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In: Math

Your local grocery store claims that on average their fresh caught salmon will weigh 2 pounds....

  1. Your local grocery store claims that on average their fresh caught salmon will weigh 2 pounds. You want to test to see if their claim is correct so you gather a simple random sample of 45 packages of their fresh caught salmon, weigh each package, and find that the average weight of these packages is 1.76 pounds. Based on years of data, the grocery store determined that the standard deviation ? = 0.08 pounds. What is the probability of obtaining the sample that you got? Do you think the grocery store is wrong to say that on average their packages of salmon weigh 2 pounds? Why or why not?

Solutions

Expert Solution

Given that,
population mean(u)=2
standard deviation, σ =0.08
sample mean, x =1.76
number (n)=45
null, Ho: μ=2
alternate, H1: μ!=2
level of significance, α = 0.05
from standard normal table, two tailed z α/2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 1.76-2/(0.08/sqrt(45)
zo = -20.125
| zo | = 20.125
critical value
the value of |z α| at los 5% is 1.96
we got |zo| =20.125 & | z α | = 1.96
make decision
hence value of | zo | > | z α| and here we reject Ho
p-value : two tailed ( double the one tail ) - ha : ( p != -20.125 ) = 0
hence value of p0.05 > 0, here we reject Ho
ANSWERS
---------------
null, Ho: μ=2
alternate, H1: μ!=2
test statistic: -20.125
critical value: -1.96 , 1.96
decision: reject Ho
p-value: 0
the probability of obtaining the sample is 0
we have enough evidence to support the claim that on average their fresh caught salmon will weigh 2 pounds.
yes,
i think the grocery store is wrong to say that on average their packages of salmon weigh 2 pounds
because, if their claim is correct so you gather a simple random sample of 45 packages of their fresh caught salmon,
weigh each package then average is 1.76 pounds.

milcah answered 11 months ago
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