Applying statistical analysis skills to real-world decision making is key in modern business and it can make a company to be ahead competitively. Even in today’s workplace, you can have an immediate competitive edge over other new employees, and even those with more experience, by applying statistical analysis skills. Chose any company that you have observed that it is not utilizing its data as your case study. Do some background research on the company? Write an essay (report) outlining some statistical data analysis that the company can use in its decision making. Relate how data analysis can be attained by using built-in R-programming packages or functions.

Prove that if two of the opposite sides of a quadrilateral are respectively the greatest and the least sides of the quadrilateral, then the angles adjacent to the least are greater than their opposite angles

Given the above three sets of data, we want to compare the three seasons using the ANOVA. Answer the following questions:

1. Using proper notation, write the null and alternative hypothesis statements.

2. In the context of the problem posed, interpret the results of the test and make a conclusion about the hypotheses.

****You must be provide concise explanations in your solutions in order to receive credit****

Here is a simple probability model for multiple-choice tests. Suppose that each student has probability p of correctly answering a question chosen at random from a universe of possible questions. (A strong student has a higher p than a weak student.) The correctness of answers to different questions are independent. Jodi is a good student for whom p = 0.8.

(a) Use the Normal approximation to find the probability that Jodi scores 74% or lower on a 100-question test. (Round your answer to four decimal places.)

(b) If the test contains 250 questions, what is the probability that Jodi will score 74% or lower? (Use the normal approximation. Round your answer to four decimal places.)

(c) How many questions must the test contain in order to reduce the standard deviation of Jodi's proportion of correct answers to half its value for a 100-item test?

Test the given claim. Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, P-value, and then state the conclusion about the null​ hypothesis, as well as the final conclusion that addresses the original claim. Among

20912091

passenger cars in a particular​ region,

227227

had only rear license plates. Among

344344

commercial​ trucks,

4848

had only rear license plates. A reasonable hypothesis is that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars. Use a

0.100.10

significance level to test that hypothesis.

a. Test the claim using a hypothesis test.

b. Test the claim by constructing an appropriate confidence interval.

7. A recent Iowa straw poll for the Democratic Primary found the following number of supporters for these candidates (Observed Frequencies).

a) Specify the null and alternative hypotheses for a chi-square Goodness of Fit test of candidate preference.

b) Fill in the table below with the expected frequencies.

c) Use the observed and expected frequencies to calculate a chi-square Goodness of Fit test to decide if people in Iowa have a preference for any of the candidates, using alpha = .05. Report the critical value and your decision.

A roulette wheel has 38 slots, numbered 0, 00, and 1 to 36. The slots 0 and 00 are colored green, 18 of the others are red, and 18 are black.The dealer spins the wheel and at the same time rolls a small ball along the wheel in the opposite direction. The wheel is carefully balanced so that the ball is equally likely to land in any slot when the wheel slows. Gamblers can bet on various combinations of numbers and colors. (a)If you bet on “red,” you win if the ball lands in a red slot. What is the probability of winning with a bet on red in a single play of roulette? (b)You decide to play roulette four times, each time betting on red. What is the distribution of X, the number of times you win? (c)If you bet the same amount on each play and win on exactly four of the eight plays, then you will “break even.” What is the probability that you will break even? (d)If you win on fewer than four of the eight plays, then you will lose money. What is the probability that you will lose money?

Given the following information, is the grade dependent on gender? Test at the 0.05 level. State the hypotheses and identify the claim, find the critical value(s), compute the test value, make the decision, summarize the results. A B C D or lower

Males 8 17 25 10

Females 12 10 21 7

Does the average Presbyterian donate more than the average Catholic in church on Sundays? The 44 randomly observed members of the Presbyterian church donated an average of $22 with a standard deviation of $12. The 58 randomly observed members of the Catholic church donated an average of $17 with a standard deviation of $10. What can be concluded at the αα = 0.10 level of significance?

1. For this study, we should use Select an answert-test for the difference between two independent population meansz-test for a population proportiont-test for the difference between two dependent population meansz-test for the difference between two population proportionst-test for a population mean
2. The null and alternative hypotheses would be:   
3.   

H0:H0:  Select an answerp1μ1 ?=<≠> Select an answerμ2p2 (please enter a decimal)   

H1:H1:  Select an answerp1μ1 ?=><≠ Select an answerμ2p2 (Please enter a decimal)

3. The test statistic ?tz = (please show your answer to 3 decimal places.)
4. The p-value = (Please show your answer to 4 decimal places.)
5. The p-value is ?≤> αα
6. Based on this, we should Select an answerfail to rejectrejectaccept the null hypothesis.
7. Thus, the final conclusion is that ...
   • The results are statistically insignificant at αα = 0.10, so there is statistically significant evidence to conclude that the population mean amount of money that Presbyterians donate is equal to the population mean amount of money that Catholics donate.
   • The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the mean donation for the 44 Presbyterians that were observed is more than the mean donation for the 58 Catholics that were observed.
   • The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the population mean amount of money that Presbyterians donate is more than the population mean amount of money that Catholics donate.
   • The results are statistically insignificant at αα = 0.10, so there is insufficient evidence to conclude that the population mean amount of money that Presbyterians donate is more than the population mean amount of money that Catholics donate.

