What would one conclude about the null hypothesis that a sample of N = 46 with a mean of = 104 could reasonably have been drawn from a population with the parameters of = 100 and s = 8? Use a = 0.05 2 tail . A) accept H₀ B) reject H₁ C) reject H₀ D) retain H₀

Question

Quizplus · Accepted Answer

We use the t-test for this question since we do not know the population standard deviation. The formula for the t-statistic is:

t = (x̄ - μ) / (s / √n)

where x̄ is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.

Plugging in the values, we get:

t = (104 - 100) / (8 / √46) = 2.33

Using a two-tailed test with α = 0.05 and df = 45 (n-1), from the t-distribution table, the critical values are ±2.013. Since our calculated t value (2.33) is greater than the critical value (2.013), we reject the null hypothesis. Therefore, we can conclude that the sample with a mean of 104 could not have reasonably been drawn from a population with a mean of 100 and standard deviation of 8.

What Would One Conclude About the Null Hypothesis That a Sample