3. Patient satisfaction. Scores derived from a patient satisfaction survey are Normally distributed with μ =...
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?
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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