A hospital is offering three cardiac rehabilitation programs that are identical

Question

A hospital is offering three cardiac rehabilitation programs that are identical in content but are offered at three different times. The hospital would like to determine if the three slots are equally popular or convenient for patients. A total of 100 patients are involved in the study and each patient is asked to select the one day and time that is most convenient. Test whether the three day and time options are equally popular (i.e., test whether the proportions are each equal to .33). Use alpha=.05. Give each of the following to receive full credit: 1) the appropriate null and alternative hypotheses; 2) the appropriate test; 3) the decision rule; 4) the calculation of the test statistic; and 5) your conclusion including a comparison to alpha or the critical value. You MUST show your work to receive full credit. Partial credit is available.

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Tuesday

6-7:30 pm

Wednesday

4:30-6 pm

Saturda

8:30-10 am

# of patients

46

33

21

Tuesday

6-7:30 pm

Wednesday

4:30-6 pm

Saturda

8:30-10 am

# of patients

46

33

21

Explanation / Answer

(1) Null HYpothesis : H0 : The three day and time options are equally popular. all proportions are equal to 0.33. p1 = p2 = p3 = 0.333

Alternative Hypothesis : Ha : The three day and time options are not equally popular.

(2) We will use chi - square statistic here

(3) HEre deicision Rule is to reject the null hypothesis if X2 > X2df, 0.05 where dF = 3-1 = 2

HEre epected value = 100/3 = 33.33

Here chi - square statistic X2 = 4.81 + 0.00 + 4.56 = 9.38

(4) Here for dF = 2 and alpha = 0.05

critcical chi - square value is X2cr = 5.9915

(5) Here  X2 >  X2cr so we shall reject the null hypothesis and can conclude that the three day and time options are not equally popular.

Time status Number of patients (o) Expected (E) (O - E)^2/E Tuesayd 46 33.33 4.81 Wednesday 33 33.33 0.00 Saturday 21 33.33 4.56 Sum 100 100 9.38

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