SOLUTION: Karen wants to advertise how many chocolate chips are in each Big Chip cookie at her bakery. She randomly selects a sample of 41 cookies and finds that the number of chocolate chip

Algebra ->  Probability-and-statistics -> SOLUTION: Karen wants to advertise how many chocolate chips are in each Big Chip cookie at her bakery. She randomly selects a sample of 41 cookies and finds that the number of chocolate chip      Log On


   

Question 1198501: Karen wants to advertise how many chocolate chips are in each Big Chip cookie at her bakery. She randomly selects a sample of 41 cookies and finds that the number of chocolate chips per cookie in the sample has a mean of 9.4 and a standard deviation of 2.9. What is the 99% confidence interval for the number of chocolate chips per cookie for Big Chip cookies? Enter your answers accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).
Found 2 solutions by Theo, ana.osuna:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
sample mean is 9.4
sample standard deviation is 2.9
sample size is 41

sample standard error is 2.9 / sqrt(41) = .4529039095

at 99% confidence interval, the two tailed critical t-score with 40 degrees of freedom is equal to plus or minus 2.7045.

the t-score formula is t = (x-m)/s
t is the t-score
x is the raw score
m is the sample mean
s is the standard error

when t = -2.7045, the formula becomes -2.7045 = (x-9.4)/.4529039095.
solve for x to get x = -2.7045 * .4529039095 + 9.4 = 8.175.
round to 8.2.

when t = 2.7045, the formula becomes 2.7045 = (x-9.4)/.45290390095.
solve for x to get x = 2.7045 * .45290390095 + 9.4 = 10.625.
round to 10.6.

your solution is that the 99% confidence interval for the number of chocolate chips on each big chip cookie is 8.2 to 10.6.

to confirm the t-score value, i used the critical value calculator at https://calculator-online.net/critical-value-calculator/

Answer by ana.osuna(1) About Me  (Show Source):
You can put this solution on YOUR website!
Assume that a sample is used to estimate a population mean
μ
μ
. Find the 90% confidence interval for a sample of size 969 with a mean of 83.5 and a standard deviation of 19.9. Enter your answer as a tri-linear inequality accurate to 3 decimal places.