Question

The number of hours that each student in marketing class spent studying for the last exam has a normal distribution with a population standard deviation of 1.4 hours and an unknown population mean. If a random sample of 30 students is taken and results in a sample mean of 6.9 hours, find a 95% confidence interval for the population mean. Use the tool below to calculate your confidence interval. Choose the correct confidence level, sample mean, population standard deviation, and sample size. Then view the confidence interval indicated on the x-axis to find your answer. Please note, you'll need to use the sliders above the graph to change the x-axis markers. Round your answers to 2 decimal places. Set the sliders in order from top to bottom.

Answer 1

To calculate the 95% confidence interval for the population mean, use the formula: Confidence Interval = sample mean ± (critical value * (population standard deviation / sqrt(sample size))).

The 95% confidence interval for the population mean is (6.36, 7.44) hours.

Step-by-step explanation:

To calculate the 95% confidence interval for the population mean, we can use the formula:

Confidence Interval = sample mean ± (critical value * (population standard deviation / sqrt(sample size)))

In this case, the sample mean is 6.9 hours, the population standard deviation is 1.4 hours, and the sample size is 30. The critical value for a 95% confidence level can be found using a normal distribution table or a calculator. The critical value at a 95% confidence level is approximately 1.96.

Plugging in the given values into the formula, we get:

Confidence Interval = 6.9 ± (1.96 * (1.4 / sqrt(30))) = (6.9 - 0.539, 6.9 + 0.539) = (6.36, 7.44)

Therefore, the 95% confidence interval for the population mean is (6.36, 7.44) hours.