Question

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 1 year ago
Next > < Previous

Related Solutions

The Chesapeake Grocery Store is a small local grocery that only carries fresh produce, poultry, and...
The Chesapeake Grocery Store is a small local grocery that only carries fresh produce, poultry, and meat that are grown or raised in the 50-mile radius of the grocery. The store also carries other typical grocery items (such as packaged and canned goods). The owner of the grocery, George Lampe, employs about 35–40 people. You are a local CPA with a small firm in the Chesapeake area, and George has retained you as his independent auditor. You are currently reviewing...
Customers arrive at a local grocery store at an average rate of 2 per minute. (a)...
Customers arrive at a local grocery store at an average rate of 2 per minute. (a) What is the chance that no customer will arrive at the store during a given two minute period? (b) Since it is a “Double Coupon” day at the store, approximately 70% of the customers coming to the store carry coupons. What is the probability that during a given two-minute period there are exactly four (4) customers with coupons and one (1) without coupons? (c)...
The produce manger at the local grocery store must determine how many pounds of bananas to...
The produce manger at the local grocery store must determine how many pounds of bananas to order weekly. Based upon past experience, the demand for bananas is expected to be 100,150, 200, or 250 pounds with the following probabilities: 100lbs 0.20; 150lbs 0.25; 200lbs 0.35, 250lbs 0.20. The bananas cost the store $.45 per pound and are sold for $.085 per pound. Any unsold bananas at the end of each week are sold to a local zoo for $.30 per...
Assume that a customer shops at a local grocery store spending an average of ​$150 a​...
Assume that a customer shops at a local grocery store spending an average of ​$150 a​ week, resulting in the retailer earning a ​$25 profit each week from this customer. Assuming the shopper visits the store all 52 weeks of the​ year, calculate the customer lifetime value if this shopper remains loyal over a​ 10-year life-span. Also assume a 4 percent annual interest rate and no initial cost to acquire the customer. This customer yields ​$1300 per year in profits...
Assume that a customer shops at a local grocery store spending an average of ​$400 a​...
Assume that a customer shops at a local grocery store spending an average of ​$400 a​ week, resulting in a retailer profit of ​$40 each week from this customer. Assuming the shopper visits the store all 52 weeks of the​ year, calculate the customer lifetime value if this shopper remains loyal over a​ 10-year life span. Also assume a 3 percent annual interest rate and no initial cost to acquire the customer. The customer yields ​$ nothing per year in...
The produce manager at the local Pig & Whistle grocery store must determine how many pounds...
The produce manager at the local Pig & Whistle grocery store must determine how many pounds of bananas to order weekly. Based upon past experience, the demand for bananas is expected to be 100, 150, 200, or 250 pounds with the following probabilities: 100lbs 0.20; 150lbs 0.25, 200lbs 0.35, 250lbs 0.20. The bananas cost the store $.45 per pound and are sold for $.085 per pound. Any unsold bananas at the end of each week are sold to a local...
Historically consumers purchase a household average of 7.8 pounds of salmon a month. Your client, a...
Historically consumers purchase a household average of 7.8 pounds of salmon a month. Your client, a consortium of farm raised Atlantic salmon producers, has begun feeding their farm raised salmon a special, (but expensive) feed that has a pigment in it that will turn the flesh of the farm raised Atlantic salmon (normally pink) to a deep red that is similar to the color of wild caught pacific salmon. They predict that the introduction of this enhanced farm raised salmon...
Zingo's Grocery store claims that customers spend an average of 5 minutes waiting for service at...
Zingo's Grocery store claims that customers spend an average of 5 minutes waiting for service at the stores deli counter. A random sample of 45 customers was timed at the deli counter, and the average service time was found to be 5.75 minutes. Historically the standard deviation for waiting time is 1.75 minutes per customer.      a. Find the 95% confidence interval for the mean time that customers wait at the deli counter.      b. Is there sufficient evidence to...
Zingo's Grocery store claims that customers spend an average of 5 minutes waiting for service at...
Zingo's Grocery store claims that customers spend an average of 5 minutes waiting for service at the stores deli counter. A random sample of 45 customers was timed at the deli counter, and the average service time was found to be 5.75 minutes. Historically the standard deviation for waiting time is 1.75 minutes per customer.      a. Find the 95% confidence interval for the mean time that customers wait at the deli counter.      b. Is there sufficient evidence to...
Zingo's Grocery store claims that customers spend an average of 5 minutes waiting for service at...
Zingo's Grocery store claims that customers spend an average of 5 minutes waiting for service at the stores deli counter. A random sample of 45 customers was timed at the deli counter, and the average service time was found to be 5.75 minutes. Historically the standard deviation for waiting time is 1.75 minutes per customer. a. Find the 95% confidence interval for the mean time that customers wait at the deli counter. b. Is there sufficient evidence to indicate that...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT