Answer:
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
Step-by-step explanation:
<u><em>Step(i):-</em></u>
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
<u><em>Step(ii):-</em></u>
<u><em>Null hypothesis:-H₀: </em></u> (μ) = 12
<em>Alternative Hypothesis: H₁</em> : μ < 12
Test statistic
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
<u><em>Final answer:-</em></u>
The EMS director wants to service goal of 12 minutes or less is being achieved
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