 5.

One sample T summary confidence interval:

μ : Mean of population

99% confidence interval results: MeanSample Mean Std. Err. DF L. Limit U. Limit μ 4.70 494.

There is a 99% confidence level that the mean of the vein size after application of nitroglycerin is between 4 and 5.

  1. (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? Using an alpha of 0, 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

H 0  : μ = 72

HA : μ ≠ 72

Hypothesis test results: Variable Sample Mean

Std. Err. DF T-Stat P- value Resting HR

75 2. 7

16 1. 6

The value of t is 1. The t statistic is not significant because the p value is > .05.

One sample T confidence interval:

μ : Mean of variable

Two sample T hypothesis test:

μ 1  : Mean of Divorced MentalHlth μ 2  : Mean of Married MentalHlth μ 1  - μ 2  : Difference between two means H 0  : μ 1  - μ 2  = 0 HA : μ 1  - μ 2  ≠ 0 (with pooled variances)

Hypothesis test results: DifferenceSample Diff. Std. Err. DF T-Stat P-value μ 1 - μ 2 5.34090912 862 0.

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.

  1. (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

  2. (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

  3. (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 SD 21 (variance) = 49 1 = 25

mean group 2 = 74 SD 22 (variance) = 59 2 = 25

What are the degrees of freedom and the value of t? Using α=0 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:

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

HA : μ 1  - μ 2  ≠ 0 (with pooled variances)

Hypothesis test results: Differenc e

Sample Diff.

Std. Err. DF T-Stat P- value μ 1  - μ 2 4 2. 2

48 1. 5

Degrees of freedom is 48 and the value of t is 1. The results are not significant because the p value is greater than .05.

  1. (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, df = 25, α = 0. Significant b. t = 2, df = 25, α = 0. Significant

c. t = 5, df = 10, α = 0. Significant d. t = 2, df = 20, α = 0. Not significant

  1. (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., 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

  2. (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

SourceDF SS MS F-Stat P- value 3

  1. (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.

Analysis of Variance results:

Data stored in separate columns.

Column statistics

Column n Mean Std. Dev. Std. Error Divorced MentalHlth 44 41. 3

  1. 7

  2. 1 Married MentalHlth 44 47. 2

  3. 1

  4. 8 Never married MentalHlth

62 47. 1

  1. 5

  2. 1

ANOVA table

Source DF SS MS F-Stat P- value Column s

2 1095. 4

547 4. 8

Error 14 7

  1. 7

  2. 6 Total 14 9

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Week 2 Assignment

Course: Intro to Biomedical Statistics (BST 322)

327 Documents
Students shared 327 documents in this course

University: National University (US)

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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:

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