Question

Emergency rooms have reason to suspect that visits increase on the weekends. A recent report indicates that Monday through Thursday represent 10% per day of the weekly total visits while Friday accounts for 15%, Saturday 25% and Sunday 20%. If your ER has the following pattern, Monday, 120, Tuesday, 130, Wednesday 110, Thursday 95, Friday 160, Saturday 280 and Sunday 105. Does your facility have the same pattern as the recent report at the 10% level

Answer 1

No the facility dose not have the same pattern as the recent report at the 10% level

Explanation:

To determine if the Facility have the same pattern ; Perform Chi squared test for Goodness of fit

state the hypothesis

H0 : μ = same pattern

Ha : μ ≠ same pattern

expected frequency ( E ) = proportion * summation of frequency

summation of frequency = 1000

degree of freedom = 7 - 1 = 6

Next : Calculate the expected frequency (E) , (O-E)²/E. given that the observed frequency and expected proportion is given

For Monday

expected frequency = proportion * frequency = 0.1 * 1000 = 100

(O-E)²/E. = ( 120 - 100 )^2 / 100 = 4.0.

observed frequency ( O ) , expected frequency ( E )

For Tuesday

E = 0.1 * 1000 = 100

(O-E)²/E = ( 130 - 100 )^2 / 100 = 9.0

Repeat same calculations for Wednesday through Sunday

Then perform Chi-squared test

X² = Σ(O-E)²/E = 63.642

∝ = 0.1

df = 6

hence P-value = 0.000 ( =chisq.dist.rt(test-stat,df)

since P-value < ∝ ; we will fail to reject Ha hence we reject H0