Question

Suppose the germination periods, in days, for grass seed are normally distributed. If the population standard deviation is 3 days, what minimum sample size is needed to be 90% confident that the sample mean is within 1 day of the true population mean?

Answer 1

Answer: 25

Explanation:

Given : Level of confidence = 0.90

Significance level :
`\alpha=1-0.90=0.10`

Critical value :
`z_(\alpha/2)=1.645`

Margin of error :
`E=\text{ 1 days}`

Standard deviation:
`\sigma=\text{ 3 day}`

The formula to find the sample size :
`n=((z_(\alpha/2)\sigma)/(E))^2`

`n=(((1.645)(3))/(1))^2=24.354225\approx25`

Hence, the minimum sample size needed= 25.