1. a)What is your null hypothesis regarding sepal lengths for the two species? And what is your alternate hypothesis?
b) Describe your hypotheses in terms of your test statistic: what would be the t under the null hypothesis, H₀, and what would be the statement about t under your alternate hypothesis H_a?  Would you do a one- or non-(i.e., two-sided) directional test? Why?

Find the minimum sample size n needed to estimate μ for the given values of​ c, σ​, and E.

c=0.95, σ=7.2, and E=1

Assume that a preliminary sample has at least 30 members.

n=___ (Round up to the nearest whole​ number.)

Because some people are unable to stand to have their height measured, doctors use the height from the floor to the knee to approximate their patients’ height (in cm).

a. Use Excel to determine the correlation coefficient of this data

b. Use Excel to determine the regression equation of this data

c. Find the overall height from a knee height of 45.3 cm

d. Find the overall height from a knee height of 52.7 cm

Use R studio to do this problem. This problem uses the wblake data set in the alr4 package. This data set includes samples of small mouth bass collected in West Bearskin Lake, Minnesota, in 1991. Interest is in predicting length with age. Finish this problem without using Im()

(a) Compute the regression of length on age, and report the estimates, their standard errors, the value of the coefficient of determination, and the estimate of variance. Write a sentence or two that summarizes the results of these computations

(b) Obtain a 99% confidence interval for from the data. Interpret this interval in the context of the data.

(c) Obtain a prediction and a 99% prediction interval for a small mouth bass at age 1 . Interpret this interval in the context of the data.

The following data represent the calories and​ sugar, in​ grams, of various breakfast cereals.

Use the data above to complete parts​ (a) through​ (d).

a. Compute the covariance.

b. Compute the coefficient of correlation.

c. Which do you think is more valuable in expressing the relationship between calories and

sugar—the covariance or the coefficient of​ correlation? Explain.

d. What conclusions can you reach about the relationship between calories and​ sugar?

One of the questions Rasmussen Reports included on a 2018 survey of 2,500 likely voters asked if the country is headed in right direction. Representative data are shown in the DATAfile named RightDirection. A response of Yes indicates that the respondent does think the country is headed in the right direction. A response of No indicates that the respondent does not think the country is headed in the right direction. Respondents may also give a response of Not Sure.

(a)What is the point estimate of the proportion of the population of respondents who do think that the country is headed in the right direction? (Round your answer to four decimal places.)

(b)At 95% confidence, what is the margin of error for the proportion of respondents who do think that the country is headed in the right direction? (Round your answer to four decimal places.)

(c)What is the 95% confidence interval for the proportion of respondents who do think that the country is headed in the right direction? (Round your answers to four decimal places.)

___to ___

(d)What is the 95% confidence interval for the proportion of respondents who do not think that the country is headed in the right direction? (Round your answers to four decimal places.)

____ to ____

(e)Which of the confidence intervals in parts (c) and (d) has the smaller margin of error? Why?

The confidence interval in part (c) has a (Smaller or Larger) margin of error than the confidence interval in part (d). This is because the sample proportion of respondents who do think that the country is headed in the right direction is  (closer to .5 / closer to 1 / farther from .5 / farther from 1) than the sample proportion of respondents who do not think that the country is headed in the right direction.

Dataset:

553 - No

70 - Not Sure

384 - Yes

Consider the following hypothesis test.

A sample of 40 provided a sample mean of 26.8. The population standard deviation is 6.

(a)

Find the value of the test statistic. (Round your answer to two decimal places.)

(b)

Find the p-value. (Round your answer to four decimal places.)

p-value =

(c)

At

α = 0.01,

state your conclusion.

Reject H₀. There is sufficient evidence to conclude that μ > 25.Reject H₀. There is insufficient evidence to conclude that μ > 25.     Do not reject H₀. There is sufficient evidence to conclude that μ > 25.Do not reject H₀. There is insufficient evidence to conclude that μ > 25.

(d)

State the critical values for the rejection rule. (Round your answer to two decimal places. If the test is one-tailed, enter NONE for the unused tail.)

test statistic≤test statistic≥

State your conclusion.

Reject H₀. There is sufficient evidence to conclude that μ > 25.Reject H₀. There is insufficient evidence to conclude that μ > 25.     Do not reject H₀. There is sufficient evidence to conclude that μ > 25.Do not reject H₀. There is insufficient evidence to conclude that μ > 25.

The two-sample t-test is applied to compare whether the average difference between two groups is significant or if it is due instead to random chance.

