Please Use R studio to answer this question

NY Marathon 2013 the table below shows the winning times (in minutes) for men and women in the new york city marathon between 1978 and 2013. (the race was not run in 2012 because of superstorm sandy.) assuming that performances in the big apple resemble performances elsewhere, we can think of these data as a sample of performance in marathon competitions. Create a 90% confidence interval for the mean difference in winning times for male and female marathon competitors.

Disk drives have been getting larger. Their capacity is now often given in terabytes​ (TB) where 1 TBequals1000 ​gigabytes, or about a trillion bytes. A survey of prices for external disk drives found the data shown to the right. For this​ data, we want to predict Price from Capacity.

Capacity: price:

.5 59.00

1 77.45

2 115.00

3 105.95

4 142.45

6 423.95

8 599.79

12 1075.45

32 4463

What is the intercept?

QUESTION 25

1. In the table below, find Jim's score on the Computer Lab Project.

   What is Jim's percentile rank on this project? Report as a whole number (e.g., 75).

   Student	Computer Lab Project Score	Major	Comfort with Computer (Scale: 1 = low, 2 = medium, 3 = high)
   Mary	19	Nursing	1
   Susan	18	Social Work	2
   Brad	22	Physical Therapy	3
   Betty	22	Nursing	3
   John	27	Nursing	2
   Larry	21	Nursing	3
   Jim	29	Physical Therapy	1
   Martha	30	Physical Therapy	3

QUESTION 26

1. In the table below, find the scores on the Computer Lab Project.

   What is the probability that Jim could have gotten a score that would be equal to or greater than a Z of 1.5 (Z≥1.5)?

   Report as a proportion with 2 decimals (e.g., 0.33).

   Student	Computer Lab Project Score	Major	Comfort with Computer (Scale: 1 = low, 2 = medium, 3 = high)
   Mary	19	Nursing	1
   Susan	18	Social Work	2
   Brad	22	Physical Therapy	3
   Betty	22	Nursing	3
   John	27	Nursing	2
   Larry	21	Nursing	3
   Jim	29	Physical Therapy	1
   Martha	30	Physical Therapy	3

QUESTION 27

1. In the table below, find the scores on the Computer Lab Project.

   Compute the probability of getting a z-score equal to or less than +1.64 (Z≤+1.64) and express it as a percentile.

   Report as a whole number (e.g., 75).

   Student	Computer Lab Project Score	Major	Comfort with Computer (Scale: 1 = low, 2 = medium, 3 = high)
   Mary	19	Nursing	1
   Susan	18	Social Work	2
   Brad	22	Physical Therapy	3
   Betty	22	Nursing	3
   John	27	Nursing	2
   Larry	21	Nursing	3
   Jim	29	Physical Therapy	1
   Martha	30	Physical Therapy	3

When do creative people get their best ideas? USA Today did a survey of 966 inventors (who hold U.S. patents) and obtained the following information.

(a) Assuming that the time interval includes the left limit and all the times up to but not including the right limit, estimate the probability that an inventor has a best idea during each time interval: from 6 A.M. to 12 noon, from 12 noon to 6 P.M., from 6 P.M. to 12 midnight, from 12 midnight to 6 A.M. (Enter your answers to 3 decimal places.)

(b) Do the probabilities add up to 1? Why should they?

No, because they do not cover the entire sample space.Yes, because they cover the entire sample space.    Yes, because they do not cover the entire sample space.No, because they cover the entire sample space.

What is the sample space in this problem?

12AM-12PM6AM-6PM    6AM-12AMthe entire day

The results of sampling independent populations:
sample 1 from population 1
• mean 1000
• sample standard deviation 400
• sample size 50

sample 2 from population 2
• mean 1250
• sample standard deviation 400
• sample size 50
Test the HO: population 1 mean = population 2 mean at alpha = 0.01. HA: population 1 mean =/ population2 mean. This is a two-tailed test with both a negative lower critical value and a positive upper critical value. Separate variances is assumed.

