with a sample mean of 15, sample standard deviation of 6.1, and a sample size of 9, we can use a one-sample t-test with the following formula:
t = (x̄ - μ) / (s / √n)
where:
x̄ = sample mean
μ = hypothesized population mean (Ho)
s = sample standard deviation
n = sample size
Substituting the given values:
t = (15 - 10) / (6.1 / √9)
t = 2.459
Using a significance level of 0.05 and a one-tailed test (Ha: μ > 10), the critical t-value with 8 degrees of freedom is 1.86 (obtained from a t-table or calculator).
Since the calculated t-value (2.459) is greater than the critical t-value (1.86), we reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis that the true population mean is greater than 10.
To compute for the p-value, we can use a t-distribution table or calculator with 8 degrees of freedom and a one-tailed test. The p-value associated with a t-value of 2.459 is approximately 0.019. Since the p-value is less than the significance level of 0.05,we reject the null hypothesis and conclude that the sample provides strong evidence that the true population mean is greater than 10.
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Verified answer
Answer:
To test the hypothesis:
Ho: μ = 10
Ha: μ > 10
with a sample mean of 15, sample standard deviation of 6.1, and a sample size of 9, we can use a one-sample t-test with the following formula:
t = (x̄ - μ) / (s / √n)
where:
x̄ = sample mean
μ = hypothesized population mean (Ho)
s = sample standard deviation
n = sample size
Substituting the given values:
t = (15 - 10) / (6.1 / √9)
t = 2.459
Using a significance level of 0.05 and a one-tailed test (Ha: μ > 10), the critical t-value with 8 degrees of freedom is 1.86 (obtained from a t-table or calculator).
Since the calculated t-value (2.459) is greater than the critical t-value (1.86), we reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis that the true population mean is greater than 10.
To compute for the p-value, we can use a t-distribution table or calculator with 8 degrees of freedom and a one-tailed test. The p-value associated with a t-value of 2.459 is approximately 0.019. Since the p-value is less than the significance level of 0.05,we reject the null hypothesis and conclude that the sample provides strong evidence that the true population mean is greater than 10.
Step-by-step explanation:
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