Use good references,

1. Briefly, describe the difference between Unpaired Two-Sample T-test and Paired Two-Sample T-test.

2. Provide an application example for Unpaired Two-Sample T-test, and stablish the Ho and Ha Hypotheses.

3. Provide an application example for Paired Two-Sample T-test, and stablish the Ho and Ha Hypotheses.

4. Explain the purpose of P-values and its application in the context of your two examples.

When selecting a sample, there are several methods of selection available.

A company with hundreds of employees has hired a third party human resources agency. The agency is to study the employees and their level of job satisfaction, and to discover if the company needs to change anything about its management of human resources.

As part of this study, the agency wants to survey a selection of employees from within the company. Four members of the agency propose four different sampling plans for the survey.

Alvin: 'The marketing department of the company is reflective of the rest of the company in terms of job satisfaction. We should simply survey that department.'

Bonnie: 'We have access to the names of every employee in the company. We should survey 50 people from the company by putting every name in a list and choosing 50 names completely at random.'

Crystal: 'The company is made up of 60% men and 40% women. I believe that men and women will have different levels of job satisfaction, and we should force our sample to have 60% men and 40% women.'

Donald: 'As Bonnie says, we should put every name in a list. However, we should only pick one person at random, from the first ten people on the list, and then pick every tenth person thereafter.'

a)The member that is proposing a cluster sample is:

1) Alvin
2) Bonnie
3) Crystal
4) Donald

b)From the list below, select the correct statement about sampling selection methods:

1) Systematic sampling guarantees that every sample of a given size stands an equal chance of being selected.
2) Stratified sampling guarantees that every sample of a given size stands an equal chance of being selected.
3) Cluster sampling guarantees that every sample of a given size stands an equal chance of being selected.
4) None of the above statements are correct.

A bank has been losing customers over the past year. Whenever a customer closes their account with the bank, they are always asked why (so the bank has some idea of the services that it needs to improve). However, it would like to gather more information on what its current customers think, to see if there are any other areas that it needs to work on.

The bank has 100,000 customers. Every customer name is put into an ordered list, effectively giving each customer a number from 1 to 100,000. The bank then generates 500 unique random numbers between 1 and 100,000 and selects the customers that correspond to these numbers. The bank surveys these 500 customers.

This is an example of:

A computer training group would like to compare the effectiveness of two modes of training. The first mode of training is a short 20 minute interactive one-on-one tutorial with the participant and the second mode is a one hour video that the participant watches.

A random sample of 100 people are invited to take part in the tutorial, which is followed by a test to measure competency at the tasks covered. The proportion of people that pass this test (to 2 decimal places) is 0.36. Similarly, a random sample of 175 people are invited to watch the video, which is also followed by the same test. The proportion of people that pass this test (to 2 decimal places) is 0.48.

Let Pi symbol1 denote the population proportion of people that would pass the competency test after taking the tutorial. Similarly, let Pi symbol2 denote the population proportion of people that would pass the competency test after watching the video.

Construct a 95% confidence interval for the difference between these two proportions (Pi symbol1 - Pi symbol2). Give your answers to 3 decimal places. You may find this standard normal table useful.

≤ Pi symbol1 - Pi symbol2 ≤

Problem 9-13 (Algorithmic)

Romans Food Market, located in Saratoga, New York, carries a variety of specialty foods from around the world. Two of the store’s leading products use the Romans Food Market name: Romans Regular Coffee and Romans DeCaf Coffee. These coffees are blends of Brazilian Natural and Colombian Mild coffee beans, which are purchased from a distributor located in New York City. Because Romans purchases large quantities, the coffee beans may be purchased on an as-needed basis for a price 11% higher than the market price the distributor pays for the beans. The current market price is $0.47 per pound for Brazilian Natural and $0.62 per pound for Colombian Mild. The compositions of each coffee blend are as follows:

Romans sells the Regular blend for $3.2 per pound and the DeCaf blend for $4.3 per pound. Romans would like to place an order for the Brazilian and Colombian coffee beans that will enable the production of 900 pounds of Romans Regular coffee and 500 pounds of Romans DeCaf coffee. The production cost is $0.89 per pound for the Regular blend. Because of the extra steps required to produce DeCaf, the production cost for the DeCaf blend is $1.09 per pound. Packaging costs for both products are $0.25 per pound. Formulate a linear programming model that can be used to determine the pounds of Brazilian Natural and Colombian Mild that will maximize the total contribution to profit.

