The following excerpt is from the racial profiling data collection resource center In 2006, the New York City Police Department stopped a half-million pedestrians for suspected criminal involvement. Raw89 percent of the stops involved nonwhites. Do these statistics point to a racial bias in police officers' decisions to stop particular pedestrians? o they indicate that officers are particularly intrusive when stopping nonwhites?

Write a report that answers the questions posed using the fact thst 44% of New York City residents were classified as white in 2006. In your report, cite some shortcomings in using the proportion of white residents in the city to formulate likelihoods.

Dr. X would like to examine the relative effectiveness of two teaching methods for improving college students’ statistical skills. A control group in which students received no training is also included in the study. A sample of 30 college students is randomly selected from the subject pool. These individuals are then randomly assigned to one of the three teaching methods. The dependent variable is a measure of statistical skills after one semester.

1. Specify a research hypothesis (2 pts)

2. Specify a null hypothesis (2 pts )

3. Create the dataset according to the observations above and read it into R. In your original dataset, the categorical variable may contain a set of values. Relabel the categorical variable with corresponding labels (see descriptions above) by forming a new variable. To demonstrate your work, show the R scripts, the variable names, and the first 3 rows of your data. (10 pts)

4. Calculate the means and standard deviations of each group. Answer this question with R. To show your work, copy and paste the R-script and output below. (5 pts)

5. Compute the F-statistic and effect size with R. To show your work, copy and paste the R-script and output below. (5 pts)

6. Based on the calculation of F, make a decision whether reject or do not reject the null hypothesis. (2 pts)

7. Based on the calculation of F, perform post-hoc analyses with R if necessary. Briefly summarize your findings. (5 pts)8. Report your findings in APA format. (5 pts).

"Apple CEO wants to launch another high range phone at a price point of 30% more than the current price. As a data scientist what will be your suggestion to him to ensure that sales will not be impacted by price spike?

Guidelines :

• The word limit is 200 words.
• You are asked to reflect on and respond to the above question and post your views
• Your replies/answers should be thoughtful & add value
• You are to write your opinion about the topic in discussion and your response should have some originality.
• You should refrain from posting any definitions of theories & concepts.

1) Use the normal distribution and the sample results to complete the test of the
hypotheses. Use a 5% significance level. Assume the results come from a
random sample.
a) Test ?!: ? = 15 ?? ?!: ? > 15 using the sample results ? = 17.2 , ? =
6.4 with ? = 40
b) Test ?!: ? = 100 ?? ?!: ? < 100 using the sample results ? = 91.7 , ? =
12.5 with ? = 30
c) Test ?!: ? = 500 ?? ?!: ? ≠ 500 using the sample results ? = 432 , ? =
118 with ? = 75

2) Use the Student-t distribution and the sample results to complete the test of
the hypotheses. Use a 5% significance level. Assume the results come from a
random sample, and if the sample size small, assume the underlying
distribution is relatively small.
a) Test ?!: ? = 10 ?? ?!: ? > 10 using the sample results ? = 13.2 , ? =
8.7 with ? = 12
b) Test ?!: ? = 120 ?? ?!: ? < 120 using the sample results ? = 112.3 , ? =
18.4 with ? = 100
c) Test ?!: ? = 4 ?? ?!: ? ≠ 4 using the sample results ? = 4.8 , ? = 2.3 with
? = 15

3) A t-test for a mean uses a sample of 15 observations. Find the t-test statistic
value that has a P-value of 0.05 when the alternative hypothesis is
a) ?!: ? ≠ 0
b) ?!: ? > 0
c) ?!: ? < 0

4) A study has a random sample of 20 subjects. The t-test statistic for testing
?!: ? = 100 is ? = 2.40. Find the approximate P-vale for alternative
a) ?!: ? ≠ 100
b) ?!: ? > 100
c) ?!: ? < 100

The owner of Maumee Ford-Mercury-Volvo wants to study the relationship between the age of a car and it selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year.

The regression equation is Ŷ=11.18-0.49X, the sample size is 12 and the standard error of the slope is 0.23. Use the .05 significance level. Can we conclude that the slope of the regression line is less than zero?

(NEED ALL THE WORKINGS AND STEP)

Q #5 The computers of six faculty members in a certain department are to be replaced. Two of the faculty members have selected laptop machines and the other four have chosen desktop machines. Suppose that only two of the setups can be done on a particular day, and the two computers to be set up are randomly selected from the six (implying 15 equally likely outcomes; if the computers are numbered 1, 2,…, 6, then one outcome consists of computers 1 and 2, another consists of computers 1 and 3, and so on).

a. What is the probability that both selected setups are for laptop computers?

b. What is the probability that both selected setups are desktop machines?

c. What is the probability that at least one selected setup is for a desktop computer?

d. What is the probability that at least one computer of each type is chosen for setup?

A nutritionist wants to determine how much time nationally people spend eating and drinking. The record shows that the mean was 1.5 hours. Suppose for a random sample of 921 people age 15 or​ older, the mean amount of time spent eating or drinking per day is 1.62 hours with a standard deviation of 0.71 hour. What is the upper boundary of the 95% C.I.?

