Suppose we have a random sample of size n=100 drawn from a population with a mean of μ=50 and a standard deviation of σ=10. We want to test the null hypothesis H0: μ=48 against the alternative hypothesis H1: μ≠48 using a two-tailed test with a significance level of α=0.05. What is the decision and p-value of this hypothesis test?
Suppose we have a random sample of size n=100 drawn from a population with a mean of μ=50 and a standard deviation of σ=10. We want to test the null hypothesis H0: μ=48 against the alternative hypothesis H1: μ≠48 using a two-tailed test with a significance level of α=0.05. What is the decision and p-value of this hypothesis test?
Chapter9: Sequences, Probability And Counting Theory
Section9.7: Probability
Problem 3SE: What is an experiment?
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Question
Suppose we have a random sample of size n=100 drawn from a population with a mean of μ=50 and a standard deviation of σ=10. We want to test the null hypothesis H0: μ=48 against the alternative hypothesis H1: μ≠48 using a two-tailed test with a significance level of α=0.05. What is the decision and p-value of this hypothesis test?
Expert Solution
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Step 1
The test statistic is calculated as (x̄-μ0)/(σ/√n), where x̄ is the sample mean, μ0 is the hypothesized mean under the null hypothesis, and n is the sample size. Plugging in the numbers, we get (50-48)/(10/√100)=2.
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