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Test statistic and p-value for sample

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Calculate the test statistic and p-value for each sample.
a. H0: μ = 60 versus H1: μ = 60, α = .025, ¯x = 63, σ= 8, n = 16
b. H0: μ ≥ 60 versus H1: μ < 60, α = .05, ¯x = 58, σ= 5, n = 25
c. H0: μ ≤ 60 versus H1: μ > 60, α = .05, ¯x = 65, σ= 8, n = 36

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The test statistic and p-value for each sample is determined.

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Calculate the test statistic and p-value for each sample.
a. H0: μ = 60 versus H1: μ = 60, α = .025, ¯x = 63, σ = 8, n = 16
b. H0: μ ≥ 60 versus H1: μ < 60, α = .05, ¯x = 58, σ = 5, n = 25
c. H0: μ ≤ 60 versus H1: μ > 60, α = .05, ¯x = 65, σ = 8, n = 36

Assumptions:
σ =Population standard deviation.
The data follows a normal distribution.
With these two assumptions, the Z test can be used for given data.
Hypothesis Test for mean:

Assuming you have a large enough sample such that the central limit theorem holds, or you have a sample of any size from a normal population ...

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