IHP 525 4-2 Problem Set Statistical Inference and Hypothesis Testing PDF

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Christina Carmody

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? p =1/20= 0.05 n= 50 Normal approximation to binomial is valid when np>5 and nq >5; here, np= 2.5 and nq= 47.5 hence Normal approximation to binomial is not valid. Binomial distribution is applicable here, X b(n= 50, p= 0.05). X is defined as asthma affects. 2. Misconceived hypotheses. What is wrong with each of the following hypothesis statements? a) H0: μ = 100 vs. Ha: μ ≠ 110 The null and alternative hypothesis is set up so that one or the other is true. the statistic shoulder be the same as the way it is written it is possible for neither to be true. b) H0: x = 100 vs. Ha: x < 100 or could write as H0: x >= 100 vs. Ha: x < 100 The hypotheses need to address the parameter not the statistic. c) H0: p^ = 0.50 vs. Ha: p^ ≠ 0.50 The hypothesis statements should address population parameter (p) not sample statistic (pˆ). 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. a) What is the standard error (SE) of x for these data? 7.5 SEx= =1.25 √ 36 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.

Problems retrieved from Gerstman, B. B. (2015). Basic biostatistics: Statistics for public health practice (2nd ed.). Burlington, MA: Jones and Bartlett. ISBN: 978-1-284-03601-5

Christina Carmody

47.5

48.75 48.8

50

51.25

52.5

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. The yellow line on the bell curve. 48.8−50 =−0.96 Zstat = 1.25 48.8 is only a little less than 1 standard deviation below µ0. Therefore, this wouldn’t be uncommon and wouldn’t provide strong evidence against H0. d) What is the two-sided alternative hypothesis for this scenario? Ha: µ ≠ 50 e) Find the corresponding p-value for your z-statistic using Table B. Zstat of -0.96 is 0.1685 f) Draw a conclusion for this study scenario based on your results. The sample mean is 1.2 less than 50, which would disprove the null hypothesis and prove the alternative hypothesis as the sample mean is not the same and less than 50. Since the P-value is 0.1685 making it >0.10 this makes the difference to be not statistically significant.

Problems retrieved from Gerstman, B. B. (2015). Basic biostatistics: Statistics for public health practice (2nd ed.). Burlington, MA: Jones and Bartlett. ISBN: 978-1-284-03601-5...