Question

One class, 15 students took a math test, and the average for this group of students was 8.2, with an estimate of the standard deviation of 0.85. What interval should the population average be at, with a 99% confidence level?

a. 8.2±0.17
b. 8.2±0.34
c. 8.2±0.42
d. 8.2±0.50

Answer 1

To find the interval for the population average with a 99% confidence level, we use the formula: sample mean ± critical value × (estimated standard deviation / √sample size). Simplifying the equation gives us the interval of 8.2 ± 0.50. This corresponds to option d. 8.2±0.50.

Step-by-step explanation:

To find the interval within which the population average should be at with a 99% confidence level, we can use the formula: sample mean ± critical value × (estimated standard deviation / √sample size).

In this case, the sample mean is 8.2, the estimated standard deviation is 0.85, and the sample size is 15. The critical value for a 99% confidence level is 2.93.

Plugging in these values, we get: 8.2 ± 2.93 × (0.85 / √15). Simplifying this gives us: 8.2 ± 0.50.

Therefore, the interval should be 8.2 ± 0.50, which corresponds to the option d. 8.2±0.50.