Question

1.We want to obtain a sample to estimate a population mean. Based on previous evidence, researchers believe the population standard deviation is approximately σ=41.6. We would like to be 95% confident that the esimate is within 1.5 of the true population mean. How large of a sample size is required?

n=

2.You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ=73.4. You would like to be 98% confident that your estimate is within 10 of the true population mean. How large of a sample size is required? Do not round mid-calculation.

n =

3.You want to obtain a sample to estimate how much parents spend on their kids birthday parties. Based on previous study, you believe the population standard deviation is approximately σ=41.4 dollars. You would like to be 90% confident that your estimate is within 2.5 dollar(s) of average spending on the birthday parties. How many moms do you have to sample? Do not round mid-calculation.

n =

Answer 1

Solution :

1) Given that,

Population standard deviation = = 41.6

Margin of error = E = 1.5

At 95% confidence level the z is,

= 1 - 95%

= 1 - 0.95 = 0.05

/2 = 0.025

Z_/2 = 1.96

sample size = n = [Z_/2* / E] ²

n = [ 1.96 * 41.6 / 1.5]²

n = 2954.71

Sample size = n = 2955

2) Given that,

Population standard deviation = = 73.4

Margin of error = E = 10

At 98% confidence level the z is,

= 1 - 98%

= 1 - 0.98 = 0.02

/2 = 0.01

Z_/2 = 2.326

sample size = n = [Z_/2* / E] ²

n = [2.326 * 73.4 / 10]²

n = 291.48

Sample size = n = 292

3) Given that,

Population standard deviation = = 41.4

Margin of error = E = 2.5

At 90% confidence level the z is,

= 1 - 90%

= 1 - 0.90 = 0.10

/2 = 0.05

Z_/2 = 1.645

sample size = n = [Z_/2* / E] ²

n = [ 1.645 * 41.4 / 2.5]²

n = 742.08

Sample size = n = 743