Rivera assignment 2

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National University *

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322

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Statistics

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Feb 20, 2024

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Uploaded by CountSalmon4044

BST 322 Week 2 Assignment 1. (1 pt) What is the probability of rolling a four with a six-sided die? ® P (rolling 4) = 1/6 = 0.166 or 17% What is the probability that a person can roll 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) * P (roll a four) * P (roll a four) = 1/6%1/6*1/6 = .00462 which is .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 yield a more accurate estimate because of the larger population sample to collect from. Population A is 50 and Population B is 20. While population increase, SEM decreases. The larger the data, the closer the results to the mean. 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? e At 95% confidence level, the mean vein size after nitroglycerin application is between the lower limit of 4.39 and upper limit of 5.01. H : Mean of population 95% confidence interval results: Mean Sample Mean Std. Err. DF L. Limit U. Limit M 4.7 0.15556349 49 4.3873835 5.0126165 *For a 99% confidence interval? * At 99% confident level, the mean vein size after the nitroglycerin application is between the lower limit of 4.28 and 5.12. One sample T summary confidence interval: M : Mean of population 99% confidence interval results: Mean Sample Mean Std. Err. DF L.Limit U. Limit [V 4.7 0.15556349 49 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 1015 65 016 75 1017 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 0.05, is the t statistic significant? Why? O The value of t =1.5653936, the t statistic is not significant because the P-Value is greater than 0.05 One sample T hypothesis test: { : Mean of variable Hy: p=72 Ha:p#72 Hypothesis test results: Variable Sample Mean Std. Err. DF T-Stat P-value Resting HR 75.352941 2.1419157 16 1.5653936 0.1371

O At the 95% interval the resting HR is between the lower rate of 70.81 and upper rate of 79.89. g: Mean of variable 95% confidence interval results: Variable Sample Mean Std. Err. DF L. Limit U. Limit Resting HR 75.352941 2.1419157 16 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. O The study has an average heart rest rate is 72 beats per minutes (BPM). The critical value of 0.05 with the t stat of 1.57 being less than the value 2.12 on the t-table (textbook pg. BEP-3). The p value in the study is 0.137 is greater than 0.05. With 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. 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. O The result is insignificant because the P-value (0.3245) is greater than critical value 0.05. One sample T hypothesis test: H : Mean of variable Ho:p =45 Ha: p #45 Hypothesis test results: Variable Sample Mean Std. Err. DF T-Stat P-value MentalHIth 45.88 0.89021125 149 0.98852941 0.3245 7. (1 pt) Write a few sentences that could be used to report the results obtained for the t-test in Exercise 6.

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O The study conducted in the inner city of Philadelphia, the mental health outcome of 150 women with a national mean of 45, the P-value of .3245 is greater than critical value 0.05. The t-stat 0.99 for this study is less than the 1.97 on the t-table (textbook pg. BEP-3). With these results, the data is insignificant and the null hypothesis is rejected. 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? O The result is significant because the P-value is less than critical value 0.05 Two sample T hypothesis test: M1 : Mean of Divorced MentalHIth M, : Mean of Married MentalHIth M1 - M2 : Difference between two means Ho:M1-Hp2=0 Ha:ph-p2#0 (with pooled variances) Hypothesis test results: Difference Sample Diff. Std. Err. DF T-Stat P-value Hi1 - M2 -5.3409091 2.3386091 86 -2.2837973 0.0248 *What hypothesis did you test? Copy and paste your StatCrunch output into your submission document for full credit. O The hypothesis was that, those married would have same mental health score as those who are divorce. The result is significant because P- value 0.0248 is less than 0.05. 9. (2 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 3 independent variables. 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 because IV is unrelated to DV

(type of birth at home or hospital has nothing in common with ability of a patient after surgery in 48 hrs.) 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 because 3 independent variables or groups 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?; (variance) = 49.1n, = 25 mean group 2 = 74.1 SD?, (variance) = 59.7n,= 25 *What are the degrees of freedom and the value of ¢t ? Using a=0.05 for a two-tailed test, O The degree of freedom is 48, T-Stat is 0.26. The result is not significant because the P - value 0.7969 is greater than the critical value 0.05 *Is this ¢ statistic significant? Show your calculations (or StatCrunch output) for full credit. O The t statistic is not significant because the P - value 0.7969 is greater than the critical value 0.05 Two sample T summary hypothesis test: {1 : Mean of Population 1 H, : Mean of Population 2 Hi - M2 : Difference between two means Ho:p1-p2=0 Ha:p1-p2#0 (with pooled variances) Hypothesis test results: Difference Sample Diff. Std. Err. DF T-Stat P-value Hy = M2 4 15.459495 48 0.25874066 0.7969 12. (1 pt) For each of the following t values (a-d), indicate whether the ¢ statistic is statistically significant for a two-tailed test, at the specified alphas: a. t=2.90, df = 25, a = 0.01 O significant

b. t=2.20, df = 25, a = 0.05 O significant (oA t=5.52,df =10, a =0.01 O significant d. t=2.02, df = 20, a = 0.05 O 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? O The result is not significant because the P-value 0.9162 is greater than the critical value 0.05. Two sample T hypothesis test: H, : Mean of Married GPCOG H2 : Mean of Never married GPCOG M1 - Y2 : Difference between two means Ho:p1-p2=0 Ha:p1-p2#0 (with pooled variances) Hypothesis test results: Difference Sample Diff. Std. Err. DF T-Stat P-value M1 - M2 0.081378299 0.77132198 104 0.10550497 0.9162 *What hypothesis did you test? O The hypothesis was to test the difference in GPCOG between the married and never married living in urban city of Philadelphia. *Did you try a "pooled" variances test here in StatCrunch? Why or why not? Copy and paste your StatCrunch output into your submission document for full credit. O Yes, I tried pooled variance test, it however, wasn't useful because two the sample groups were different and shared no common variables.

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