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?

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

Step-by-step 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