A standard deck of 52 cards is shuffled and dealt. Let X1 be the number of cards appearing before the first ace, X2 the number of cards between the first and second ace (not counting either ace), X3 the number between the second and third ace, X4 the number between the third and forth ace, and X5 the number after the last ace. It can be shown that each of these random variables Xi had the same distribution, i=1,2,...,5, and you can assume this to be true.

a) Write down a formula for P(Xi=k), 0≤k≤48

b) Show that E(Xi)= 9.6 (Hint:Don't use your answer to part a)

c) Are X1,X2,...,X5 pairwise independent? Prove your answer.

Download the dataset CARS1 from BlackBoard. a. Do not worry about outliers. Assume the data is correct and any outliers will remain in the dataset. b. Do scatterplot and analyze the results. c. Test for correlation (correlation coefficient) d. Regress weight (column 2) against gas mileage in the city (column 1). Make sure you make gas mileage the dependent (Y) variable. e. Determine and fully explain R2 MPG City Weight 19 3545 23 2795 23 2600 19 3515 23 3245 17 3930 20 3115 22 3235 17 3995 22 3115 23 3240 17 4020 18 3220 19 3175 20 3450 19 3225 17 3985 32 2440 29 2500 28 2290

Engineers at the American Lighting Company recently developed a new three-way light bulb that they say is more energy efficient than the company’s existing three-way light bulb. The also claim that the bulb will outlast the current bulb, which has an average lifetime of 700 hours. The standard deviation (σ) for the lifetime of bulbs is 75 hours. The American Lighting Company has decided that before it begins full scale production on the new light bulbs it should take a sample of 225 bulbs and determine whether the mean life of the new bulb exceeds the old bulb’s 700 hours. The sample of 225 bulbs gave a sample mean of 704 hours. Assuming a significance level of .05 perform all hypothesis testing steps. Does the sample support the claim that the average lifetime of the new bulb is longer?

In the healthy handwashing survey, it was found the 64% of adult Americans operate the flusher of toilets in public restrooms with their foot. Suppose you survey a random sample of 740 adult American women aged 18-24 years. Use normal approximation to the binomial to approximate the probability of following.

a) check the conditions for normal distribution approximation

c)determine probability of exactly 500 of those surveyed flush toilets in public restrooms with their foot.

d) determine probability of no more than 490 of those surveyed flush toilets in public restrooms with their foot.

Poissson distribution

In order to control the polishing quality of a lens, a certain company is used to finish the number of spots on the surface considering the defective lens if 3 or more spots appear on it. The average rate is 2 defects per cm2. Calculate the probability that a 4cm2 lens will not be classified as defective.

The health of the bear population in a park is monitored by periodic measurements taken from anesthetized bears. A sample of the weights of such bears is given below. Find a​ 95% confidence interval estimate of the mean of the population of all such bear weights. The​ 95% confidence interval for the mean bear weight is the following.

data table 80 344 416 348 166 220 262 360 204 144 332 34 140 180

We are attempting to see if we can justify the additional expense of premium fuel over economy; i.e., we will only use premium fuel if we are convinced that it actually helps mpg. For each of the 25 cars at our disposal, we randomly picked one fuel to use first, drove the car until nearly empty, and calculated mpg when refilling the tank. We then filled it with the other fuel, repeating the process, obtaining mpg for that fuel, driving over the same roads.  

Explain why it would be important to randomize the order in which we test two gasoline types. Give a specific example of how not randomizing might cause a problem with this design.

PART 1: Determining the Appropriate Test

Assume that the following three questions appeared on a survey that is being used to collect data on consumer behavior for your company.

Question 1:         Do you subscribe to Netflix? (Circle One)                               YES         NO

Question 2:         What is your monthly average income in dollars?               $__________

Question 3:         In which of the 5 U.S. regions do you reside? (Circle one)

                                Northeast           Southwest          West          Midwest        Southeast

1. You want to determine if a relationship exists between the U.S. region in which the consumer resides and whether or not they are a subscriber to Netflix.

1. Which test should you run to help you answer this question? (ANOVA or Chi-Square test)

2. Given your answer in part “A” above, set up the null and alternative hypotheses to begin your test.

2. Now assume that you want to determine if the average monthly income of a consumer is different among groups of people living in different regions of the United States.

1. Which test should you run to help you answer this question? (ANOVA or Chi-Square test)

2. Given your answer in part “A” above, set up the null and alternative hypotheses to begin your test.

PART 2: Analysis of a Chi-Square test

Assume that a research study was conducted that included the following survey questions:

Question 1:         Have you ever attended an event at the city Performing Arts Center?       YES         NO

Question 2:         Have you ever attended an event at the city Athletic Center?                       YES         NO

A sample of 93 people answered the survey questions. The research team utilized Minitab statistical software to create the results shown below. You will find a contingency table with the Chi-Square test statistic and p-value at the bottom.

---------------------------------------------------------------------------------------------------------------------------------

CHI-SQUARE TEST FOR ASSOCIATION: PERFORMING ARTS CENTER ATTENDANCE, ATHLETIC CENTER ATTENDANCE

Rows: Performing Arts Center Attendance                        Columns: Athletic Center Attendance

Cell Contents:                        Count

                                                Expected Count   

Review the study and the Minitab results. Then answer the following questions:

1. If you want to determine if a relationship exists between whether or not a person attended an event at the Performing Arts center and whether or not the person attended an event at the Athletic Center, set up the null and alternative hypotheses to begin your test.

2. Find the p-value in the output. Draw a conclusion about your hypotheses based on this p-value. Be sure to explain your answer. Why did you draw the conclusion that you did?