Part I Hypothesis Testing and Confidence Intervals One Sampl

Part I: Hypothesis Testing and Confidence Intervals (One Sample): Exercise
A nutrition laboratory tests 40 “reduced sodium” hot dogs, finding that the mean sodium content is 310 mg, with a standard deviation of 36 mg. Find a 95% confidence interval for the mean sodium content of this brand of hot dog. Be sure to check all necessary assumptions and conditions, and interpret your interval within the context of the problem.

Conduct a hypothesis test at the .025 level as to whether the mean sodium content level is 300mg. Provide the: H0,Ha, test statistic and approximate P-value. Interpret your decision about the hypotheses in the context of the claim.

Solution

CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=310
Standard deviation( sd )=36
Sample Size(n)=40
Confidence Interval = [ 310 ± t a/2 ( 36/ Sqrt ( 40) ) ]
= [ 310 - 2.023 * (5.69) , 310 + 2.023 * (5.69) ]
= [ 298.48,321.52 ]