Question

Six measurements were made of the magnesium ion concentration (in parts per million, or ppm) in a city's municipal water supply, with the following results. It is reasonable to assume that the population is approximately normal.

162, 151, 158, 170, 173, 161
Based on a 99% confidence interval for the mean magnesium ion concentration, is it reasonable to believe that the mean magnesium ion concentration may be greater than 185.5? (Hint: you should first calculate the 99% confidence interval for the mean magnesium ion concentration.)

Answer 1

No, it is not reasonable to believe that the mean magnesium ion concentration may be greater than 185.5 based on the 99% confidence interval for the mean.

Step-by-step explanation:

To determine if it is reasonable to believe that the mean magnesium ion concentration may be greater than 185.5, we first need to calculate the 99% confidence interval for the mean magnesium ion concentration using the given data. The formula for calculating the confidence interval is:

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

Using the given data, the sample mean is 164.17, the standard deviation is 7.05, and the sample size is 6. The critical value for a 99% confidence level with a sample size of 6 is 3.707.

Plugging these values into the formula, we get:

Confidence Interval = 164.17 ± (3.707 * 7.05 / sqrt(6))

After calculation, the confidence interval is approximately (155.42, 172.92). Since 185.5 is outside of this range, it is not reasonable to believe that the mean magnesium ion concentration may be greater than 185.5.