Question

A hospital director is told that 56%56% of the emergency room visitors are insured. The director wants to test the claim that the percentage of insured patients is under the expected percentage. A sample of 360 patients found that 180 were insured. At the 0.10 level, is there enough evidence to support the director's claim?

A.) There is sufficient evidence to support the claim that the percentage of insured patients is under 56%

B.) There is not sufficient evidence to support the claim that the percentage of insured patients is under 56%

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H0 : p = 0.56

Ha : p < 0.56

= x / n = 180 / 360 = 0.50

P0 = 0.56

1 - P0 = 1 - 0.56 = 0.44

Test statistic = z =

= - P0 / [P0 * (1 - P0 ) / n]

= 0.50 - 0.56 / [(0.56 * 0.44) / 360 ]

Test statistic = z = -2.29

P(z < -2.29 )

P-value = 0.011

= 0.10

P-value <

Reject the null hypothesis .

A.) There is sufficient evidence to support the claim that the percentage of insured patients is under 56%