Question

A nutrition laboratory tests 60 ​"reduced sodium" hot​ dogs, finding that the mean sodium content is 305 ​mg, with a standard deviation of 35 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.

Answer 1

Given, n = 60,

The mean sodium content is 305 ​mg, with a standard deviation of 35 mg. Z^* = 1.96

​a) ​95% confidence interval for the mean sodium content of this brand of hot dog

  

b) Assumptions we have made in this​ inference

  A random sample or randomized experiment should be used to obtain the data.

  The sampling distribution of , (the sample mean) needs to be approximately normal. This is true if our parent population is normal or if our sample is reasonably large .

   Individual observations need to be independent. If sampling without replacement, our sample size shouldn't be more than 10%, percent of the population.

Yes, the appropriate conditions​ are satisfied

c) Interpretation:

The 95% confidence interval defines a range of values (296.14, 313.86) that we can be 95% certain contains the population mean.

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