Question

In: Statistics and Probability

Homser, Lake Oregon has an Atlantic salmon catch-and-release program that has been very successful. The average...

Homser, Lake Oregon has an Atlantic salmon catch-and-release program that has been very successful. The average Fisherman's catch has been on average 8.8 Atlantic salmon per day (Source: National Symposium on catch and release fishing, Humboldt State University). Suppose that a new quota system restricting the number of fishermen has been put into effect this season. A random sample of 16 fishermen yielded a mean and standard deviation of and s = 3.45 catches per day. The histogram to the right shows the sample distribution. Assuming the catch per day has an approximate normal distribution, use a significance level of 0.05 to test whether the average is different than 8.8 now that the restriction has been put in place. ()

1) a. What is the p-value for the test? Is it one or two sided?

b. Calculate a 95% confidence interval for µ. Show all work

c. Interpret the results from the hypothesis test and confidence interval in the context of the problem.

Solutions

Expert Solution

Let , the sample mean be .

To calculate the P value, we need to compute the test statistic first. Since the population standard deviation is unknown to us and the sample size is not sufficiently large we will be using single sample t test for mean to test the given hypothesis.

The formula for the test statistic is given by :

where, n = sample size = 16 ; s = sample standard deviation = 3.45 ; ;

So, (I am unable to compute the value of T as the sample mean is not mentioned in the question.Please mention it in the comments section  so that I can do it for you, and I will definitely edit/upade the final answer here. Otherwise you can do it by yourself by putting the sample mean value in the formula given above). Let the computed value of T is t.

Then, P-value is : 2*{P( T> t)} . Since T follows a student's t distribution with degrees of freedom (n-1)=(16-1)=15, this probabilty 2*{P(T>t)}  can be calculated using excel's TDIST(x,deg_freedom, tails) where x = (put the computed T value) , deg_freedom = 15 , tails = 2 (since this is a two tailed test) . By enttering this you will get the p-value.

This is a two sided p-value, because we are testing the hypothesis that against    .

b) The formula for the 95% confidence interval is :

(please put the value of sample mean to get the final answer)

c) If the computed P-value in above exceeds 0.05 and the confidence interval contains the value 8.8, conclude that there is sufficient evidence to warrant the rejection of the claim that  the average is different than 8.8 now aftert the restriction has been put in place.

  If the computed P-value in above is less than 0.05 and the confidence interval does not contain the value 8.8, conclude that , there is insufficient evidence to reject the claim that  the average is different than 8.8 now aftert the restriction has been put in place.

If you are having any trouble doing the above by yourself , please mention the sample mean value in the comment, I will do it for you and update my answer. Thank you so much!


Related Solutions

Homser Lake, Oregon, has an Atlantic salmon catch and release program that has been very successful....
Homser Lake, Oregon, has an Atlantic salmon catch and release program that has been very successful. The average fisherman’s catch has been μ=8.8 Atlantic salmon per day. (Source: National Symposium on Catch and Release Fishing, Humboldt State University). Suppose that a new quota system restricting the number of fishermen has been put into effect this season. A random sample of fishermen gave the following catches per day: 12 6 11 13 5 0 3 7 8 7 6 3 9...
mcdonalds has been very successful in its international expansion. in some ways it has remaind very "american" in everything it does
mcdonalds has been very successful in its international expansion. in some ways it has remaind very "american" in everything it does. people around the workd want an american experience when they go to mcdonalds. however, the company knows the importance of service culture and for this reason, service culture is an important part of mcdonalds business model. analyze how the exisrence of service culture must have contributed to the success of mcdonalds
Now, assume that the tennis racquet manufacturer has been very successful in manufacturing and marketing a...
Now, assume that the tennis racquet manufacturer has been very successful in manufacturing and marketing a single line of inexpensive tennis racquets, aimed at beginners and casual players. The manufacturer’s current distribution channel is through large discount retailers, such as Kmart and Walmart. Recently, three major sporting goods chains also began to carry the racquets. The company puts most of its promotion budget into sales promotion to the retailers and into in-store displays. The competitive advantage for this company is...
A lake has been acidified to a pH of 4.698. If the lake has a volume...
A lake has been acidified to a pH of 4.698. If the lake has a volume of 9.12×10^4 cubic meters, what mass, in kg, of CaO must be added to raise the pH to a value of 7.00? =kg CaO Hint: The reaction of CaO with water is: CaO + H2O---> Ca(OH)2
Why has the barefoot doctors program been so successful in china or japan?
Why has the barefoot doctors program been so successful in china or japan?
Audio Co. Manages a chain of stores that sell audio systems. It has been very successful,...
Audio Co. Manages a chain of stores that sell audio systems. It has been very successful, but also many failures. The analysis of these failures has led it to adopt the policy of not opening a store unless they are reasonably sure that at least 15% of the students of the place have stereo systems with a cost of $ 1,100 or more. In a survey of 300 of the 2,400 students at a small arts school in the Midwest,...
Pick a local (city, region, or country) brand that has been very successful competing against the...
Pick a local (city, region, or country) brand that has been very successful competing against the bigger global brands in its product category. What are the elements of its strategy that have enabled it to achieve this success?
Your uncle has always owned several companies and has been very successful despite not studying Finance...
Your uncle has always owned several companies and has been very successful despite not studying Finance in university. He has heard about several finance methods to evaluate whether to take on a project or not. Explain to him what the three basic decisions that a financial manager must make when overseeing a company. (1 mark) Explain to him what the ultimate objective of a financial manager is. Explain to him what characteristics the best methods have to determine whether or...
Mando Paints (MAPS)       Mando Paints (MAPS)) manufactures a paint additive that has been very successful in...
Mando Paints (MAPS)       Mando Paints (MAPS)) manufactures a paint additive that has been very successful in the metallic paint line of automotive paints. The company prides itself in making the paints that car owners buy better. MAPS is in the process of preparing its 2019 fiscal year master budget and has presented you with the following information. The company has a December 31st fiscal year-end. 1. The budgeted December 31, 2018 balance sheet for the company is shown below. MAPS...
The Olsen Mining Company has been very successful in the last five years. Its $1,000 par...
The Olsen Mining Company has been very successful in the last five years. Its $1,000 par value convertible bonds have a conversion ratio of 34. The bonds have a quoted interest rate of 9 percent a year. The firm’s common stock is currently selling for $46.10 per share. The current bond price has a conversion premium of $10 over the conversion value. a. What is the current price of the bond? (Do not round intermediate calculations and round your final...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT