Patient satisfaction. Scores derived from a patient satisfaction survey are Normally distributed with = 50 and

Question:

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 SE of for these data?

(b) We seek evidence against the hypothesis that a particular group of patients comes from a population in which μ = 50. Sketch the curve that describes the sampling distribution of 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 a sample of n = 36 finds an of 48.8. Mark this finding on the horizontal axis of your sketch. Then calculate the zstat for the result. Does this observation provide strong evidence against H0?