Question

Noise levels at 4 volcanoes were measured in decibels yielding the following data: 153,156,168,138 Construct the 99% confidence interval for the mean noise level at such locations. Assume the population is approximately normal.

Step 1 of 4: Calculate the sample mean for the given sample data. Round your answer to one decimal place.

Step 2 of 4: Calculate the sample standard deviation for the given sample data. Round your answer to one decimal place.

Step 3 of 4: Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Step 4 of 4: Construct the 99% confidence interval. Round your answer to one decimal place.

Answer 1

1)

Sample mean = X / n

= 615 / 4

= 153.75

2)

Sample standard deviation = sqrt [ X² - n ² / n-1 ]

= sqrt [ 95013 - 4 * 153.75² / 3 ]

= 12.3390

3)

t critical value at 0.01 significance level with 3 df = 5.841

4)

99% confidence interval for is

- t * S / sqrt(n) < < + t * S / sqrt(n)

153.75 - 5.841 * 12.3390 / sqrt(4) < < 153.75 + 5.841 * 12.3390 / sqrt(4)

117.7 < < 189.7

99% CI is ( 117.7 , 189.7 )