please help explain this.

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 93 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.

State the null and alternate hypotheses.

H₀: p ≥ 0.6; H₁: p < 0.6

H₀: 𝜇 ≤ 0.6; H₁: 𝜇 > 0.6    

H₀: 𝜇 ≥ 0.6; H₁: 𝜇 < 0.6

H₀: 𝜇 = 0.6; H₁: 𝜇 ≠ 0.6

H₀: p = 0.6; H₁: p ≠ 0.6

H₀: p ≤ 0.6; H₁: p > 0.6

Can you help explain the why and how we choose these?

I thought this one would be correct atH₀: 𝜇 = 0.6; H₁: 𝜇 < 0.6

but that's not even an option so now i'm confused as to what is the correct response.

Answer 1

This test is comparing the mortality rate to the previous value of 0.6. Therefore, this test isn't a test for a mean; instead, it is a test for a proportion. That is why the μ symbol is not needed in the hypotheses, but the p symbol should be used instead.

Regarding the = sign in the null hypothesis... some teachers teach that it's OK to use the = sign every time in the null hypothesis. But technically, the sign used in the null should be the opposite of the sign used in the alternative hypothesis. So, since the < sign is used in H₁, then the opposite of that, ≥, would be needed in the null hypothesis.

Therefore, the correct set of hypotheses should be H₀ : p ≥ 0.6; H₁ : p < 0.6.