Question

A nutrition laboratory tests 50 ​"reduced sodium" hot​ dogs, finding that the mean sodium content is 307 ​mg, with a standard deviation of 37 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

Result:

A nutrition laboratory tests 50 ​"reduced sodium" hot​ dogs, finding that the mean sodium content is 307 ​mg, with a standard deviation of 37 mg.

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

​ n=50

Mean =307

SD=37

Table value t at 50-1 =49 DF is 2.0096

= ( 296.4847, 317.5153)

Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation	37
Sample Mean	307
Sample Size	50
Confidence Level	95%
Intermediate Calculations
Standard Error of the Mean	5.2326
Degrees of Freedom	49
t Value	2.0096
Interval Half Width	10.5153
Confidence Interval
Interval Lower Limit	296.4847
Interval Upper Limit	317.5153

b) What assumptions have you made in this​ inference? Are the appropriate conditions​ satisfied?

​The samples are random and come from normal population. Since ample size is large( > 30), the appropriate conditions​ satisfied.

c) Explain clearly what your interval means.

We are 95% confident that of mean sodium content of all ​"reduced sodium" hot​ dogs falls in the interval ( 296.4847, 317.5153).