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
are the requirements all satisfied?
○ a. yes. the conditions for a binomial distribution are satisfied, and there is enough information to determine that the sample is a simple random sample.
○ b. no. the sample size is not greater than 30, the sample does not appear to be from a normally distributed population, and there are no observations above 85 sec.
○ c. no. the sample size is not greater than 30, the sample does not appear to be from a normally distributed population, and there is not enough information given to determine whether the sample is a simple random sample.
○ d. no. the conditions for a binomial distribution are not satisfied, and there is not enough information given to determine whether the sample is a simple random sample.

Explanation:

• Sample size: The sample size \(n = 12<30\). For a hypothesis test about a population mean when \(\sigma\) (population standard deviation) is unknown, if \(n < 30\), we need to assume the population is normally distributed or check for normality.
• Normality: The data values \(0,0,2,14,42,50,56,62,78,180,198,567\) have extreme values (e.g., \(567\) is an outlier), so the sample does not seem to come from a normally - distributed population.
• Simple random sample: The problem statement only says “twelve different video games showing alcohol use were observed” but does not explicitly state that it is a simple random sample. There is not enough information to confirm this requirement.

So, the requirements for the hypothesis test about the population mean (\(t\) - test for a mean when \(\sigma\) is unknown) are not all satisfied.

Answer:

C. No. The sample size is not greater than 30, the sample does not appear to be from a normally distributed population, and there is not enough information given to determine whether the sample is a simple random sample.