4-2 Problem Set Statistical Inference and Hypothesis Testing

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1 4-2 Problem Set: Statistical Inference and Hypothesis Testing 4-2 Problem Set: Statistical Inference and Hypothesis Testing Jennifer St. Denis Southern New Hampshire University IHP-525-Q3468 Biostatistics 24TW3 Dr. Struwe March 24, 2024

2 4-2 Problem Set: Statistical Inference and Hypothesis Testing IHP 525 Module Four Problem Set 1. Pediatric asthma survey, n = 50. Suppose that asthma affects 1 in 20 children in a population. You take an SRS of 50 children from this population. Can the normal approximation to the binomial be applied under these conditions? If not, what probability model can be used to describe the sampling variability of the number of asthmatics? From the given data , Sample size (n) = 50 P(asthma attack) = p = (1/20) = 0.05 Here, n*p*(1-p) = 50 * 0.05 * (1- 0.05) = 2.375 < 5 Explanation: For normal approximation, the value of n*p*(1-p) should be greater than or equal to 5 np(1-p) < 5, so we cannot use normal approximation. Here, we use a binomial probability model to describe the sampling variability of the number of asthmatics. Using the binomial probability model, P(X=x) = ncx * p^x * (1-p)^(n-x) X ~ Binomial (50, 0.05) Explanation: Using the binomial probability model, we can describe the sampling variability here Answer- Normal approximation cannot be used 2. Misconceived hypotheses. What is wrong with each of the following hypothesis statements? a) H 0 : μ = 100 vs. H a : μ ≠ 110 b) H 0 : x̄ = 100 vs. H a : x̄ < 100 or could write as H 0 : x̄ >= 100 vs. H a : x̄ < 100 c) H 0 : p^ = 0.50 vs. H a : p^ ≠ 0.50 a) Both parameter values are different in the null and alternate hypotheses. They should be the same for HO it is 100 and for Ha it is 110 b) HO and Ha use parameter( µ) and not statistics( x̄) c) HO and Ha use parameter( p) and not statistics( p^)

3 4-2 Problem Set: Statistical Inference and Hypothesis Testing 3. Patient satisfaction. Scores derived from a patient satisfaction survey are Normally distributed with μ = 50 and σ = 7.5, with high scores indicating high satisfaction. An SRS of n = 36 is taken from this population. From the given data: a) What is the standard error (SE) of x for these data? b) We seek to discover if a particular group of patients comes from this population in which μ = 50. Sketch the curve that describes the sampling distribution of the sample mean under the null hypothesis. Mark the horizontal axis with values that are ±1, ±2, and ±3 standard errors above and below the mean. c) Suppose in a sample of n = 36 from this particular group of patients the mean value of x is 48.8. Mark this finding on the horizontal axis of your sketch. Then compute a z statistic for this scenario and make sure it matches your sketch. d) What is the two-sided alternative hypothesis for this scenario? e) Find the corresponding p-value for your z-statistic using Table B. f) Draw a conclusion for this study scenario based on your results.

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4 4-2 Problem Set: Statistical Inference and Hypothesis Testing

5 4-2 Problem Set: Statistical Inference and Hypothesis Testing References Gerstman, B. (2015). Basic Biostatistics: Statistics for Public Health Practice (2 ed.). Burlington, MA: Jones & Bartlett Learning. Hosmer, D.W. and Lemeshow, S. and May, S. (2008) Applied Survival Analysis: Regression Modeling of Time to Event Data: Second Edition [Data set], John Wiley and Sons Inc., New York, NY. Pearson Education. Released 2014. StatCrunch, June 2016 Update Version [Computer Software]. New York City, NY. Pearson Corporation

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