Worksheet 9. Fall 2022-1 (1)
docx
keyboard_arrow_up
School
University of Washington *
*We aren’t endorsed by this school
Course
105
Subject
Mathematics
Date
Feb 20, 2024
Type
docx
Pages
7
Uploaded by AgentEchidna7357
Math 146 Online Worksheet #9 Name_______________________
Hypothesis Testing for Two Means & Proportions and Date _________________/35pts Correlation/Regression 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.
1.
Percentage of E-mail Users:
Technology is dramatically changing the way we communicate. In 1997, a
survey of 880 U.S. households showed that 149 of them use e-mail (based on data from The World Almanac and Book of Facts). Use those sample results to test the claim that more than 15% of U.S. households use e-mail. Use a 0.05 significance level. A) State hypotheses in symbols and determine which one is the claim.
State hypotheses in words in the context of the problem. Ho: p=.15
amount of US households that use email
H1: p > .15 claim
claim is that more than 15% use email
B) Critical Value Type of test (
circle the answer
): right-tailed, left-tailed, two-tailed
Significance level: a=.05
Is the critical value z or t
?
_z?___________
Critical value: ______1.645__________________
C) Test Value is: z = 1.605 p = .0543
D) Decision: Circle your answer Reject Ho /
Do not Reject Ho E) Conclusion: There is not enough evidence to support the claim that more than 15% of households use email
2. Commuting Times for College Students
: The mean travel time to work for Americans is 25.3 minutes. An employment agency wanted to test the mean commuting times for college graduates and those with only some college. Researchers obtained the following data: College Graduates
Workers with some college
Sample size 35
30
Sample Mean 40.5 minutes
34.8 minutes
Population Standard dev
8.2 minutes
6.3 minutes
Question:
At 0.05 level of significance, can we conclude that the mean commuting time for college graduates is higher than workers with some college? A) Let: mean commuting time for college graduates mean commuting time for workers with some college
S
tate hypotheses in symbols and determine which one is the claim.
State hypotheses in words in the context of the problem. Ho: u1-u2=0
college grads have an equal amount of commuting time as workers
H1:
u1-u2>0
college grads have a higher commute time than workers
B) Critical Value Type of test (
circle the answer
): right-tailed, left-tailed, two-tailed
Significance level: a=.05
Is the critical value z or t
?
_z_____
Critical value: ____1.645___________
C) Test Value is: D) Decision: Circle your answer Reject Ho /Do not Reject Ho z=3.165
E) Conclusion: There is enough evidence to support the claim
3.
Bipolar Depression Treatment
:
In clinical experiments involving different groups of independent samples, it is important that the groups are similar in ways that affect the experiment. In an experiment designed to test the effectiveness of paroxetine for treating bipolar depression, subjects were measured using the Hamilton depression scale with the results given below (based on data from “Double-Blind, Placebo-Controlled Comparison of Imipramine and Paroxetine in the Treatment of Bipolar Depression” by Nemeroff et al., American Journal of Psychiatry, Vol.158, No.6) Based on the results, does it appear that the two populations have different means at the 0.05 significance level? Should paroxetine be recommended as a treatment for bipolar depression? Hamilton Depression Rating Scale:
https://qxmd.com/calculate/calculator_146/hamilton-depression-rating-scale-ham-d-or-hdrs
Placebo group
Paroxetine treatment group
S
1
= 3.87
S
2
= 3.91
A) Let: mean depression level for the placebo group mean depression level for the treatment group State hypotheses in symbols and determine which one is the claim.
State hypotheses in words in the context of the problem. Ho: u1-u2=0
depression levels for placebo vs treatment group
H1:
u1-u2 does not equal 0
claim
depression level means are differrent between both groups
B) Critical Value Type of test (
circle the answer
): right-tailed, left-tailed
, two-tailed
Significance level: a=.05
Is the critical value z or t
?
__t____
Critical value: _+-1.665______________ not sure if this is corect
C) Test Value is: t= 1.321 or p =.1909 D) Decision: Circle
your answer Reject Ho /
Do not Reject Ho E) Conclusion: There is not enough evidence to support the claim
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
4. Improving Study Habits: As an aid for improving students’ study habits, nine students were randomly selected to attend a seminar on the importance of education in life. The table shows the number of hours
each student studied per week before and after the seminar. At 5% significance level, did attending the seminar increase the number of hours the students studied per week? Student
1
2
3
4
5
6
7
8
9
Before
9
12
6
15
3
18
10
13
7
After
9
17
9
20
2
21
15
22
6
A) State hypotheses in symbols and determine which one is the claim.
