Find the critical value for H0: 𝜇=20, Ha: 𝜇<20,𝛼=0.05
Question
Find the critical value for H0: 𝜇=20, Ha: 𝜇<20,𝛼=0.05
Solution
To find the critical value for this one-tailed test, we will use the Z-distribution (standard normal distribution) because the population standard deviation is known.
Here are the steps:
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Identify the significance level, α. In this case, α = 0.05.
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Since this is a left-tailed test (Ha: μ < 20), we will find the critical value on the left side of the distribution.
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Look up the critical value for α = 0.05 in a Z-table. The critical value that corresponds to 0.05 in the left tail of the distribution is -1.645.
So, the critical value for this hypothesis test is -1.645.
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