Worksheet 8.Spring2020 (3)
docx
keyboard_arrow_up
School
University of Washington *
*We aren’t endorsed by this school
Course
STAT340
Subject
Mathematics
Date
Feb 20, 2024
Type
docx
Pages
4
Uploaded by AgentEchidna7357
Math 146 Online Worksheet #8 Name_______________________ Hypothesis Testing: Z- test and T- test for the Mean Date________________________
Perform the following steps. You may use the critical region method or the p-value method in making your decision. a) Clearly state the hypotheses in symbols
and in words, and identify which one is the claim. b) Determine the nature of test (left-tailed, right-tailed or two-tailed). Determine which critical value is used, z
or t
? Use the guidelines below. c) Compute the test value. For the P-value method, give the both the test value and the p-value. d) Make the decision to reject or
do NOT reject the null hypotheses.
e) Make the conclusion in the context of the problem.
IMPORTANT NOTE:
●
The hypotheses statements for Problem #1 have been constructed as an example. Use these as template for constructing the Ho and H1 statements for problems #2-5. ●
When testing hypothesis involving population means, there are two types of critical values. Use the appropriate critical value using the guidelines below:
❖
Critical Z values
are used if the population standard deviation is known. Use the Z Values chart
on page 414 Figure 8-9. ❖
Critical T values
are used if the population standard deviation is NOT known.
The critical t-values
are found in Table F in Appendix A (page 652).
Problems:
1. Ford Taurus Assembly Time: Let x be a random variable that represents assembly times for the Ford Taurus. The Wall Street Journal reported that the average assembly time is μ
=
38
hours. A modification to the assembly procedure has been made. Experience with this new method indicates that the population standard deviation of the assembly time is 1.2 hours. It is thought that the average
assembly time may be reduced by this modification. A random sample of 47 new Ford Taurus automobiles coming off the assembly line showed the average assembly time of the new method to be
x
=
37.5
hours. Does this indicate that the average assembly time has been reduced? Use
α
=
0.01
. A) To be investigated/CLAIM: Do the data indicate that the average assembly time has been reduced?
The key word “reduced” translates to “less than” so the claim is H1. State hypotheses in symbols and determine which one is the claim.
State hypotheses in words in the context of the problem. Ho: µ = 38 hours
The average assembly time for the Ford Taurus is 38 hours. (
Note: This is saying the new method does not reduce the average assembly time.) H1: µ < 38 hours, CLAIM
The average assembly time for the Ford Taurus using the new method is less than 38 hours. B) Critical Value: -2.33 C) Test Value is:-
2.856 Type of test (
circle the answer
): right-tailed, left-tailed, two-tailed
Significance level: a=.01
Is the critical value z or t
?
__z____
Critical value: __-2.33_____________
D) Decision: Circle the answer and explain why:
Reject Ho / Do not Reject Ho E) Conclusion: There is enough evidence to support the claim that the average assembly time for the Ford Taurus using the new method is less than 38
2. Fuel Additives
: The Environmental Protection Agency publishes data regarding the miles per gallon of all cars. A researcher claims that fuel additives increase the miles per gallon of cars driven under highway driving conditions. The mean miles per gallon of all large cars manufactured in 1999 without the fuel additives is 25.1 mpg with σ
=
3.9
(based on data obtained from the EPA). A researcher obtained a random sample of 35 large cars manufactured in 1999, added a fuel additive, drove the cars
and calculated the cars’ mileage. The test showed that the mean mileage of the 35 large cars was 26.8 miles per gallon. Does this indicate that the fuel additives really increase the mileage of cars? Use
. A) State hypotheses in symbols and determine which one is the claim.
State hypotheses in words in the context of the problem. Ho: : u=25.1
The mean miles of gallon that all large cars can drive without fuel additives. H1: u > 25.1 claim
With fuel additives the mileage of cars increases and is more than 25.1
B) Critical Value +1.65 C) Test Value is:2.58 Type of test (
circle the answer
): right-tailed, left-tailed, two-tailed
Significance level: .05 = a
Is the critical value z or t
?
