Question

3a. A pet food marketing company wants to find the average age of dogs in a city and first needs to find out how large a sample “n” it will need.  The company wants to be 95% confident that their estimate will be accurate within 6 months (0.5 year). From a previous study the population standard deviation is known to be 2.9 years. For Question 3a, fill in the blank with the Z sub alpha/2 value (positive, of course) of the 95% confidence interval you will use in your calculation.

3b.  For Question 3b, give your answer for how large a sample (n) will be necessary to conduct the study. How large a sample (n) will be necessary for the study?  (be sure to round up your answer to a whole number/ones place)  

Answer 1

The following information is provided,
Significance Level, α = 0.05, Margin or Error, E = 0.5, σ = 2.9

The critical value for significance level, α = 0.05 is 1.96.

The following formula is used to compute the minimum sample size required to estimate the population mean μ within the required margin of error:
n >= (zc *σ/E)^2
n = (1.96 * 2.9/0.5)^2
n = 129.23

Therefore, the sample size needed to satisfy the condition n >= 129.23 and it must be an integer number, we conclude that the minimum required sample size is n = 130
Ans : Sample size, n = 130 or 129