Question

A study revealed that the 30-day readmission rate was 32.8 percent for 376 patients who received...

A study revealed that the 30-day readmission rate was 32.8 percent for 376 patients who received after-hospital care instructions (e.g., how to take their medications) compared to a readmission rate of 44.3 percent for 375 patients who did not receive such information.

(a) Choose the appropriate hypotheses to see whether the admissions rate was lower for those that received the information. Assume ππ 1 is the proportion of those that received the information and ππ 2 is the proportion of those that did not.

a. H0: ππ 1 − ππ 2 ≥ 0 vs. H1: ππ 1 − ππ 2 < 0

b. H0: ππ 1 − ππ 2 = 0 vs. H1: ππ 1 − ππ 2 ≠ 0

c. H0: ππ 1 − ππ 2 ≥ 0 vs. H1: ππ 1 − ππ 2 > 0

  • a

  • b

  • c

(b) Find the p-value for the test. (Do not round the intermediate calculations and round x1 and x2 to the nearest whole number. Round your answer to 4 decimal places.)

p-value             

(c-1) What is your conclusion at α = 0.05?

We  (Click to select) (can) (cannot   conclude) that the admissions rate was lower for those who received the information.

(c-2) What is your conclusion at α = 0.10?

We  (Click to select) (can) (cannot   conclude) that the admissions rate was lower for those who received the information.

Please explain and give details of each response

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

Given : n1=376 , p1=32.8%=0.328 , n2=375 , p2=44.3%=0.443

The pooled estimate is ,

P=(n1p1+n2p2)/(n1+n2)=(376*0.328+375*0.443)/(376+375)=0.3854

Q=1-P=0.6146

(a) Hypothesis : Vs  

The test statistic is ,

b) The p-value is ,

p-value=

; From standard normal distribution table

c-1) Decision : Here , p-value=0.0006 < 0.05

Therefore , reject Ho.

Conclusion : Hence , we can conclude that the admissions rate was lower for those who received the information.

c-2) Decision : Here , p-value=0.0006 < 0.10

Therefore , reject Ho.

Conclusion : Hence , we can conclude that the admissions rate was lower for those who received the information.

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