3. Patient satisfaction. Scores derived from a patient satisfaction survey are Normally distributed with u = 50 and o = 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 u = 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, 12, and 13 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> 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. Draw a conclusion for this study scenario based on your results