Question

Charity (stats lyke me!) armonte (it's not the Chi-thang) and courtney (kai Q laytras roole), known for their slogan; "A little Wii will rot your brain, but a little stats, will put you on Khrack!," were happy that "stats" was finally over, of course, they would miss their awesome professor, and so decided to solve the following for the missed values.

a. The Hu's Pat-Hat Now Group needed to find how many cars to sample to be within 0.001 of the mean. If they had an σ equal to 0.02 cars and a confidence level of 95% find the sample size needed.

b. Sheila and Lesley, of Nobody Uses Facebook! wanted to determine the percentage of college students that use Snapchat instead of Instagram to do their project on. How many students should they survey to be 96% confident that the sample percentage of college students that used Snapchat instead of Instagram to do their project on is within 5 percentage points? Assume that there is no prior information.

Answer 1

Solution :

a) Z/2 = Z0.025 = 1.96  

sample size = n = [Z/2* / E] 2

n = [1.96 * 0.02 / 0.001]2

n = 1536.64

Sample size = n = 1537

b) Given that,

=  1 - = 0.5

margin of error = E = 0.05

At 96% confidence level

= 1 - 96%

= 1 - 0.96 =0.04

/2 = 0.02

Z/2 = Z0.02  = 2.05

sample size = n = (Z / 2 / E )2 * * (1 - )

= (2.05 / 0.05 )2 * 0.5 * 0.5

= 420.25

sample size = n = 421