A nutrition laboratory tests 50 "reduced sodium" hot dogs, finding that the mean sodium content is 314 mg, with a standard deviation of 36 mg.
a) Find a 95% confidence interval for the mean sodium content of this brand of hot dog.
b) What assumptions have you made in this inference? Are the appropriate conditions satisfied?
c) Explain clearly what your interval means. The nutrition lab tests hotdogs again, this time using a sample of 60 "reduced sodium" hot dogs. The new sample produces a mean of 318 mg of sodium, and the standard deviation is 32 mg.
d) Should this larger sample of hot dogs produce a more accurate estimate of the mean sodium content? Explain.
e) What is the standard error of the mean sodium content? Recall that the standard error is the estimate of the standard deviation of the sample mean.
f) Find and interpret a 95% confidence interval.
g) Food labeling regulations require that any food identified as "reduced sodium" must have at least 30% less sodium than its regular counterpart. If regular franks average 465 mg of sodium, should this brand be labeled "reduced"? Explain, using your confidence interval.