Question

A test was conducted with H0​:μ=10 and H1​=10 and 95% confidence interval for μ was: [−12,8]. We have enough information to reject or fail to reject the null at 0.05 significance level from the above information. True False Question 20 (5 points) One factor at a time design fails to consider any possible interaction between the factors. True False Question 21 (5 points) Identify the population: Members of the Theater Club plan to sell popcorn as a fundraiser for their Shakespeare production. They Survey 100 students at random about their favorite flavors of popcorn. 46 students like butter, 20 like cheese, and 34 like caramel. The club concluded that all students prefer butter. 100 students 46 students All students 34 students Question 22 (3 points) The sample mean yˉ​ is a point estimator of the population mean μ, and the sample variance S2 is a point estimator of the population variance σ2. True False

Answer 1

False: The confidence interval alone doesn't provide enough information to reject or not reject the null hypothesis.

True: One factor at a time design overlooks interactions between factors.

Step-by-step explanation:

In the first question, a confidence interval is provided for the population mean (μ) along with the null hypothesis (H₀: μ = 10) and an alternative hypothesis (H₁ ≠ 10). However, without knowing the actual sample mean or standard deviation, we cannot make a definitive decision regarding the null hypothesis at the 0.05 significance level. The decision would typically involve comparing the hypothesized value with the confidence interval bounds.

The second question discusses the limitation of a one-factor-at-a-time design, which focuses on individual factors without considering their interactions. This approach may overlook potential combined effects, leading to an incomplete understanding of the factors' impact.

Regarding the third question, the population in the survey is all students, as the Theater Club intends to make an inference about the entire student population based on the sampled 100 students. However, the conclusion drawn by the club is an overgeneralization, as preferences within the sampled 100 students cannot be assumed to represent the entire population.

Finally, the fourth question clarifies the distinction between the sample mean (ȳ) and the sample variance (S²) as point estimators for the population mean (μ) and population variance (σ²), respectively. It notes that the sample standard deviation (S) is the appropriate point estimator for the population standard deviation (σ).