Question

Suppose 2% of students drink more than 3 cups of coffee each day. To check this claim, a researcher randomly selected a sample of 123 students and found that 3 drink more than 3 cups of coffee each day. What is the sampling distribution of the sample proportion? (Round your answers to four decimal places, if needed.)

The distribution of the sample proportion of students drinking more than 3 cups of coffee each day is may not be normal with a mean of ? and a standard deviation of .?

Answer 1

The sampling distribution of the sample proportion of students drinking more than 3 cups of coffee each day is approximately normal with a mean of 0.02 and a standard deviation of 0.0137.

Step-by-step explanation:

The sampling distribution of the sample proportion can be approximated using a normal distribution when the sample size is large enough. In this case, the researcher randomly selected a sample of 123 students, which is considered a large enough sample size. So, we can assume that the sampling distribution of the sample proportion of students drinking more than 3 cups of coffee each day follows a normal distribution.

The mean of the sampling distribution is equal to the true population proportion, which is 2%. So, the mean of the sampling distribution is 0.02.

The standard deviation of the sampling distribution is calculated using the formula: sqrt((p * (1 - p)) / n), where p represents the true population proportion and n represents the sample size. In this case, p = 0.02 and n = 123. Plugging in these values, we get sqrt((0.02 * (1 - 0.02)) / 123) ≈ 0.0137.

Therefore, the distribution of the sample proportion of students drinking more than 3 cups of coffee each day is approximately normal with a mean of 0.02 and a standard deviation of 0.0137.