You should explain the confidence intervals you create along with explanations of the meaning of your answers and business implications for each problem.

Scenario:

You have been asked once again to study the mean tuition at private universities throughout the United States. You will also again study the proportions of universities throughout the United States that regularly award more than 50% of their students some form of financial aid. The specific questions you will be asked to answer are stated below. In addition, appropriate sample data for the studies you will be accomplishing is given below. Answer the following questions concerning the situations posed.

2.) Once again, as has happened in the past, you are very much in doubt concerning the validity of the known population standard deviations in the tuitions charged by private universities. Therefore, you wish to conduct your study with the knowledge that the population standard deviations are unknown. These unknown population standard deviations will be estimated using sample standard deviations. You collect random samples of the tuitions at private universities east and west of the Mississippi River. The data that has been collected is shown in appendix one. At both the 5% and 10% levels of significance, are there any differences in the mean tuition rates at private universities east and west of the Mississippi River? Based upon the procedure you use to compare the means in this problem, once again, if the software allows for it, find 95% and 90% confidence intervals for the difference in the mean tuition rates for universities both east and west of the Mississippi River. Explain their meanings in the context of the problem. As you did in the previous problem, of the procedure allows for it, use these intervals to confirm the results of the hypothesis tests in the problem. Use the 95% confidence interval to confirm the results at which you arrived at the 5% level of significance and use the 90% confidence interval to confirm the results at which you arrived at the 10% level of significance.

Appendix One (Tuition)

East of the Mississippi River:

$21,165 $20,435 $29,110 $11,890 $19,500 $21,450

$22,250 $18,450 $22,225 $21,550 $19,990 $18,255

$23,350 $24,110 $20,000 $21,340 $22,500 $23,185

$19,080 $24,320 $17,850 $19,990 $16,760 $12,460

$18,150

West of the Mississippi River:

$17,740 $13,000 $19,550 $18,450 $15,050 $18,600

$18,000 $17,500 $16,900 $21,000 $19,990 $14,520

$18,400 $15,000 $19,750 $17,450 $15,575 $13,260

$12,375 $19,750 $15,560 $17,880 $13,450 $16,660

$20,000

1.)In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 51 and a standard deviation of 4. Using the empirical rule (as presented in the book), what is the approximate percentage of daily phone calls numbering between 43 and 59?

2.)A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 38 months and a standard deviation of 3 months. Using the empirical rule (as presented in the book), what is the approximate percentage of cars that remain in service between 41 and 47 months?

3.)he physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 60 and a standard deviation of 8. Using the 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 52 and 60?

The probability of finding a seafood restaurant in a small beach town is 37/100. You decide to look in 15 different small beach towns for a seafood restaurant.

What are the potential outcomes of finding seafood restaurants in each town?

What are the potential outcomes of finding seafood restaurants in 5 or fewer towns?

What are the potential outcomes of finding seafood restaurants in 10 of the towns?

Please explain the calculations and reasoning.

A random sample of the price of gasoline from 30 gas stations in a region gives the statistics below. Complete parts​ a) through​ c).

y=$3.29 s=$0.27

A. Find a 95​% confidence interval for the mean price of regular gasoline in that region. ($__,$__)

B. Find a 90​% confidence interval for the mean price of regular gasoline in that region. ($__,$__)

C. If we had the same statistics from a sample of 80 ​stations, what would the​ 95% confidence interval be​ now?

Find the Z value form both Skewness and Kurtosis, respectively. Then decide on normality based on 5% significance level

Kurtosis -0.58587 Skewness -0.13581, N=100

Lafayette Public School System has three high schools to serve a district divided into five areas. The capacity of each high school, the student population in each area, and the distance (in miles) between each school and the center of each area are listed in the table below:

(Part a - 8 points) Formulate and list the linear program for the above problem to minimize the total student-miles traveled per day. You do NOT need to solve your listed linear program.  

(Part b - 2 points) If Capedot High School will be closed to conserve the school system’s resources and its budget, how will you efficiently revise your linear program to cope with this school closing?

Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.80. a) Compute a 95% CI for the true average porosity of a certain seam if the average porosity for 15 specimens from the seam was 4.85. (Round your answers to two decimal places.) (b) Compute a 98% CI for true average porosity of another seam based on 17 specimens with a sample average porosity of 4.56. (Round your answers to two decimal places.) (c) How large a sample size is necessary if the width of the 95% interval is to be 0.39? (Round your answer up to the nearest whole number.) specimens d) What sample size is necessary to estimate true average porosity to within 0.24 with 99% confidence? (Round your answer up to the nearest whole number.)

According to an international aviation firm, fatal accidents occur in just around one in every five million flights. With about 100,000 flights per 24 hour day worldwide, this means fatal accidents happen at a rate of 1 per 50 days. This translates to an average of 0.6 accidents per month. Assume that the number of fatal air accidents worldwide follows a Poisson distribution with l=0.6 per month.