A researcher wishes to prove that less than 40% of students support the changes announced by the Ford
government in January 2019 to tuition, the Ontario Student Assistance Program, and student fees. If 32% of all
students support the changes, what is the chance that a random sample of 250 students provides insufficient proof
to meet a 5% significance level? In other words, what is the probability of a Type II error? Answer with hypotheses in
formal notation, TWO fully-labelled graphs, a quantitative analysis & the requested probability

Honeydew bottles honey jars and sells them through retail channels. The weight on the sticker says 20 oz and Honeydew claims its bottles have a weight that is normally distributed with a mean of 20 oz and std dev of 2 oz. The retailer has been receiving several complaints lately and decides to measure a sample of 4 jars and finds weights of 18, 20, 17 and 19 oz respectively.

a. The retailer complains to Honeydew if he is 95% confident that the mean is lower than advertised. Does he complain?

b. If the retailer’s customers return any jar under 18 oz in weight, what fraction of the retailer’s sales result in a return?

c. Assuming Honeydew’s claim is true, what is their current sigma capability? What can they do to reduce the fraction of returns to 5%? What then would the new sigma capability be?

Read the scenario about hypothesis testing and answer the questions below.

Scenario: George wants to study what animals make better pets. Based on the research available George thinks that Birds will be greater than Lizards as pets. (use symbols i.e. >,<, =, ≠, ≥, ≤ or write it out in words)

Question 1: What is the alternative hypothesis?

Question 2: What is the Null hypothesis?

Question 5: If the data show that birds make worse pets, what decision did George find regarding the Null Hypothesis? (reject/fail to reject)

• Suppose that X1, ..., Xn form a random sample from a uniform distribution for on the interval [0, θ]. Show that T = max(X1, ..., Xn) is a sufficient statistic for θ.

A school newspaper reporter decides to randomly survey 20 students to see if they will attend Tet (Vietnamese New Year) festivities this year. Based on past years, she knows that 23% of students attend Tet festivities. We are interested in the number of students who will attend the festivities.

• In words, define the Random Variable X.

• Part (b)

  List the values that X may take on.

  X = 0, 1, 2, ..., 23 X = 1, 2, 3, ..., 20  X = 1, 2, 3, ..., 23 X = 0, 1, 2, ..., 20

• Part (c)

  Give the distribution of X.
  X ~  

• Part (d)

  How many of the 20 students do we expect to attend the festivities? (Round your answer to the nearest whole number.)
  student(s)

• Part (e)

  Find the probability that at most 6 students will attend. (Round your answer to four decimal places.)

• Part (f)

  Find the probability that more than 4 students will attend. (Round your answer to four decimal places

"Achievement test scores are declining all around us," brooded Professor Probity. "Here are my final exam scores for last year and this year on the same exam." What did Professor Probity discover? (18 pts).

This Year | Last Year (this year on the left, last year in the right column)

29    27

27    28

26    25

22    24

19    22

15    20

14    18

10    16

10    12

Indicate:

a. a statement of your hypotheses in words (2 pts)

b. the t-value you compute (5 pts)

c. your decision regarding H₀ and why, and (2 pts)

d. Results of homogeneity of variance test and effect size, if appropriate

e. an APA conclusion based on your results (4 pts)

3. A dealer in recycled paper places empty trailers at various sites; these are gradually filled by individuals who bring in old newspapers and the like. The trailers are picked up (and replaced by empties) on several schedules. One such schedule involves pickup every second week. This schedule is viable if the average amount of recycled paper is more than 1600 cubic feet per two-week period. The dealer’s records for 26 two-week periods show the following volumes (in cubic feet) at a particular site: 1660 1820 1590 1440 1730 1680 1750 1720 1900 1690 1850 1770 1410 1570 1700 1900 1800 1770 2010 1580 1620 1690 1510 1420 1400 1705 a. Please construct and interpret the 92% and 98% confidence intervals for the population mean amount of recycled paper clearly showing all the necessary steps. What would be the probability that the population mean amount of paper could be greater than the upper limit of the 92% confidence interval? Please explain which confidence interval is wider and why. What do you think will happen to the margins of error and the confidence intervals if the sample size was to be increased to 35 observations? Please justify your answer. [5 points] b. Based on the confidence intervals you have constructed do you think the proposed schedule is viable? Please explain how arrived at your answer. [2 points] c. Using the given data and at 2% level of significance, please test whether the proposed schedule is viable. Show the necessary steps and explain your conclusion. Is your test result consistent with the conclusion you arrived at based on the 98% confidence interval you constructed under question (a) above? Please explain.

