In: Math
A Nielsen study indicates that 18-to-34 year olds spend a mean of 93 minutes whatching video on their smartphones per week. Assume that the amount of time watching video on a smartphone per week is normally distributed and that the standard deviation is 15 minutes.
1- What is the probability that an 18- to 34 year old spends less than 77 minutes watching video on his or her smartphone per week?
2- What is the probability that an 18- to 34- year old spends between 77 minutes and 109 minutes watching video on his or her smartphone per week?
3- What is the probability that an 18- to 34 year old spends more than 109 minutes watching video on his or her smartphone per week?
4- One percent of all 18- to 34- year olds will spend less than how many minutes watching video on his or her smartphone per week?
(Type it if possible)
In: Math
To get published in an academic journal, you have to prove something "interesting." As a result, most academics begin their research by investigating hypotheses that, all else equal, are unlikely to be true. Suppose each research project begins with a research claim that has a 10% chance of being correct.
They then perform a study that satisfies the following two properties:
1) The probability that they correctly *find* an important result given that their *claim* is true is 50% 2) The probability that they incorrectly *find* an important result given that their *claim* is false is 5%
If they find an important result they are published. What is the probability that their claim was true, given that they were published?
In: Math
In the college population, the mean reading comprehension test score is μ = 75 and σ = 25. A researcher wanted to investigate the effect of listening to hip-hop music on reading comprehension. She randomly selected a sample of n = 100 college students. The sample of students completed a reading comprehension test while hip-hop music was played in the background the sample mean reading comprehension score was M = 68.
Do the data indicate a significant effect of hip-hop music on reading comprehension? Use a two-tailed z - test with p < .05 to answer this research question.
- Null and alternative hypotheses
- All computational steps of the z-test
- Critical z-value used for decision about H0
- Decision about H0 (i.e., reject or fail to reject)
- If the effect is significant, compute the Cohen's d to establish the size of the effect - is the effect small, medium or large?
- Conclusion in APA style: interpretation of the z-test outcome to answer the research question. Is there a significant effect of hip-hop music on reading comprehension or not? If there is a significant effect, address in your conclusion the direction of the effect (i.e., is the effect positive or negative/is there an improvement or decline of reading comprehension?) and report the Cohen's effect size.
Please explain in very broken down and simple steps, thank you!
In: Math
Bhola Bhikhu is thinking about adding a new stock to her portfolio. Based on advice from a friend who claimed to make a lot of money, she decides to use the price to earnings ratio (P/E) as the only measurement of the performance of a stock. Bhola selects several possible stocks based on this measurement and will select one stock from the bundle. She assigns each of the selected stocks an equal chance of being selected. Stock one has a price to earnings ratio of 20, Stock two has an P/E of 22, Stock three has a P/E of 20, Stock four has a P/E of 18, and Stock five has a P/E of 16, and Stock six has a P/E of 20. Let ? denote the random variable representing the price to earnings ratio for the selected stock.
a) Create a PMF table for the random variable ?.
b) What is the probability that Bhola selects a stock with a P/E greater than 17?
c) Given that Bhola selects a stock with a P/E of at least 19, what is the probability that the P/E is over 20?
d) Given that Bhola selects a stock with a P/E greater than 17, what is the probability that the P/E is at most 22?
e) Find the expected value of ? and standard deviation of �
In: Math
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