Question

In: Statistics and Probability

The owner of a trout farm routinely measures the lengths of his trouts. He randomly took...

The owner of a trout farm routinely measures the lengths of his trouts. He randomly took 31 trouts last Friday from his pond and measured their lengths. The mean length was 26.1 centimeters with a standard deviation of 1.8. Estimate the true mean length of all trouts in his farm using a 90% confidence interval.

(a) The limits of the confidence interval are calculated by x¯±tsn‾√x¯±tsn , where

x¯=

t= (Round to 3 decimal places.) Please explain how to find this!

s=

n=

(b) The 90% confidence interval for the true mean length is: ( , ) (Round to 3 decimal places.)

Solutions

Expert Solution


Solution :

Given that,

= 26.1

s = 1.8

n = 25

Degrees of freedom = df = n - 1 = 31 - 1 = 30

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

t /2,df = t0.05,30 = 1.697

Margin of error = E = t/2,df * (s /n)

= 1.697 * ( 1.8 / 31)

= 0.549

Margin of error = 0.549

The 90% confidence interval estimate of the population mean is,

- E < < + E

26.1 - 0.549 < < 26.1 + 0.549

25.551 < < 26.649

(25.551, 26.649 )

orchestra answered 2 years ago
Next > < Previous

Related Solutions

The weight of trout in a fish farm follows the distribution N(200,502). A trout is randomly...
The weight of trout in a fish farm follows the distribution N(200,502). A trout is randomly selected. (a) What is the probability that its weight does not exceed 175g? (b) What is the probability that its weight is greater than 230g? (c) What is the probability that its weight is between 225g and 275g? (d) What is the probability that out of eight trout selected randomly from the fish farm, less than three of them will not weigh more than...
A biologist measures the lengths of a random sample 45 mature brown trout in a large...
A biologist measures the lengths of a random sample 45 mature brown trout in a large lake and finds that the sample a mean weight of 41 pounds. Assume the population standard deviation is 3.7 pounds. Based on this, construct a 99% confidence interval for the mean weight of all mature brown trout in the lake. Round your anwers to two decimal places. < μ
Mario, the owner of Best Pizzeria, took the first $2,000 he earned from his business and...
Mario, the owner of Best Pizzeria, took the first $2,000 he earned from his business and placed it into a Fidelity savings plan. At the end of 5 years, he closed the account and withdrew $2,850. What was the annual rate of interest he earned?   N = I = PV = PMT = FV = P/Y =
A farmer weighs 10 randomly chosen watermelons from his farm and he obtains the following values...
A farmer weighs 10 randomly chosen watermelons from his farm and he obtains the following values (in lbs): 7.72,9.58,12.38,7.77,11.27,8.80,11.10,7.80,10.17,6.00 Assuming that the weight is normally distributed with mean μ and and variance σ2, find a 95% confidence interval for μ.
1.Joe is the owner of a large farm, and Joe wants to be certain that his...
1.Joe is the owner of a large farm, and Joe wants to be certain that his farm will continue to be used for agricultural purposes after his death. Since none of Joe’s children are interested in maintaining the farm, Joe decides to sell his farm to Lou on condition that Lou uses the farm for agricultural purposes. If Lou fails to do so, ownership of the farm will instantly transfer to a charitable organization called the Farming Preservation Society. What...
Jake routinely directly holds his own stocks. He updates the stocks in his portfolio every week,...
Jake routinely directly holds his own stocks. He updates the stocks in his portfolio every week, trying to pick the stocks that will perform the best over the next week. Jake is managing his assets using ________. an active investing strategy a passive investing a mutual fund a bank Suppose that you own stock in a company that sells flour. If you wanted to diversify to protect your portfolio against the risk that severe flooding might cause crop failure, leading...
b. Ben took up a loan to purchase a farm machine. The terms of his loan...
b. Ben took up a loan to purchase a farm machine. The terms of his loan require him to make quarterly payments of $3,434 over 7 years. The relevant rate of interest is 7.2% per year, compounded quarterly. For the same amount of loan and interest rate, will Ben pay off the loan sooner if he makes quarterly payments of $3,876 instead? Show all relevant calculations to support your answer.
Gren Plant Holdings farm manager argued that if he increased all four inputs on his farm...
Gren Plant Holdings farm manager argued that if he increased all four inputs on his farm by 1 percent, output would increase by 1 percent. The extension worker argued that the elasticities of the output for each of the four inputs was less than one-fourth; therefore, he said that the farm managers output should increase by more than 1 percent. A graduate of University of Boston of Agriculture Economics sided with the extension worker because, she said …” My thesis...
Bob the Farmer grows vegetables at his farm in South Dakota. He grows his vegetables for...
Bob the Farmer grows vegetables at his farm in South Dakota. He grows his vegetables for sale to food companies. On November 1, he sells his vegetables to Granny’s Pie Company for $65,000, inclusive of 13% VAT. Granny’s Pie Company uses his vegetables to produce savory meat and vegetable pies (they’re huge in the UK). After the production of the pies is complete, Granny’s Pie Company sells the pies to Winn Dixie Grocery Stores for $140,000, inclusive of 13% VAT....
Bob the Farmer grows vegetables at his farm in South Dakota. He grows his vegetables for...
Bob the Farmer grows vegetables at his farm in South Dakota. He grows his vegetables for sale to food companies. On November 1, he sells his vegetables to Granny’s Pie Company for $65,000, inclusive of 13% VAT. Granny’s Pie Company uses his vegetables to produce savory meat and vegetable pies (they’re huge in the UK). After the production of the pies is complete, Granny’s Pie Company sells the pies to Winn Dixie Grocery Stores for $140,000, inclusive of 13% VAT....
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT