The National Sporting Goods Association (NSGA) conducted a survey of the ages of individuals that purchased skateboarding footwear. The ages of this survey are summarized in the following percent frequency distribution. Assume the survey was based on a sample of 200 individuals.
| Age of User | Percent Frequency | |
| Under 14 years old | 37 | |
| 14 to 17 years old | 27 | |
| 18 to 24 years old | 16 | |
| 25 to 34 years old | 8 | |
| 35 to 44 years old | 5 | |
| 45 to 64 years old | 7 |
Calculate the mean and the standard deviation of the age of individuals that purchased skateboarding shoes. Use 10 as the midpoint of the first class. (Do not round intermediate calculations. Round your answers to 2 decimal places.)
Mean-
Variance-
Standard Deviation-
In: Math
Define a joint distribution for two random variables (X,Y) such that (i) Cov(X,Y)=0 and (ii) E[Y I X] is not equal to E[Y].
How do I define a joint distribution that satisfies both (i) and (ii) above at the same time?
Please give me an example and explanation of how it meets the two conditions.
In: Math
A company that develops over-the-counter medicines is working on a new product that is meant to shorten the length of sore throats. To test their product for effectiveness, they take a random sample of 100 people and record how long it took for their symptoms to completely disappear. The results are in the table below. The company knows that on average (without medication) it takes a sore throat 6 days or less to heal 42% of the time, 7-9 days 31% of the time, 10-12 days 16% of the time, and 13 days or more 11% of the time. Can it be concluded at the 0.01 level of significance that the patients who took the medicine healed at a different rate than these percentages?
Hypotheses:
H0: There is no difference/a difference in duration of sore throat for those that took the medicine.
H1: There is no difference/a difference in duration of sore throat for those that took the medicine.
Enter the expected count for each category in the table below.
|
6 days or less |
7-9 days |
10-12 days |
13 or more days |
|
|
Duration of Sore Throat |
47 |
38 |
10 |
5 |
|
Expected Counts |
After running a Goodness of Fit test, can it be concluded that there is a statistically significant difference in duration of sore throat for those that took the medicine?
Yes/No
In: Math
The medical community unanimously agrees on the health benefits of regular exercise, but are adults listening? During each of the past 15 years, a polling organization has surveyed americans about their exercise habits. In the most recent of these polls, slightly over half of all American adults reported that they exercise for 30 or more minutes at least three times per week. The following data show the percentages of adults who reported that they exercise for 30 or more minutes at least three times per week during each of the 15 years of this study.
| Year | Percentage of Adults Who Exercise 30 or more minutes at least three times per week |
| 1 | 41.8 |
| 2 | 45.4 |
| 3 | 47.4 |
| 4 | 45.7 |
| 5 | 46.6 |
| 6 | 44.6 |
| 7 | 47.8 |
| 8 | 51.3 |
| 9 | 49.4 |
| 10 | 49.2 |
| 11 | 49.5 |
| 12 | 52.5 |
| 13 | 50.5 |
| 14 | 55 |
| 15 | 52.5 |
In: Math
|
Problem Set 2: Linear Regression Analysis Research Scenario: A social psychologist is interested in whether the number of days spent in a refugee camp predicts trauma levels in recently resettled refugees. He interviews 17 refugees to determine how many days they spent in a refugee camp before being resettled, then administers the Harvard Trauma Questionnaire Part IV (HTQ Part 4), where a higher score indicates higher levels of trauma (Mollica et al., 1992). He compiles the information in the table below. Using this table, enter the data into a new SPSS data file and run a linear regression analysis to test whether days in a refugee camp predict HTQ-4 scores. Create a scatterplot with a regression line to show the relationship between the variables. |
|
Days Spent in Refugee Camp |
HTQ Part 4 Score |
|
12 |
0.4 |
|
73 |
1.1 |
|
60 |
0.9 |
|
105 |
2.3 |
|
98 |
1.7 |
|
76 |
0.3 |
|
89 |
0.7 |
|
173 |
2.6 |
|
189 |
3.1 |
|
203 |
3.0 |
|
138 |
1.9 |
|
215 |
2.5 |
|
71 |
0.7 |
|
67 |
1.2 |
|
63 |
1.8 |
|
184 |
2.9 |
|
63 |
0.6 |
In: Math
Reid Harper, the manager at Modix Hotel, makes every effort to ensure that customers attempting to make phone reservations do not have to wait too long to speak with a reservation specialist. Since the hotel accepts phone reservations 24 hours a day, Reid is especially interested in maintaining consistency in service. Reid wants to determine if the variance of wait time in the early morning shift (12:00 am – 6:00 am) differs from that in the late morning shift (6:00 am – 12:00 pm). He uses independently drawn samples of wait time for phone reservations for both shifts for the analysis; a portion of the data is shown in the accompanying table. Assume that wait times are normally distributed.
