Answer :
The p-value for the test is found as 0.05 for the given hypothesis.
Given,Sample mean = 59.1 km
Sample standard deviation = 2.31 km
Population is normally distributed
P-value for the test is to be determined.
To find the p-value, we need to perform a hypothesis test. Here, we have to test whether the null hypothesis is true or not.
Hypothesis statements:
Null hypothesis (H0): µ = 60 km (The population mean is 60 km)
Alternative hypothesis (Ha): µ ≠ 60 km (The population mean is not equal to 60 km)
Level of significance, α = 0.05
Z-score formula is given as,Z = (x - µ) / (σ/√n)
Where,x = Sample mean = 59.1 km
µ = Population mean
σ = Standard deviation of the population = 2.31 km
n = Sample size
We have,σ/√n = 2.31/√n
For α = 0.05, the two-tailed critical values are ±1.96
Now, the calculated Z-score is given as,
Z = (59.1 - 60) / (2.31/√n)
Z = - (0.9) * ( √n / 2.31)
P(Z < -1.96) = 0.025 and P(Z > 1.96) = 0.025
P-value = P(Z < -1.96) + P(Z > 1.96)
P-value = 0.025 + 0.025
P-value = 0.05
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