Question

A research scientist wants to know how many times per hour a certain strand of bacteria reproduces. The mean is found to be 10 reproductions and the population standard deviation is known to be 1.9 . If a sample of 782 was used for the study, construct the 98% confidence interval for the true mean number of reproductions per hour for the bacteria.

Answer 1

The confidence interval is (9.842, 10.158)

Or,

CI = 10 ± 0.158

Explanation:

Sample Mean = M = 10

Standard Deviation = S = 1.9

Sample Size = 782

we need 98% significance

for this, we get the z score of 2.326

Hence we find the upper and lower limits of the confidence interval,

Now, z(S)/√n = (2.326)(1.9)/√(782)

= 0.158

Then,

Upper limit = M + z(S)/√n

Upper limit = 10 + 0.158

Upper limit = 10.158

Lower limit = M - z(S)/√n

Lower limit = 10 - 0.158

Lower limit = 9.842

Hence the confidence interval is (9.842, 10.158)