Question

2. A study is being conducted to compute the price of a hand cream. The researcher needs the error range of the price to be within $1, and suspects that the population standard deviation would be around $29.

a. What sample size would we require if we desired a 99 percent confidence level?

b. What about if we keep the confidence level 95%, but decide that our acceptable error is $4?

Answer 1

a) The minimum sample with a given standard deviation

=29 at a 99% confidence interval is calculated as:

Where Zc is the critical value at a 99% confidence interval calculated using excel formula =NORM.S.INV(0.995) which results in Zc=2.576

and E is margin of error E=1

Now the minimum sample is calculated as:

b) If the confidence interval is 95% the Zc value changes which are again calculated using excel formula for normal distribution as =NORM.S.INV(0.975) which results in Zc=1.96

and given that E, the margin of error= 4.

The Minimum sample is calculated as: