Question

To form a confidence interval for H, a sample of n=196 was selected. The sample showed a mean of x = 307 with a standard deviation of s=39.6. The desired confidence level is

99.7 percent.
The value of the multiplier is
A. 1
B. 3
C. 1.96
D. 2.576
E. 1.282

Answer 1

The desired z-score multiplier for a 99.7 percent confidence interval is typically 3, corresponding to the extreme ends of the z-distribution table.

Therefore, the correct answer is: option b) 3

Step-by-step explanation:

To form a confidence interval for a population mean (H), using a sample mean (x) of 307, standard deviation (s) of 39.6, and a sample size (n) of 196, with a desired confidence level of 99.7 percent, we need to determine the appropriate z-score multiplier.

Given the high confidence level, we look towards the extreme ends of the z-score table, which indicates that the value associated with the middle 99.7 percent (or 3 standard deviations either side of the mean in a normal distribution) is typically represented by a z-score of 3.

Thus, the correct answer for the value of the multiplier in this scenario is B. 3.