4. The main access road to suburban shopping mall sometimes becomes severely congested. On weekdays, excluding holidays, the average number of vehicles going toward the mall between 9:00 AM and 7:00 PM that pass a counter is 11,260. The highway department tried to improve traffic flow by changing stoplight cycles and improving turn lanes. For the first seven non-holiday weekdays after the changes, the volumes were 10,690, 11,452, 12,316, 12, 297, 11,889, 10911, and 12,647. A local politician who reviewed the results said that the data proved there had been significant improvement in traffic volume. At 5% level of significance, is this a reasonable conclusion to draw from the given data? Please show the necessary steps and explain your conclusion. What will happen to the probability of type II error if you were to redo the test at 1% level of significance?

For each the following questions,
• Define the appropriate parameter(s)
• State Ho and Ha
• Choose the correct model from the following list:
I. Test for a single mean II. Test for a single proportion III. Test for two means, independent samples IV. Test for mean difference, dependent sampling V. Test for two proportions, independent samples
a. You want to support the claim that male bass singers are taller than male tenor singers.

Parameter(s):

Hypotheses: Ho: __________________ Ha: __________________ Model to use: ______

b. You want to reject the claim that no more than 10% of students will suffer financial hardship if tuition increased.

Parameter(s):

Hypotheses: Ho: __________________ Ha: __________________ Model to use: ______

c. You want to support the claim that people spend, on average, more time on the Internet than they do watching television. 200 people will be asked how much time they spent on the TV and on the Internet.

Parameter(s):

Hypotheses: Ho: __________________ Ha: __________________ Model to use: ______

d. You want to test the claim that the average age for a community college student is over 27. You want to support this claim and sample 20 students.

Parameter(s):

Hypotheses: Ho: __________________ Ha: __________________ Model to use: ______

e. Is there a difference in mean overall quality of tomatoes bought at farmers markets versus at grocery stores? Tomatoes are purchased at 30 randomly selected farmers markets and 40 randomly selected highend grocers. Their mean overall quality is compared.

Parameter(s):

Hypotheses: Ho: __________________ Ha: __________________ Model to use: ______

f. A hospital surgery review board wants to determine if the proportion of patients undergoing a particular surgery who are cured is greater than the proportion that are cured by the current non-surgical standard treatment.

Parameter(s):

Hypotheses: Ho: __________________ Ha: __________________ Model to use: ______

g. A higher education centered non-profit organization wants to determine if the percentage of entering freshmen that graduate is lower at a public university than at a private college. Parameter(s):

Hypotheses: Ho: __________________ Ha __________________ Model to use: ______

h. Does the home team have an advantage in NBA basketball games? In a study of 25 games, the visiting team’s points were compared to the home team’s points.

Parameter(s):

Hypotheses: Ho: __________________ Ha: __________________ Model to use: ______

i. A hypothesis test is performed to determine if recent female college graduates are subject to pay discrimination, earning less on average for similar work than recent male college graduates with similar qualifications.

Parameter(s):

Hypotheses: Ho: __________________ Ha: __________________ Model to use: ______

An inexpensive restaurant featuring steak dinners makes most of its profit from side orders suggested to diners by the staff. As an experiment, the restaurant owner rewarded each server with 10% of the price of all side orders made through the server. After 10 days, the owner computed the side-order volume per customer for each of 41 servers. The data are in column 1 of the Excel data file named ‘Side Orders’. The reward policy will be profitable if the mean volume is more than $2.40 per customer. At the 10% level of significance, is there a strong evidence in the data that the policy will, in fact be profitable? Please show the necessary steps and explain your conclusion