Question

To study the bacteria colonies count in the west basin of Lake Macatawa, 13 samples of water were taken from the west basin. The mean colonies count in these samples was 11.95 with the variance 153.76. Find a 95% lower confidence bound for the mean colonies count in the west basin. ON > 11.95 – 6.13 ou > 11.95 - 7.49 none of the answers provided here ON > 11.95 – 6.09 ON > 11.95 – 5.66

Answer 1

Answer)

As the population variance is unknown here we will use t distribution to estimate the interval

N = 13

Mean = 11.95

S.d = √153.76

Degrees of freedom is = n-1 = 12

For 12 dof and 95% confidence level

Critical.value t from t table is 2.18

Margin of error (MOE) = t*s.d/√n = 2.18*√153.76/√13 = 7.4932

Lower limit = mean - moe = 11.95 - 7.49

So answer is

u > 11.95 - 7.49