1) Kristen worked a total of 257 shifts. What is the sampling distribution for t

Question

1) Kristen worked a total of 257 shifts. What is the sampling distribution for the proportion of shifts containing a death if 257 shifts were sampled at random?

2) 40 of Kristen Gilbert's shifts had at least one death on shift. This accounts for 15.56% of her shifts. Calculate the corresponding Z-statistic if we assume her shifts represent a random sample of all shifts.

Hospital is suspicious that Kristin the nurse, has caused many patient deaths. At this particular hospital a death during a shift occurred 4.5% of shifts. Considering a death on shift a 1 and no deaths a 0, a single shift has an expected value (or mean) of 0.045, and a standard deviation of sqrt(0.045*0.955)=0.2073. We wish to show that there is evidence that shifts worked by Kristen had a higher proportion of deaths on shift than a typical shift.

Explanation / Answer

P^ -  proportion of shifts containing a death

n = 257 , E(P^) = 0.045

sd (P^) = sqrt(p^q^/n) = sqrt(0.045*0.955/257)=0.0129312

{note that your calculation of sd is wrong , you did not consider n)

P^ follow N(0.045 ,0.0129312^2 )

2)Z = (p -p^)/sd(p^)

= (0.1556 - 0.045)/0.0129312

= 8.55295718

z-critical for alpha = 0.05 , z = 1.645

since TS > critical value ,    { 8.55295718 > 1.645}

we reject the null and coclude that   there is evidence that shifts worked by Kristen had a higher proportion of deaths on shift than a typical shift.

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