Question

A tow truck company suspects that the lifespan of certain tires is less than the 28,000 miles they were offered. To verify if its suspicion is true, the company purchases 40 tires, places them in its trucks and measures the life of each one. The results are presented in the rate below.

Presumed known standard deviation = 1300 miles

26579 27965 26868 25070 26488

25834 27355 28039 32237 25523

28331 29103 24439 32850 28942

27474 27618 25645 27497 28183

27475 27697 28524 27704 26873

27232 31633 29363 26857 28017

27396 26982 28007 26293 25828

28256 25679 22594 31000 24208

If we perform a hypothesis test with α = 0.1,

a. What can we conclude? Is the company correct in its suspicions? Respond based on evidence - Clearly define hypotheses, areas of acceptance and rejection, test statistic and CONCLUDE in full sentence

b. If we wanted to construct a confidence interval for µ with an error of not more than 25 miles, what sample size should we use?

c. If the actual average is 27,800 miles, what would be the probability of making a type II error? What would it mean in this case to make a type II error?

Answer #1

A company claims that the average lifespan of a bicycle tire
that they manufacture is 1200 miles. You randomly and independently
collect a sample of 31 of these tires and find that the average
distance these tires lasted was 1125.7 miles, with a standard
deviation of 275 miles. You suspect the company is overstating how
long their tires last. You formulate your suspicion as a left
tailed hypothesis test. Your null hypothesis is "the average
lifespan of these tires is...

A company in the food industry stores a large number of canned
goods in a central warehouse. Last year, 3% of the canned goods had
damage (for example, ugly worms or dents in the can), and the
warehouse manager suspects it could be even worse this year.
To investigate this, we randomly selected 260 of the preserves
and of these, 13 have
damage.
(a) Conduct hypothesis testing to test if the warehouse manager's
suspicions can be considered where
Acknowledged.
(b)...

A.
A supermarket claims that the average wait time at the checkout
counter is less than 9 minutes. Assume that we know that
the standard deviation of wait times is 2.5 minutes. We will test
at 5% level of significance.
Consider
H0: mu >= 9
H1: mu < 9
A random sample of 50 customers yielded an average wait time of
8.2 minutes.
What is the critical value for the Zstat (the Z-test
statistic)?
(Provide two decimal places)____________
B.
Given the...

Problem
An automobile maker claims that its newest Raptor V5s (a sports
car) have a mean fuel efficiency of 48.5 miles per gallon on
highways. A consumer advocate suspects, however, that the actual
mean fuel efficiency of the Raptor V5s on highways is less than
48.5 miles per gallon.
To test this hypothesis, the consumer advocate obtains a random
sample of 35 Raptor V5s, measures their fuel efficiencies on
highways, and calculates the sample mean fuel efficiency to be 46.2...

Do all the following problems.
I. Choose the best answer for each
multiple choice. Please use CAPITAL letters to indicate your answer
and write neatly. (30 points)
1. ____ 4.____ 7. ____ 10.____ 13.
____
2. ____ 5.____ 8. ____ 11.____ 14.
____
3. ____ 6.____ 9. ____ 12.____ 15.
____
Whenever the population standard deviation is unknown and the
population has a normal or near-normal distribution, which
distribution is used in developing an interval estimation?
A. standard distribution
B....

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