The president of a university believes the entering class this year has an average ACT score higher than previous years. The average ACT score previously had been 23. He took a sample of 100 students from this year’s entering class and found their sample mean ACT score is 26 with a sample standard deviation of 5. Is there evidence the population mean ACT score is greater than 25 at the 0.01 significance level? Referring to Scenario 3-2, what is your statistical conclusion if you conduct a one-tailed test at a 0.01 significance level?
Scenario 3-2
The president of a university believes the entering class this year has an average ACT score higher than previous years. The average ACT score previously had been 23. He took a sample of 100 students from this year’s entering class and found their sample mean ACT score is 26 with a sample standard deviation of 5. Is there evidence the population mean ACT score is greater than 25 at the 0.01 significance level?
Referring to Scenario 3-2, what is your statistical conclusion if you conduct a one-tailed test at a 0.01 significance level?
Given information-
Population mean, μ = 25
Sample size, n = 100
Sample mean, M = 26
Sample standard deviation, S.D = 5
Significance level, α = 0.01
For this study we will use right-tailed t-test statistics.
Given Hypothesis is-
Null Hypothesis, H0: μ ≤ 25
Alternate Hypothesis, Ha: μ > 25
Since here population standard deviation is unknown so using t-test statistics.
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