The paired data ((x, y)): (1,6),(5,8),(7,9),(8,0),(4,1) is considered.

(a) Find the pearson correlation coefficient

(b) Find the slope and intercept of the regression coeffients.

(c) What percent of the variation in y is described by variation in x?

Some statistics are not resistant to a single outlier. An example would be the mean value, as one extremely large of small value can tip the scales. Which of these statistics is also not resistant to outliers: median, standard deviation, IQR, range, Pearson correlation, linear regression coefficients?

QUESTION 16

1. Jon reads that 76% of Americans prefer Coke over Pepsi. He works at a local restaurant and decides to poll his customers there about their soda preference. He finds that 120 out of 150 customers surveyed prefer Coke. He would like to conduct a test of hypothesis to see if there is a significant difference between customers at his restaurant and the national results for all Americans, in terms of their preference for Coke over Pepsi. After calculating the test statistic and p-value, what would his statistical conclusion be at an alpha level of 0.10?

   	A.	Yes, do not reject Ho
   	B.	No, do not reject Ho
   	C.	Yes, reject Ho
   	D.	No, reject Ho

QUESTION 19

1. In 2017 it was reported that 46% of Americans still had landline phones in their homes. Researchers would like to see if that percentage has declined since that time. Data was collected in 2019 and of the 655 participating Americans, 265 said they still had landlines in their homes. Is this enough evidence that the percentage of Americans with landlines in their homes has significantly decreased in the past 2 years? Identify the parameter in this problem.

   	A.	true proportion of all Americans in 2019 who use their landline phone as their primary means of contact
   	B.	true proportion of all Americans in 2019 who have a landline phone in their homes
   	C.	true proportion of all Americans who have both a cell phone and a landline phone
   	D.	true proportion of all Americans in 2017 who have a landline phone in their homes

QUESTION 26

1. In 2017 it was reported that 46% of Americans still had landline phones in their homes. Researchers would like to see if that percentage has declined since that time. Data was collected in 2019 and of the 655 participating Americans, 265 said they still had landlines in their homes. Is this enough evidence that the percentage of Americans with landlines in their homes has significantly decreased in the past 2 years? After completing the full hypothesis test, what is the final conclusion?

   	A.	With 95% confidence, I do not have enough evidence to conclude that true proportion of all Americanhouseholds in 2019 that have a landline phone is significantly lower than the 2017 value of 46%.
   	B.	I am 95% confident that the true proportion of all American households in 2019 that have a landline phone is significantly lower than the 2017 value of 46%.

QUESTION 27

1. In 2017 it was reported that 46% of Americans still had landline phones in their homes. Researchers would like to see if that percentage has declined since that time. Data was collected in 2019 and of the 655 participating Americans, 265 said they still had landlines in their homes. Suppose researchers computed a 95% confidence interval for this data. Which of the following would be true?

   	A.	The value of 46% would fall within the interval.
   	B.	The value of 46% would fall outside the interval.

Assume that a set of test scores is normally distributed with a mean of 80 and a standard deviation of 15

Use the​ 68-95-99.7 rule to find the following quantities.

a. The percentage of scores less than

80 is ___%.

​(Round to one decimal place as​ needed.)

b. The percentage of scores greater than 95 is ___​%

​(Round to one decimal place as​ needed.)

c. The percentage of scores between 50 and 95 is ___​%.

​(Round to one decimal place as​ needed.)

In a random sample of four microwave​ ovens, the mean repair cost was $85.00 and the standard deviation was $12.00. Assume the population is normally distributed and use a​ t-distribution to construct a 99​% confidence interval for the population mean mu. What is the margin of error of mu? Interpret the results. The 99​% confidence interval for the population mean mu is?

Wayne is interested in two games, Keno and Bolita. To play Bolita, he buys a ticket for 1 marked with number 1..100, and one ball is drawn randomly from a collection marked with numbers 1,...,100. If his ticket number matches the number on the drawn ball he wins 75, otherwise he hey nothings and loses his 1 bet.

to play keno, he buts a ticket marked with numbers 1..4 and there are only 4 balls marked 1...4; again he wins if the ticket matches the ball draw. if he wins he gets 3, otherwise he loses his bet.

(a) What is the expected payout (expected value of net profit after buying ticket and possibly winning something) for each of these games?

(b) What is the variance and standard deviation for each of these games?

(c) If he decides to play one (and only one) of these games for a very long time, which one should he choose? If he decides to try one of these games for a couple of times, just for fun, which one should he choose?