If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)

The complete linear program is

What is the contribution to profit?

Optimal solution:

If required, round your answer to two decimal places.

Value of the optimal solution = $  

The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year’s program. Advertising alternatives include television, radio, and online. Audience estimates, costs, and maximum media usage limitations are as shown:

To ensure a balanced use of advertising media, radio advertisements must not exceed 50% of the total number of advertisements authorized. In addition, television should account for at least 10% of the total number of advertisements authorized.

1. If the promotional budget is limited to $18,800, how many commercial messages should be run on each medium to maximize total audience contact? What is the allocation of the budget among the three media? If required, round your answers to the nearest dollar.

   Let	T = number of television spot advertisements
   	R = number of radio advertisements
   	O = number of online advertisements

   	Budget ($)
   T =
   R =
   O =
   	Total Budget = $

   
   What is the maximum total audience that would be reached? Round your answer to the nearest whole number.
   
   
2. By how much would audience contact increase if an extra $100 were allocated to the promotional budget? Round your answer to the nearest whole number.

7.)     The average cholesterol content of Mighty Taco’s Super Mighty Burrito is 95 mg with a standard deviation of 7.2. Assume the variable is normally distributed.

(a)    If a single Super Mighty Burrito is purchased, find the probability it will have less than 100 milligrams of cholesterol.

(b)    If you purchase a Super Mighty 4 pack, which consists of 4 Might taco Super Mighty Burritos, find the probability that the mean of the sample will be larger than 100 milligrams of cholesterol.

Companies often develop and test hypotheses about their products. For example, car manufacturers will test their cars to determine fuel efficiency and miles per gallon. To ensure that products are safe and that they perform as advertised, regulatory and consumer protection groups also test companies’ claims.

For this Assignment, you are working at a firm that conducts independent testing for heavy industry. Recently, an automobile manufacturer has been in the news for complaints about the highway gas mileage of their latest model minivan. You receive a contract from a consumer action group to test and write a report on the company’s claim that its minivans get 28 miles per gallon on the highway. The car company agrees to allow you to select randomly 35 low-mileage fleet minivans to test their highway mileage. Your test results gave you the following data:

29.7     24.5     27.1     29.8     29.2     27.0     27.8     24.1     29.3

            25.9     26.2     24.5     32.8     26.8     27.8     24.0     23.6     29.2

            26.5     27.7     27.1     23.7     24.1     27.2     25.9     26.7     27.8                

            27.3     27.6     22.8     25.3     26.6     26.4     27.1     26.1

Complete the following and include your results and responses in your report (use alpha = 0.05):

• List the null and alternative hypotheses for the two-tail test for the mean. Calculate the observed value of the test statistic and the associated p-value. (75–150 words, or 1–2 paragraphs)
  • Is the observed test statistic in the critical region? Is the p-value higher or lower than your alpha? (75–150 words, or 1–2 paragraphs)
  • Note: Include your calculations. If your calculations are submitted separately, make note of where they can be found.
• List the null and alternative hypotheses for the one-tail test of the mean. Calculate the observed value of the test statistic and the associated p-value. (75–150 words, or 1–2 paragraphs)
  • Is the observed test statistic in the critical region? Will the p-value be higher or lower than your alpha? (75–150 words, or 1–2 paragraphs)
  • Note: Include your calculations. If your calculations are submitted separately, make note of where they can be found.

Conclusions

In your report, use the confidence interval information and the results of the hypothesis testing to provide support for your conclusions and recommendations to the company. Specifically:

Question 1. What conclusions did you reach? What did you learn about the situation by using each method? Did one method offer more conclusive proof than another? (150–225 words, or 2–3 paragraphs)

Question 2. Based on your results, do you support the company’s claim that their minivans get 28 miles per gallon? (75 words, or 1 paragraph)

Question 3. Summarize the details of your test methods and the results from each statistical method you used. Explain the findings so that executives from both the agency and the company can understand your conclusion. (150–225 words, or 2–3 paragraphs)

Question 4. Finally, present recommendations for actions that the company might take to use your findings to better serve their customers in the future. (75 words, or 1 paragraph)

3) In the data from the first problem, one of the scores of a winning team was 131 points. Use what you learned in CH. 3-2, plus the calculated mean and standard deviation, to answer the following question: Is 131 points an unusual score for this group of data? Why or why not? Support your answer by telling me what you did to come to your conclusion. Calculated MEAN (round to the nearest whole number):

FREQUENCY DISTRIBUTION TABLE