Question

A wild strain of Atlantic salmon has a mean fat content of 8.5 grams. A dietician is concerned that the fat content in farm-raised Atlantic salmon is greater than the wild strain.

a) What would be the null and alternative hypothesis for testing whether the average content of fat in farm raised Atlantic salmon is greater than 8.5 grams?

b) Calculate the P-value if a sample of 35 farm-raised salmon fillets had a sample average of 10.5 grams with a sample standard deviation of 5.12 grams.

c) Calculate a 99% confidence interval for the true average fat content of farm raised salmon.

Answer 1

a)

H0: = 8.5

Ha: > 8.5

b)

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 10.5 - 8.5 ) / ( 5.12 / √(35) )
t = 2.31

From T table, with test statistics of 2.31 and df of 34,

p-value = 0.0135

c)

99% Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.01 /2, 35- 1 ) = 2.728
10.5 ± t(0.01/2, 35 -1) * 5.12/√(35)
Lower Limit = 10.5 - t(0.01/2, 35 -1) 5.12/√(35)
Lower Limit = 8.1391
Upper Limit = 10.5 + t(0.01/2, 35 -1) 5.12/√(35)
Upper Limit = 12.8609
99% Confidence interval is ( 8.14 , 12.86 )