Problem 6: R simulation.

Use different color lines and appropriate legend to

(1) plot the density functions of χ 2 k for k = 1, 2, 3, 4, 6, 9 in one figure;

(2) plot the density functions of tk for k = 3, 5, 10, 30 and N(0, 1) distribution in one figure. Describe respectively what you observe when the degree of freedom increases.

A random sample of 25 items is drawn from a population whose standard deviation is unknown. The sample mean (x-bar) is 850. Construct a confidence interval with 95% confidence for the different values of s. Do not forget to use the t distribution in this case. a. Assume s = 15. b. Assume s = 30. c. Assume s = 60. d. Describe how the confidence interval changes as s increases.

Nike took a risk on Colin Kaepernick for its “Dream Crazy” #JustDoIt campaign. The first ad aired on national TV September 6, 2018. A year from now they will assess whether the risk paid off. To answer this question they will collect weekly sales data from September 6, 2018 – September 5, 2019 and compare it to 52 weeks of sales data over the previous year, September 6, 2017 to September 5, 2018. For each data point, they will record the date and sales. a. How would you analyze this data? • State the null and alternative hypothesis. • What statistical test would you use?

USING EXCEL The XO Group Inc. conducted a survey of 13,000 brides and grooms married in the United States and found that the average cost of a wedding is $29,858 (XO Group website, January 5, 2015). Assume that the cost of a wedding is normally distributed with a mean of $29,858 and a standard deviation of $5600. What is the probability that a wedding costs less than $20,000? What is the probability that a wedding costs between $20,000 and $30,000? For a wedding to be among the 5% most expensive, how much would it have to cost?

1. A researcher wants to determine whether the time spent online per day is related to gender. A random sample of 315 adults was selected and the results are shown below. Test the hypothesis that the time spent online per day is related to gender. Use α = 0.05.

1. Identify the null hypothesis, Ho, and the alternative hypothesis, Ha.
2. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.
3. Find the critical value(s) and identify the rejection region(s).
4. Find the appropriate standardized test statistic. If convenient, use technology.
5. Decide whether to reject or fail to reject the null hypothesis.
6. Interpret the decision in the context of the original claim.

a dice can have 6 sides and are numbered 1,2,3,4,5, and 6. The odds of getting an odd number are the same. The chance of getting an even number is the same. The chance of getting an odd number is twice the chance of getting an even number.
a. Determine the opportunity to get the number 3.
b. The dice is thrown three times. Determine the odds of getting two numbers 5 and one number 4.
c. The dice is tossed a hundred times. Use the approximation to determine the chances of getting an even number at most 37 times.

1. Andrew plans to retire in 38 years. He plans to invest part of his retirement funds in stocks, so he seeks out information on past returns. He learns that over the entire 20th century, the real (that is, adjusted for inflation) annual returns on U.S. common stocks had mean 8.7% and standard deviation 20.2%. The distribution of annual returns on common stocks is roughly symmetric, so the mean return over even a moderate number of years is close to Normal.

(a) What is the probability (assuming that the past pattern of variation continues) that the mean annual return on common stocks over the next 38 years will exceed 12%?

2. Sheila's doctor is concerned that she may suffer from gestational diabetes (high blood glucose levels during pregnancy). There is variation both in the actual glucose level and in the blood test that measures the level. A patient is classified as having gestational diabetes if the glucose level is above 140 miligrams per deciliter (mg/dl) one hour after having a sugary drink. Sheila's measured glucose level one hour after the sugary drink varies according to the Normal distribution with μ = 120 mg/dl and σ = 10 mg/dl.

(b) If measurements are made on 4 separate days and the mean result is compared with the criterion 140 mg/dl, what is the probability that Sheila is diagnosed as having gestational diabetes?

discuss the sensitivity of outliers for mean, median, interquartile range, range, variance and standar deviation

Does gender influence the satisfaction reported by library patrons?

(a) " 18 women and 14 men reported that they were not satisfied with the library service.

(b) " 33 women and 20 men reported that they were satisfied.

(c) " 57 women and 85 men reported that they were very satisfied with the service.

In a study of the accuracy of fast food​ drive-through orders, Restaurant A had 211 accurate orders and 71 that were not accurate. a. Construct a 95​% confidence interval estimate of the percentage of orders that are not accurate. b. Compare the results from part​ (a) to this 95​% confidence interval for the percentage of orders that are not accurate at Restaurant​ B: 0.226 < p < 0.323. What do you​ conclude? Need answer to both a. and b. Thanks.