Question

he response times for a random sample of 40 medical emergencies were tabulated. The sample mean is 13.25 minutes. The population standard deviation is believed to be 3.2 minutes. The EMS director wants to perform a hypothesis test, with a .05 level of significance, to determine whether the service goal of 12 minutes or less is being achieved.

Answer 1

The calculated value Z = 2.5 > 1.96 at 0.05 level of significance

The null hypothesis is rejected

The Alternative hypothesis is rejected

The EMS director wants to service goal of 12 minutes or less is being achieved

Explanation:

Step(i):-

Given that the size of the random sample = 40

Given that the mean of the sample (x ⁻) = 13.25

Given that the standard deviation of the Population = 3.2 minutes

Level of significance = 0.05

The mean of the Population (μ) = 12

Step(ii):-

Null hypothesis:-H₀: (μ) = 12

Alternative Hypothesis: H₁ : μ < 12

Test statistic

`Z = (x^(-)-mean )/((S.D)/(√(n) ) )`

`Z = (13.25-12 )/((3.2)/(√(40) ) )`

Z = 2.5

The tabulated value Z₀.₀₅ = 1.96

The calculated value Z = 2.5 > 1.96 at 0.05 level of significance

The null hypothesis is rejected

The Alternative hypothesis is rejected

Final answer:-

The EMS director wants to service goal of 12 minutes or less is being achieved