Question

A hospital reported that the normal death rate for patients with extensive burns (more than 40% of skin area) has been significantly reduced by the use of new fluid plasma compresses. Before the new treatment, the mortality rate for extensive burn patients was about 60%. Using the new compresses, the hospital found that only 44 of 95 patients with extensive burns died. Use a 1% level of significance to test the claim that the mortality rate has dropped since using the new treatment.

What are we testing in this problem?

single meansingle proportion    

What is the level of significance?


State the null and alternate hypotheses.

H₀: p ≤ 0.6; H₁: p > 0.6H₀: p = 0.6; H₁: p ≠ 0.6    H₀: μ ≥ 0.6; H₁: μ < 0.6H₀: p ≥ 0.6; H₁: p < 0.6H₀: μ = 0.6; H₁: μ ≠ 0.6H₀: μ ≤ 0.6; H₁: μ > 0.6

What sampling distribution will you use?

The standard normal.The Student's t.    

What is the value of the sample test statistic? (Round your answer to two decimal places.)


Estimate the P-value.

P-value > 0.2500.125 < P-value < 0.250    0.050 < P-value < 0.1250.025 < P-value < 0.0500.005 < P-value < 0.025P-value < 0.005

Sketch the sampling distribution and show the area corresponding to the P-value.

Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.    At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.01 level to conclude that the mortality rate has dropped.There is insufficient evidence at the 0.01 level to conclude that the mortality rate has dropped.    

Answer 1

The statistical software output for this problem is:

From above output:

What are we testing? Single Proportion

Level of significance = 0.01

Hypotheses: 0: p ≥ 0.6; H1: p < 0.6

Sampling distribution: The standard normal.

Test statistic = -2.72

P-value < 0.005

At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.

There is sufficient evidence at the 0.01 level to conclude that the mortality rate has dropped.