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 by test the claim that the sample is from a population with a mean greater than 85 sec? are the requirements all satisfied?
77 15 558 53 0 57 207 43 192 0 2 60
what requirements must be satisfied? select all that apply.
a. either the population is normally distributed, or n>30, or both
b. the conditions for a binomial distribution must be satisfied.
c. the sample observations must be a simple random sample.
d. at least one observation must be above or below 85 sec.

Explanation:

For testing a claim about a population mean, the sample must be a simple random sample (to ensure representativeness). Also, if the population standard deviation \(\sigma\) is unknown (which is often the case when dealing with sample data like this), we use the \(t -\)test. The \(t -\)test has the requirement that either the population is normally distributed, or the sample size \(n>30\) (by the Central Limit Theorem, for large \(n\), the sampling distribution of the sample mean \(\bar{x}\) is approximately normal). The binomial distribution conditions (fixed number of trials, two - outcome per trial, independent trials, constant probability of success) are not relevant here as we are dealing with continuous data (time in seconds). And the condition about at least one observation above or below 85 sec is not a fundamental requirement for the hypothesis test about the population mean.

Answer:

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