A tire company claims that the lifetimes of its tires average 50,000 miles. The standard deviation of tire lifetimes is known to be 5000 miles. You sample 100 tires and will test the hypothesis that the mean tire lifetime is at least 50,000 miles against the alternative that it is less. Assume, in fact, that the true mean lifetime is 49,500 miles. a) State the null and alternate hypotheses. Which hypothesis is true? b) It is decided to reject H0 if the sample mean is less than 49,400. Find the level and power of this test. c) If the test is made at the 5% level, what is the power? d) At what level should the test be conducted so that the power is 0.80? e) You are given the opportunity to sample more tires. How many tires should be sampled in total so that the power is 0.80 if the test is made at the 5% level?

Question
Asked Feb 23, 2020
2 views

A tire company claims that the lifetimes of its tires average 50,000 miles. The standard deviation of tire lifetimes is known to be 5000 miles. You sample 100 tires and will test the hypothesis that the mean tire lifetime is at least 50,000 miles against the alternative that it is less. Assume, in fact, that the true mean lifetime is 49,500 miles. a) State the null and alternate hypotheses. Which hypothesis is true? b) It is decided to reject H0 if the sample mean is less than 49,400. Find the level and power of this test. c) If the test is made at the 5% level, what is the power? d) At what level should the test be conducted so that the power is 0.80? e) You are given the opportunity to sample more tires. How many tires should be sampled in total so that the power is 0.80 if the test is made at the 5% level?

check_circle

Expert Answer

Step 1

Statistics homework question answer, step 1, image 1

Statistics homework question answer, step 1, image 2

Step 2

Statistics homework question answer, step 2, image 1

Statistics homework question answer, step 2, image 2

...

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.

Related Statistics Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: question 3

A: Click to see the answer

question_answer

Q: 1. An IQ test is designed so that the mean is 100 and the standard deviation is 23for the population...

A: Click to see the answer

question_answer

Q: Suppose that more than a decade ago high levels of lead in the blood put 82% of children at risk. A ...

A: From the provided information, More than a decade ago high levels of lead in the blood put 82% of ch...

question_answer

Q: Suppose that in a certain metropolitan area, 90% of all households have cable TV. Let x denote the n...

A: From the provided information, 90% of all households have cable TV. The probability of success (p) =...

question_answer

Q: 8. Salaries of 33 college graduates who took a statistics course in college have a​ mean, x, of $67,...

A: The provided information are:

question_answer

Q: A variable has a density curve equation y=1 for  0<x<1 and y=0 a.graph density curve b. show a...

A: Hey there! Thank you for posting the question. Since your question has more than 3 parts, we are sol...

question_answer

Q: What is Data Mining? Justify the use of data mining to support the use of multiple regression.

A: Data mining is the process of finding the hidden, valid and potentially useful patterns in the huge ...

question_answer

Q: how do you recognize when a probability problem requires the use of the basic rules of probability, ...

A: Hello there First of all, to recognize a probability problem you need to know about what is probabil...

question_answer

Q: A television station sells advertising in 15,30,60,90,120 minute blocks. The distribution of sales f...

A: The formula for mean, variance and standard deviation of a random variable X is given by: