Question

A nutrition laboratory wants to construct a 95% confidence interval for the mean sodium content of "reduced sodium" hot dogs. A preliminary study of reduced sodium hot dogs gives a standard deviation of 25mg of sodium. How many hot dogs should the researchers sample in order for the width of their confidence interval to be no more than 10 mg?

Answer 1

n > 96

Therefore, the number of samples should be more than 96 for the width of their confidence interval to be no more than 10mg

Explanation:

Given;

Standard deviation r= 25mg

Width of confidence interval w= 10mg

Confidence interval of 95%

Margin of error E = w/2 = 10mg/2 = 5mg

Z at 95% = 1.96

Margin of error E = Z(r/√n)

n = (Z×r/E)^2

n = (1.96 × 25/5)^2

n = (9.8)^2

n = 96.04

n > 96

Therefore, the number of samples should be more than 96 for the width of their confidence interval to be no more than 10mg