| Early Morning Shift | Late Morning Shift |
| 31 | 105 |
| 62 | 105 |
| 34 | 160 |
| 73 | 122 |
| 31 | 113 |
| 44 | 136 |
| 46 | 115 |
| 50 | 139 |
| 67 | 138 |
| 75 | 134 |
| 58 | 116 |
| 41 | 124 |
| 82 | 119 |
| 59 | 91 |
| 44 | 125 |
| 27 | 126 |
| 46 | 127 |
| 67 | 115 |
| 42 | 109 |
| 52 | 124 |
| 45 | 120 |
| 67 | 118 |
| 60 | 126 |
| 43 | 117 |
a. Select the hypotheses to test if the variance of wait time in the early morning shift differs from that in the late morning shift.
H0: σ12 / σ22 = 1, HA: σ12 / σ22 ≠ 1
H0: σ12 / σ22 ≤ 1, HA: σ12 / σ22 > 1
H0: σ12 / σ22 ≥ 1, HA: σ12 / σ22 < 1
b-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)
b-2. Find the p-value.
c. At the 10% significance level, what is your conclusion?
Reject H0, since the p-value is more than α.
Reject H0, since the p-value is less than α.
Do not reject H0, since the p-value is less than α.
Do not reject H0, since the p-value is more than α.
d. Interpret the results at α =
0.10.
The variance of wait time in the early morning shift is greater than that in the late morning shift.
The variance of wait time in the early morning shift is not greater than that in the late morning shift.
The variance of wait time in the early morning shift differs from that in the late morning shift.
The variance of wait time in the early morning shift does not differ from that in the late morning shift.
In: Math
Learning Objective 3 – Identify the Design of a particular study
1) To determine if conversations about HIV status decreases the risk of acquiring HIV among men having sex with me (MSM). From March 2008 through May 2010, persons newly diagnosed with HIV-positive men and HIV-negative men were recruited by researchers. To distinguish recent (<5 months) from longstanding (>5 months) infection, dried blood spots from people newly diagnosed with HIV were tested with the BED IgG-capture ELISA. HIV-positive men and the matched HIV-negative men completed a knowledge, attitudes, behavior and practices (KABP)-questionnaire. Researcherscompared HIV-positive men with recent infection and matched HIV-negative men among men having sex with men (MSM) regarding reported risk behavior in the previous 6 months. What type of study is this? Explain.What are its strengths and limitation?
2) Tumors of the central nervous system are the second most common group of childhood cancers in 0-14 year olds (24% of total cancers) and represent a major diagnostic group in 15-24 year olds. Researchers were interested in learning if breastfeeding was a protective factor in such tumors. Researchers identified children with a newly diagnosed intracranial tumor. All patients were recruited from one major clinical cancer treatment center. Children with brain tumors were matched to children without brain tumors that were of similar age, sex, and BMI. These healthy children were drawn from general practice lists. What type of study is this? Explain. What are its strengths and limitation?
3) A previous review showed that high stress increases the risk of occupational injury by three to five-fold. Researchers examined the effect of stress on recorded hospitalized injuries over a period of 8 years. A total of 16,385 employees of a logging company responded to the questionnaire. Perceived stress was measured with a validated single-item measure, and analyzed in relation recorded hospitalized injuries from 1986 to 2008. What type of study is this? Explain. What are its strengths and limitations?
In: Math
To determine whether there is an attendance rate drop of a national conference this year (consider as 1) than last year (consider as 2), a sample of 400 people this year and a sample of 400 people last year were selected. Given α=0.01. The data are summarized below:
This Year Last Year Difference
Attending 359 378 -19
Not Attending 41 22 19
Total number 400 400 400
(c) Is there sufficient evidence to indicate that there is an attendance rate drop of a national conference this year (consider as 1) than last year (consider as 2)?
