SAT College

Assume a recent sociological report states that university students drink 4.14 alcoholic drinks per week on average, with a standard deviation of 1.5301. Suppose Jason, a policy manager at a local university, decides to take a random sample of 150 university students to survey them about their drinking habits.
Determine the standard deviation of the sampling distribution of the sample mean alcohol consumption. Provide your answer with precision to two decimal places.

Answers

Answer 1

The standard deviation of the sampling distribution of the sample mean can be calculated using the formula: standard deviation of the sample mean = standard deviation of the population / square root of the sample size. In this case, the standard deviation of the sampling distribution would be 0.1258 (rounded to two decimal places).

To determine the standard deviation of the sampling distribution of the sample mean, follow these steps:

Note the population mean of alcohol consumption: 4.14 drinks per week.Note the population standard deviation: 1.5301.Determine the sample size: 150 university students.Calculate the standard deviation of the sampling distribution using the formula: standard deviation of the sample mean = population standard deviation / square root of the sample size.In this case, the calculation would be: 1.5301 / √150 = 0.1258 (rounded to two decimal places).The standard deviation of the sampling distribution of the sample mean alcohol consumption is 0.1258 (rounded to two decimal places).

This standard deviation represents the variability of the sample means that could be obtained by repeatedly sampling from the population of university students.

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