___z___
Critical value: __+1.65____________
D) Decision: Circle the answer and explain why:
Reject Ho / Do not Reject Ho E) Conclusion: There is enough evidence to support the claim that the average mpg is increased with fuel additives. 3. Filling Bottles:
A certain brand of apple juice is supposed to have 64 ounces of juice. Because the filling machine is not precise, the exact amount of juice varies from bottle to bottle. The quality control
manager wishes to verify that the mean amount of juice in each bottle is 64 ounces so she can be sure that the machine is not over-or-under-filling. She randomly samples 22 bottles of juice and measures the content. She obtains the following data: 63.97 63.87 64.03 63.95 63.95 64.02 64.01 63.90 63.92 63.93 63.97
64.00 63.92 63.94 63.90 64.05 63.90 64.01 63.91 63.93 63.98 64.01 Assuming that , test the hypothesis at the level of significance. A) State hypotheses in symbols and determine which one is the claim.
State hypotheses in words in the context of the problem.
Ho: 64 = u Thihs is how much ounces are supposed to be in a certain brand’s apple juice.
H1: 64 does not equal u (claim)
Because the machine is not precise the manager is testing if 64 ounces are actually in every bottle or an average.
B) Critical Value: +2.58, -2.58
C) Test Value is: z=-3.30 Type of test (
circle answer
): right-tailed, left-tailed, two-tailed
Significance level: a=.01
Is the critical value z or t
?
__z_________
Critical value: __+2.58, -2.58_____________
D) Decision: Circle the answer and explain why:
Reject Ho / Do not Reject Ho E) Conclusion: There is enough evidence to support the claim that 64 oz is in every bottle.
4. Medical: Hemoglobin Count
:
Let x
be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of whole blood. The variable x has a distribution that is approximately normal,
with population mean of about 14 for healthy adult women (based on information from Diagnostic Tests with Nursing Implications). Suppose that a female patient has taken 10 laboratory blood tests during the past year. The HC data sent to the patient’s doctor are: 15 18 16 19 14 12 14 17 15 11
Does this information indicate that the population average HC for this patient is higher than 14? Use
α
=
0.01
A) State hypotheses in symbols and determine which one is the claim.
State hypotheses in words in the context of the problem. Ho: u = 14
The average HC count in 100 mililiters of blood H1:u > 14 (claim)
Is the HC average higher than an average of 14. B) Critical Value: 2.821 C) Test Value is:1.383 Type of test: right-tailed, left-tailed, two-tailed
Significance level: a=.01
Is the critical value z or t
?
___t___
Critical value: ___2.821____________
D) Decision: Circle the answer and explain why:
Reject Ho / Do not Reject Ho E) Conclusion: There is not enough evidence to support the claim that the hc count in healthy women is higher than
14.
5. Wildlife Coyotes: A random sample of 46 adult coyotes in a region of northern Minnesota showed the average age to be x
=
2.05
years, with a sample standard deviation of 0.82 years (
based on information from the book Coyotes: Biology, Behavior and Management by M. Bekoff, Academic Press
).
However it is thought that the overall population mean age of coyotes is μ
=
1.75
years. Do the
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
sample data indicate that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years? Use α
=
0.01
.
A) State hypotheses in symbols and determine which one is the claim.
State hypotheses in words in the context of the problem. Ho: u = 1.75
The averageage of age of coyotes H1: u > 1.75 claim
The sample/test shows that coyotes in this region lived longer. B) Critical Value: 2.412 C) Test Value: 2.481 Type of test: right-tailed, left-tailed, two-tailed
Significance level: a=.01
Is the critical value z or t
?
____t________
Critical value: _2.412______________
D) Decision: Circle the answer and explain why:
Reject Ho / Do not Reject Ho E) Conclusion: There is enough evidence to support the claim coyotes living in the northern Minnesota region live longer than the average.