Group of answer choices
No
Yes
In: Math
Women’s heights are N(64, 3). Suppose female HS basketball players are N(68.2, 2.1). Which event is less likely?
Group of answer choices
A woman from the general population being taller than 67”.
A female HS basketball player being shorter than 67”.
In: Math
In: Math
A random sample of 12 second-year university students enrolled in a business statistics course was drawn. At the course's completion, each student was asked how many hours he or she spent doing homework in statistics. The data are listed below. 28 18 15 20 14 25 21 29 20 23 24 26 It is known that the population standard deviation is 6. The instructor has recommended that students devote 2 hours per week for the duration of the 12-week semester, for a total of 24 hours.
Test to determine whether there is evidence at the 0.01 significance level that the average student spent less than the recommended amount of time. Fill in the requested information below.
A. The value of the standardized test statistic: Note: For the next part, your answer should use interval notation. An answer of the form (−∞,a) is expressed (-infty, a), an answer of the form (b,∞) is expressed (b, infty), and an answer of the form (−∞,a)∪(b,∞) is expressed (-infty, a)U(b, infty).
B. The rejection region for the standardized test statistic:
C. The p-value
D. Your decision for the hypothesis test
Reject H0
Do Not Reject H1
Reject H1
Do Not Reject H0.
In: Math
In the 2015 federal election, 39.5% of the electorate voted for the Liberal party, 31.9% for the Conservative party, 19.7% for the NDP, 4.7% for the Bloc Quebecois and 3.5% for the Green party.
The most recent pool as of the launch of the 2019 election campaign shows a tie between the Liberals and the Conservatives at 33.8%. This pool was based on 1185 respondents. (a) Based on this recent pool, test whether this is sufficient evidence to conclude that the level of support for the conservatives has increased since the last election. Use the 5% level of significance and show your manual calculations. (b) Using recent pool data, build an appropriate 95% one-sided confidence interval for the true proportion of support for the conservatives. Is this CI consistent with your conclusion in a) above? (c) Would your conclusion be the same as in a) above if you had used a 10% confidence level for the hypothesis test? (d) Now, suppose you want to estimate the national level of support for the Liberals at the start of the 2019 campaign using a 95% 2-sided confidence interval with a margin of error of 1% based on the results of the last election, what sample size would be required? (e) Would the sample size calculated above be sufficient to estimate the support for the Bloc Quebecois within the same level of confidence and margin of error? If not, how many more respondents would you need?
In: Math
The maintenance manager at a trucking company wants to build a regression model to forecast the time (in years) until the first engine overhaul based on four explanatory variables: (1) annual miles driven (in 1,000s of miles), (2) average load weight (in tons), (3) average driving speed (in mph), and (4) oil change interval (in 1,000s of miles). Based on driver logs and onboard computers, data have been obtained for a sample of 25 trucks. A portion of the data is shown in the accompanying table.
|
Time until First Engine Overhaul |
Annual Miles Driven |
Average Load Weight |
Average Driving Speed |
Oil Change Interval |
|
8.1 |
42.8 |
22.0 |
50.0 |
10.0 |
|
0.9 |
98.7 |
26.0 |
49.0 |
25.0 |
|
⋮ |
⋮ |
⋮ |
⋮ |
⋮ |
|
6.1 |
61.6 |
28.0 |
54.0 |
16.0 |
a. For each explanatory variable, discuss whether
it is likely to have a positive or negative causal effect on time
until the first engine overhaul.
The effect on time is either Positive or Negative! Fill them in
below.
|
b. Estimate the regression model.
(Negative values should be indicated by a minus sign. Round
your answers to 4 decimal places.)
TimeˆTime^ = ________+_______ Miles +_______ Load + ________ Speed + _______ Oil
c. Based on part (a), are the signs of
the regression coefficients logical?