For Exercise 1 through 7, do a complete regression analysis by performing the following steps.

a.Draw the scatter plot.

b.Compute the value of the correlation coefficient.

c.Test the significance of the correlation coefficient at α = 0.01, using Table I or use the P-value method.

d.Determine the regression line equation if r is significant.

e.Plot the regression line on the scatter plot, if appropriate.

f.Predict y′ for a specific value of x, if appropriate.

3.Puppy Cuteness and Cost A researcher feels that a pet store bases the cost of puppies on the cuteness of the animals. Eight puppies were rated on their cuteness. The ratings were from 1 to 6, with 6 being the highest rating. The ratings and the cost in dollars of the puppies are shown. Is there a significant relationship between the variables? Please do by hand and show work.

Answer: 3.H₀: p = 0; H₁: ρ ≠ 0; r = 0.761; C.V. = ±0.834; d.f. = 6; do not reject. There is not a significant linear relationship between the rating and the cost. No regression analysis should be done. P = 0.0284

Recall that for a random variable to be a binomial random variable, you must have an experiment which meets the following three criteria:
1: There are exactly two outcomes for each trial.
2: There are a fixed number (n) of trials.
3: The trials are independent, and there is a fixed probability of success (p) and failure (q) for each trial.

For each of the two situations described below, please indicate if the variable X (as defined in each situation) can be considered a binomial random variable. If you think that X is a binomial variable, please explain how the situation specifically meets each of the three criteria, and identify the values of n and p. If you think X cannot be considered a binomial variable, please indicate which of the three criteria is/are not met (indicate all that apply), and provide a brief explanation for your choice(s). Hint: X can be considered a binomial random variable in only one of the two situations below, but I am not telling you which one, obviously.

Situation 1: A fair coin is tossed over and over again. Let X = the number of tosses until the third TAILS appears.

Situation 2: A box contains 10 marbles: 4 are red, 3 are white, and 3 are blue. A marble is randomly selected, returned to the box, then another marble is randomly selected. Let X = the number of red marbles selected in the two consecutive trials.

A consumer group conducted a study of SUV owners to estimate the mean highway mileage for their vehicles. A simple random sample of 91 SUV owners was selected, and the owners were asked to report their highway mileage. The following results were summarized from the sample data.

Sample Mean = 21.3 mpg

Standard Deviation = 6.3 mpg

Based on these sample data, compute and interpret a 90% confidence interval estimate for mean the highway mileage for SUVs.

The commercial for the new Meat Man Barbecue claims that it takes 20 minutes for assembly. A consumer advocate thinks that the assembly time is lower than 20 minutes. The advocate surveyed 11 randomly selected people who purchased the Meat Man Barbecue and found that their average time was 19.7 minutes. The standard deviation for this survey group was 2.1 minutes. What can be concluded at the the αα = 0.05 level of significance level of significance?

1. For this study, we should use Select an answert-test for a population meanz-test for a population proportion
2. The null and alternative hypotheses would be:

H0:H0:   ?pμ ?≠=<>   

H1:H1:   ?pμ ?<≠=>

3. The test statistic ?zt = (please show your answer to 3 decimal places.)
4. The p-value = (Please show your answer to 4 decimal places.)
5. The p-value is ?>≤ αα
6. Based on this, we should Select an answerfail to rejectrejectaccept the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest the populaton mean is significantly lower than 20 at αα = 0.05, so there is statistically significant evidence to conclude that the population mean amount of time to assemble the Meat Man barbecue is lower than 20.
   • The data suggest the population mean is not significantly lower than 20 at αα = 0.05, so there is statistically insignificant evidence to conclude that the population mean amount of time to assemble the Meat Man barbecue is equal to 20.
   • The data suggest that the population mean amount of time to assemble the Meat Man barbecue is not significantly lower than 20 at αα = 0.05, so there is statistically insignificant evidence to conclude that the population mean amount of time to assemble the Meat Man barbecue is lower than 20.

6. Paired annual rates of return data are collected from 8 randomly selected investment funds before and after The Federal Reserve cuts down interest rates. The dataset and relevant summery results are given in the table below. Suppose you are a financial analyst interested in finding out whether investment funds’ mean rate of return is significantly different before and after the interest rate adjustment.

The ALTURNATIVE hypothesis of this test is ________________________________________.

The significance level for this test should be chosen to be _______________________.

The numerical formula calculating test statistic is __________________________________________.

The test statistic is calculated to be_________________________.

The p-value is ___________________________.

Based on the p-value we _________________, (accept or reject H0)

In New York State, savings banks are permitted to sell a form of life insurance called savings bank life insurance (SBLI). The approval process consists of underwriting, which includes a review of the application, a medical information bureau check, possible requests for additional medical information and medical exams, and a policy compilation stage in which the policy pages are generated and sent to the bank for delivery. The ability to deliver approved policies to customers in a timely manner is critical to the profitability of this service to the bank. During a period of one month, a random sample of 27 approved policies was selected, and the total processing time, in days, was as shown below and stored in the file INSURANCE:

73 19 16 64 28 28 31 90 60 56 31 56 22 18

45 48 17 17 17 91 92 63 50 51 69 16 17

a. Construct and interpret a 95% confidence interval estimate of the population mean processing time. Use Minitab. (Don't worry about this one.)

b. What assumption must you make about the population distribution in order to construct the confidence interval in (a)?

c. Do you think that the assumption needed in order to construct the confidence interval estimate in (a) is valid? Explain.