Question

A food safety guideline is that the mercury in fish should be below 1 part per million​ (ppm). Listed below are the amounts of mercury​ (ppm) found in tuna sushi sampled at different stores in a major city. Construct a 99​% confidence interval estimate of the mean amount of mercury in the population. Does it appear that there is too much mercury in tuna​ sushi?

0.61 

0.82 

0.10 

0.94  

1.25 

0.55  

0.92

  

Answer 1

We need to find one sample t interval.

First we need to find sample mean and sample standard deviation (S) for given data set.

We can find the sample mean and standard deviation S of the both years using excel function =AVERAGE( ) and =STDEV.S() respectively.

Confidence interval is given by,

Lower bound =   – E

Upper bound = + E

Margin of error E = ; t is critical value follows t distribution with degrees of freedom (d.f ) = n - 1

We have n = 7 and confidence level (c) = 99% or 0.99

d.f = n-1 = 7-1 = 6  

α = 1 – c = 1- 0.99 = 0.01

Therefore t_(0.01,6) = 3.707

Margin of error E =

E = 0.5121

Lower bound = 0.7414  – 0.5121 = 0.23

Upper bound = 0.7414 + 0.5121 = 1.25

95% confidence interval estimate of the mean amount of mercury in the population is ( 0.23 , 1.25 )

Since the confidence interval contain 1 ; it appear that there is too much mercury in tuna​ sushi.