Question

1) Inspira claims that their paramedics arrive on scene of an emergency in at most 8 minutes from being dispatched. As an insurance investigator, you are asked to test this claim. You sampled 25 reports from emergency calls and found an average response time to be 8.2 minutes with a standard deviation of 0.4 minute. Assuming the population is normally distributed, what could you conclude about Inspira’s claim at the 0.01 level of significance?

2)As you were investigating Inspira’s claim you found the data from their own report, and found that their population standard deviation is 0.6. With this new information, what would you conclude about Inspira’s Claim?

Answer 1

1)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 8
Alternative Hypothesis, Ha: μ > 8

Rejection Region
This is right tailed test, for α = 0.01 and df = 24
Critical value of t is 2.492.
Hence reject H0 if t > 2.492

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (8.2 - 8)/(0.4/sqrt(25))
t = 2.5

P-value Approach
P-value = 0.0098
As P-value < 0.01, reject the null hypothesis.

2)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 8
Alternative Hypothesis, Ha: μ > 8

Rejection Region
This is right tailed test, for α = 0.01
Critical value of z is 2.326.
Hence reject H0 if z > 2.326

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (8.2 - 8)/(0.6/sqrt(25))
z = 1.67

P-value Approach
P-value = 0.0475
As P-value >= 0.01, fail to reject null hypothesis.