Question

You are a researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 35 bacteria reveals a sample mean of ¯x=66x¯=66 hours with a standard deviation of s=7s=7 hours. You would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.65 hours at a 90% level of confidence.

What sample size should you gather to achieve a 0.65 hour margin of error? Round your answer up to the nearest whole number.

n = bacteria

Answer 1

Solution :

Given that,

Population standard deviation = $\sigma$ = 7

Margin of error = E = 0.65

At 90% confidence level the t is ,

$\alpha$ = 1 - 90% = 1 - 0.90 = 0.10

$\alpha$ / 2 = 0.10 / 2 = 0.05

Z_$\alpha$/2 = Z_0.05 = 1.645

sample size = n = (Z_$\alpha$/2* $\sigma$ / E) ²

n = (1.645 *7 / 0.65)²

n = 313.83

n = 314

Sample size = 314