State hypotheses in words in the context of the problem. Ho: u1-u2 =0 difference in hours studied after seminar
H1:
u1-u2>0 claim
after attendance of seminars did the number of hours increase
B) Critical Value Type of test (
circle the answer
): right-tailed, left-tailed, two-tailed
Significance level: a=.05
Is the critical value z or t
?
___t___
Critical value: ___1.860____________
C) Test Value is: -2.8 D) Decision: Circle your answer Reject Ho /
Do not Reject Ho E) Conclusion: There is not enough evidence to support the claim
5. Testing Effectiveness of Vaccine
:
In a USA Today article about an experimental nasal spray vaccine for
children, the following statement was presented: “In a trial involving 1602 children only 14 of the 1070 who received the vaccine developed the flu, compared with 95 of the 532 who got the placebo.” The article also referred to a study claiming that the experimental nasal spray “cuts children’s chances of getting the flu.” Is there sufficient sample evidence to support the stated claim? Test at the 0.05 significance level.
Let: proportion of children who received the vaccine and developed the flu
proportion of children who received the placebo and developed the flu
A) State hypotheses in symbols and determine which one is the claim.
State hypotheses in words in the context of the problem. Ho: p1-p2=0
the null hypothesis states that there is no significant difference in
H1:
p1-p2 does not equal 0
claim
the alternative hypothesis suggests that there is a significant difference.
B) Critical Value Type of test (
circle the answer
): right-tailed, left-tailed, two-tailed
Significance level: a-.05
Is the critical value z or t
?
____z_______
Critical value: ___+-1.96____________________
C) Test Value is: z=-12.38 D) Decision: Circle your answer Reject Ho /Do not Reject Ho E) Conclusion: There is enough evidence to support the claim
6. Auto Accidents:Age:
Data for this problem are based on information taken from The Wall Street Journal. Let x
be the age in years of a licensed automobile driver. Let y be the percentage of all fatal accidents (for a given age) due to speeding. For example, the first data pair indicates that 36% of all fatal accidents of 17-year olds are due to speeding. Age (x)
17
27
37
47
57
67
77
Percentage (y)
36
35
20
12
10
7
5
Questions: a) Draw a scatter plot of the data on your calculator and determine if there is a linear correlation between the variables. Is it negative or positive relationship, how strong is the relationship between these
two variables? The plot looks to show a linear relationship and a negative correlation at that. b) Calculate the correlation coefficient r. round to 3 decimal places. r = ____-.947__________________
c) If there appears to be a linear correlation, use your calculator to find the regression line. Round your numbers to 4 decimal places. _____
44.5464 +.5679(x)
______________________
d) Interpret the slope of the regression line in the context of the problem.
For every one-year increase in age, the percentage of fatal accidents due to speeding decreases by approximately 0.3565%. Therefore, the slope indicates a negative association between age and the percentage of fatal accidents due to speeding.
e) Use the regression line to predict the percentage of all fatal accidents due to speeding for 25-year olds. 58.7439 = y=a+b(25)
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
7. The table below shows a sample of households and two variables: the number of people in the household (x) and the weekly pounds of trash generated by the household (y). Number of people in
the household (x)
Pounds of trash per week generated by
the households (y)
2
18
3
33
6
93
1
23
7
83
Questions:
a) Explain the relationship between the amount of trash per week and the number of people in the household using concepts from linear regression. Provide a comprehensive answer that includes explaining the following: (2pts)
●
How strong is the relationship between these two variables? ●
Compute the r value, round to 4 decimal places.
r = .9498
b) Find the equation of the regression line using your calculator. Round to 4 decimal places.
___.7985+12.9478(x)________________________
c) What is the slope of the regression line. Interpret the slope of the regression in this problem. What does it tell you about trash generated? Interpreting the slope it tells us that there is a positive and significant relationship between the number of
people in the household and the trash generated. On average each additional person in the household is associated with an increase of approximately 19.1429 pounds of trash per week.
d) The average size of a US household is 2.6 people (Source: US Census Bureau). Predict how much trash per week that household would be expected to generate. y=a+b(2.6) = 34.4628