Question

In: Statistics and Probability

A seafood restaurant often receives complaints from it’s patrons that the lobster is too small. The...

A seafood restaurant often receives complaints from it’s patrons that the lobster is too small. The menu lists the weight of a lobster as 462g. The next time the restaurant receives a batch of 60 lobsters it weighs them and finds the average is 451g with a standard deviation of 31g. Do you think the restaurant sells lobsters that are smaller than advertised? Perform a hypothesis test at α = 0.01

Expert Solution

Population mean: = 462,

Sample size: n= 60,

Sample mean: = 451,

Sample standard deviation: s = 31

Significance level: = 0.01

null and alternative hypothesis is

Ho: = 462

Ha: < 462

formula for test statistics is

t = -2.749

test statistics: t = -2.749

now calculate P-Value for this one tailed test with df= n-1 = 60 - 1 = 59

using following excel command we get p-value as,

P-Value = 0.0040

decision rule is,

Reject Ho if (P-Value) < ( )

Here, ( P-Value = 0.0040 ) < ( = 0.01 )

Hence,

Null hypothesis is rejected.

Therefore there is sufficient evidence to conclude that the restaurant sells lobsters that are smaller than advertised weight of 462.

orchestra answered 1 year ago

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