1. Compute the probability that no fatal air accident will happen anywhere in the world during the month of March, 2020.
2. Compute the probability that more than 3 fatal air accidents happen in a calendar month.
3. Assume that fatal air accidents happen independent of one-another. Compute the probability that no fatal air accidents will happen anywhere in the world between March 1 and May 31, 2020.
4. In the year 2018, 13 fatal air accidents were recorded. Was the year 2018 an outlier with respect to fatal air accidents? Compute the probability that a year would have 13 fatal air accidents. Note that your need to convert the monthly Poisson rate of 0.6 accidents to a yearly rate.

When a poultry farmer uses his regular feed, the newborn chickens have normally distributed weights with a mean of 62.7 oz. In an experiment with an enriched feed mixture, ten chickens are born with the following weights (in ounces). 64.9, 64.6, 65, 66.6, 64.9, 67.8, 65.9, 67.5, 61.9, 65.4 Use the α=0.05 significance level to test the claim that the mean weight is higher with the enriched feed. (a) The sample mean is x⎯⎯⎯= (b) The sample standard deviation is s= (c) The test statistic is t= (d) The critical value is t∗= (e) The conclusion is

The distribution of hemoglobin in grams per deciliter of blood is approximately N(14,1)N(14,1) in women and approximately N(16,1)N(16,1) in men.

Use software or Table B to find the answers.

(a) What percent of women have more hemoglobin than the men's mean hemoglobin? Give your answer to two decimal places.

Percent of women:

%

(b) What percent of men have less hemoglobin than the women's mean hemoglobin? Give your answer to two decimal places.

Percent of men:

%

(c) What percent of men have more hemoglobin than the women's mean hemoglobin? Give your answer to two decimal places.

Percent of men:

%

Please use ONLY one Excel file to complete case study one, and use one spreadsheet for each problem. No credit will be granted for problems that are not completed using Excel.

In 2011, when the Gallup organization polled investors, 32% rated gold the best long-term investment. But in April of 2013 Gallup surveyed a random sample of U.S. adults. Respondents were asked to select the best long-term investment from a list of possibilities. Only 168 of the 650 respondents chose gold as the best long-term investment. By contrast, only 83 chose bonds.

1. Compute the standard error for each sample proportion. Compute and describe a 99% confidence interval in the context of the question.
2. Do you think opinions about the value of gold as a long-term investment have really changed from the old 32% favorability rate, or do you think this is just sample variability? Explain.
3. Suppose we want to keep the margin of error at 4%, and we still want to construct a 99% confidence interval. What is the necessary sample size?
4. Based on the sample size obtained in part c, suppose 306 respondents chose gold as the best long-term investment. Compute the standard error for choosing gold as the best long-term investment. Compute and describe a 99% confidence interval in the context of the question.
5. Based on the results of part d, do you think opinions about the value of gold as a long-term investment have really changed from the old 32% favorability rate, or do you think this is just sample variability? Explain.

You enter Chicago subway by swiping your CTA card at a turnstile, you pay $3.75. The evasion fine( for being caught riding the subway without swiping your card) is $200. suppose that the CTA police catches only 1 in 20 people that ride the subway without swiping their card. Use the expected value of a random variable to decide whether, over a long period of time, it is cheaper to swipe your card at the turnstile or not.

Hint: Consider the random variable Y which is the amount you pay when you ride the subway without swiping your card at the turnstile.

The following data on price ($) and the overall score for 6 stereo headphones that were tested by Consumer Reports were as follows.

a. Does the t test indicate a significant relationship between price and the overall score?

The test t-Conclusion at α = .05

t = (to 2 decimal places.)

p-value is -

What is your conclusion? Use α = .05.
- Select your answer -There is a significant relationship between price and overall scoreThere is no significant relationship between price and overall scoreItem 3 .

b. Test for a significant relationship using the F test.
p-value is - Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .1greater than .1Item 4

What is your conclusion? Use α = .05.

Because p-value is - -greater than or equal toless than or equal toequal toItem 5 .05, we - Select your answer 6 H₀: β₁ is - Select your answer -greater than or equal to zeroless than or equal to zeroequal to zeroItem 7 .

c. Show the ANOVA table for these data. Round your answers to three decimal places, if necessary.

53. A simple random sample experiment is repeated four times choosing the same sample size each time. Which of the following statements can be made about the different outcomes?

A) The samples will usually be different from one another.

B) The samples will always be the same.

C) Measurements calculated from the samples will always be different.

D) The samples will always be different from one another.

E) Measurements calculated from the samples will always be the same.

Given two independent random samples with the following results:

n1=586......n2=404

x1=161.....x2=68

Can it be concluded that there is a difference between the two population proportions? Use a significance level of α=0.05 for the test.

Step 1 of 6: State the null and alternative hypotheses for the test.

Step 2 of 6: Find the values of the two sample proportions, pˆ1 and pˆ2. Round your answers to three decimal places.

Step 3 of 6: Compute the weighted estimate of p, p‾‾. Round your answer to three decimal places.

Step 4 of 6: Compute the value of the test statistic. Round your answer to two decimal places

Step 5 of 6: Determine the decision rule for rejecting the null hypothesis H0H0. Round the numerical portion of your answer to two decimal places.

Reject H0 if...

Step 6 of 6: Make the decision for the hypothesis test.

reject null hypothesis...fail to reject null hypothesis