Question

A local hospital claims that you will not wait longer than 45 minutes in the emergency room. You go out to test this claim and find a sample of 81 patients chosen at random from their emergency room, you find a sample mean of 52 minutes with a sample standard deviation of 23 minutes. Can you publicly debunk their claim (call their claim fraudulent) at the 1% significance level? Use a test stat and then a p-value to determine if your conclusion is weak or strong

Answer 1

H0: Null Hypothesis: 45 (You will not wait longer than 45 minutes in the emergency room. ) (Claim)

HA: Alternative Hypothesis: > 45 (You will wait longer than 45 minutes in the emergency room. )

n = 81

= 52

s = 23

df = 81 - 1 = 80

= 0.01

From Table, critical value of t = 2.374

Test Statistic is given by:

Since calculated value of t = 2.739 is greater than critical value of t = 2.374, the difference is significant. Reject null hypothesis.

Conclusion:
The data do not support the claim that you will not wait longer than 45 minutes in the emergency room.

By Technology,

p - value = 0.0038.

Since p - value = 0.0038 is less than = 0.01, the difference is significant. Reject null hypothesis.

Conclusion:
The data do not support the claim that you will not wait longer than 45 minutes in the emergency room.