The below signs will be filled with the word logical or not
logical!
|
d. What is the predicted time before the first
engine overhaul for a particular truck driven 57,000 miles per year
with an average load of 18 tons, an average driving speed of 57
mph, and 18,000 miles between oil changes. (Round
coefficient estimates to at least 4 decimal places and final answer
to 2 decimal places.)
|
TimeˆTime^ |
_______ years |
Excel data:
|
Time Until First Engine Overhaul |
Annual Miles Driven |
Average Load Weight |
Average Driving Speed |
Oil Change Interval |
|
8.1 |
42.8 |
22 |
50 |
10 |
|
0.9 |
98.7 |
26 |
49 |
25 |
|
8.7 |
43.2 |
18 |
67 |
19 |
|
1.4 |
111 |
27 |
60 |
24 |
|
1.4 |
102.2 |
31 |
46 |
19 |
|
2 |
97.3 |
27 |
67 |
22 |
|
2.5 |
93.3 |
19 |
59 |
17 |
|
7.6 |
54.1 |
18 |
70 |
12 |
|
8.1 |
51.2 |
24 |
47 |
20 |
|
3.9 |
84.9 |
29 |
51 |
26 |
|
0.6 |
120.3 |
30 |
50 |
20 |
|
5.3 |
77.6 |
24 |
49 |
25 |
|
5 |
68.2 |
25 |
49 |
21 |
|
5.2 |
55.4 |
28 |
53 |
21 |
|
5.3 |
66.4 |
19 |
62 |
24 |
|
8.5 |
39.8 |
15 |
45 |
16 |
|
5.8 |
52.4 |
19 |
58 |
27 |
|
6.2 |
54.5 |
24 |
47 |
14 |
|
4.2 |
75.1 |
23 |
60 |
20 |
|
6.1 |
58.4 |
19 |
50 |
13 |
|
6.7 |
52.2 |
24 |
49 |
23 |
|
6.8 |
68.3 |
21 |
56 |
24 |
|
4 |
94.3 |
19 |
55 |
21 |
|
7.6 |
45.2 |
22 |
56 |
17 |
|
6.1 |
61.6 |
28 |
54 |
16 |
Don't care how you solve as long as answers are correct. I will like for it being correct!
In: Math
10.4: Inferences About the Difference Between Two Population Proportions
In a test of the quality of two television commercials, each commercial was shown in a separate test area six times over a one-week period. The following week a telephone survey was conducted to identify individuals who had seen the commercials. Those individuals were asked to state the primary message in the commercials. The following results were recorded.
| Commercial A | Commercial B | |
| Number Who Saw Commercial | 155 | 204 |
| Number Who Recalled Message | 64 | 63 |
Use and test the hypothesis that there is no difference in the recall proportions for the two commercials.
Formulate the null and the alternative hypotheses.
- Select your answer -greater than or equal to 0greater than 0less than or equal to 0less than 0equal to 0not equal to 0Item 1
- Select your answer -greater than or equal to 0greater than 0less than or equal to 0less than 0equal to 0not equal to 0Item 2
What is the value of the test statistic (to 2 decimals)?
What is the -value (to 4 decimals)?
Does there appear to be a difference in recall proportions for the two commercials?
- Select your answer -NoYesItem 5
Compute a confidence interval for the difference between the recall proportions for the two populations (to 4 decimals).
( , )
It appears that - Select your answer -Commercial ACommercial Bneither commercial item 8 has a better recall rate.
Use and test the hypothesis that there is no difference in the recall proportions for the two commercials.
Formulate the null and the alternative hypotheses.
- Select your answer -greater than or equal to 0greater than 0less than or equal to 0less than 0equal to 0not equal to 0
- Select your answer -greater than or equal to 0greater than 0less than or equal to 0less than 0equal to 0not equal to 0
What is the value of the test statistic (to 2 decimals)?
What is the -value (to 4 decimals)?
Does there appear to be a difference in recall proportions for the two commercials?
- Select your answer -NoYes
Compute 95 % a confidence interval for the difference between the recall proportions for the two populations (to 4 decimals).
( ______, ______)
It appears that - Select your answer -
Commercial A
Commercial B
neither Commercial
Commercial none
In: Math
Imagine you are in charge of a program in which members are evaluated on five different tests at the end of the program. Why doesn't it make sense to simply compute the average of the five scores as a measure of performance rather than compute a z score for each test for each individual and average those?
In: Math