Question

twelve different video games showing alcohol use were observed. the duration times of alcohol use were recorded, with the times (seconds) listed below. what requirements must be satisfied to test the claim that the sample is from a population with a mean greater than 85 sec? are the requirements all satisfied? 78 14 567 50 0 62 198 42 180 0 2 56 what requirements must be satisfied? select all that apply. a. the sample observations must be a simple random sample. b. at least one observation must be above or below 85 sec. c. the conditions for a binomial distribution must be satisfied. d. either the population is normally distributed, or n > 30, or both.

Explanation:

• For option A: A simple random sample is a fundamental requirement for most statistical tests. If the sample is not random, it may be biased and not representative of the population, leading to inaccurate conclusions.
• For option B: This is not a requirement. The claim is about the population mean, not about having observations above or below a certain value.
• For option C: A binomial distribution is used for categorical data (success/failure). Here, the data (duration times) is numerical, so binomial distribution conditions are not relevant.
• For option D: When testing a claim about a population mean, if the population standard deviation \(\sigma\) is unknown (which is often the case), we use the \(t\) - test. The \(t\) - test assumes that either the population is normally distributed or the sample size \(n>30\) (by the Central Limit Theorem). Here \(n = 12<30\), so we need to check the normality of the population (either from prior knowledge or by looking at the sample distribution, e.g., using a normal probability plot).

Answer:

A. The sample observations must be a simple random sample; D. Either the population is normally distributed, or \(n>30\), or both.