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

Calculate the measures of forecast error using the naive (most recent value) method and the average of historical data (to 2 decimals).

A study was performed comparing the efficacy of a new pain reliever, Galproxidone, to several pain relievers commonly prescribed after orthopedic surgury. Patients were asked to rate their pain after taking each medication. The data is listed below. Perform an ANOVA to determine the relative efficacy of Galproxidone on pain relief compared to the other pain relievers. If differences exist, perform a Bonferoni post-hoc test to determine which pain relievers are different from Galproxidone. Interpret the final results in terms of relative efficacy of the pain relievers.

A local anime fan club surveyed its members regarding their viewing habits last weekend, and the following information was obtained: 37 members had watched an episode of Naruto, 47 had watched an episode of Death Note, 23 had watched both an episode of Naruto and an episode of Death Note, and 12 had watched neither Naruto nor Death Note. (Round your answers to three decimal places.) (a) What percent of the club members had watched Naruto or Death Note? % (b) What percent of the club members had watched only Naruto? % (c) What percent of the club members had watched only Death Note? %

A Chi-square test for goodness of fit is used to evaluate preferences for 8 different designs of a new automobile. With a sample of n = 500 the researcher obtained a Chi-square statistic of Chi² = 15.81. What is the correct statistical decision for this outcome (assume p <.05)?

• A. Reject the null hypothesis and conclude that there is no significant difference in preferences.

• B. Reject the null hypothesis and conclude that there is a significant difference in preferences.

• C. Fail to reject the null hypothesis and conclude that there is no significant difference in preferences.

• D. Fail to reject the null hypothesis and conclude that there is a significant difference in preferences.

Suppose the mean income of firms in the industry for a year is 55 million dollars with a standard deviation of 3 million dollars. If incomes for the industry are distributed normally, what is the probability that a randomly selected firm will earn less than 60 million dollars? Round your answer to four decimal places.

Test the hypothesis (at the .05 level of significance) that individuals who were bullied are more likely to bully others. Test the hypothesis (at the .05 level of significance) that individuals who were bullied committed more bullying than those who were not bullied

Explain the difference between convenience, non-probability, probability, stratified, clustered, and systematic samples.

Write a multi-paragraph response.

I just need each topic explained simply so I can understand and write the paragraphs

Part II: Linear Programming Model- Forbelt Corporation has a one-year contract to supply motors for all refrigerators produced by the Ice Age Corporation. Ice Age manufacturers the refrigerators at four locations around the country: Boston, Dallas, Los Angeles, and St. Paul. Plans call for the following number (in thousands) of refrigerators to be produced at each location: Boston 50 Dallas 70 Los Angeles 60 St. Paul 80 Forbelt’s three plants ae capable of producing the motors. The plans and production capacities (in thousands) are as follows: Denver 100 Atlanta 100 Chicago 150 Because of varying production and transportation costs, the profit that Forbelt earns on each lot of 1000 units depends on which plant produces the lot and which destination it was shipped to. Ship to: Produced At: Boston, Dallas, Los Angeles ,St. Paul Denver 7 , 11 . 8 13 Atlanta 20 17 . 12 10 Chicago 8 18 13 16 With profit maximization as a criterion, Forbelt’s management wants to determine how many motors should be produced at each plant and how many motors should be shipped form each plant to each destination. Find the optimal solution.

* I have the solution to the above problem, I need help with calculating profit (ex, when distribution changes)

Question 1: Refer to accompanying data set and use the 25 home voltage measurements to construct a frequency distribution with five classes. Begin with a lower class limit of 121.7 volts, and use a class width of 0.2 volt. Does the result appear to have a normal distribution? Why or why not?

Voltage Measurements from a Home   

Complete the frequency distribution below.

Answer: Fill in the blanks in voltage and frequency section.

Question 2: The data represents the daily rainfall (in inches) for one month. Construct a frequency distribution beginning with a lower level class limit of 0.00 and use a class width of 0.20. Does the frequency distribution appear to be roughly a normal distribution

Answer: Solve answer for frequency

Please show work

Suppose that in the certain country the proportion of people with red hair is 29%. Find the following probabilities if 37 people are randomly selected from the populattion of this country. Round all probabilities to four decimals.

(a) The probability that exactly 6 of the people have red hair

(b) The probability that at least 6 of the people have red hair

(c) Out of the sample of 37 people, it would be unusual to have more than people with red hair. Express your answer as a whole number.

Not sure about question f-j . looking to confirm my answers with someone

Health spending per person from a random sample of 20 countries is shown below.

1. Create a histogram by hand for the frequencies of the per capita health expenditure data.
2. What feature or features of this distribution indicate that the data are likely not from a population having a normal distribution?
3. What features of this distribution make it a good candidate to try a log transformation?
4. Calculate the natural log transformation for each data point of the sample. Create a new histogram with this transformed data, by hand.
5. What is the sample size?
6. What is the mean of the log health expenditure?
7. What is the standard deviation of the mean log health expenditure?
8. Calculate the standard error of the mean log health expenditure.
1. Calculate the 95% confidence interval for the mean log health expenditure and interpret it in full sentences.
10. What are the 95% confidence intervals on the non-log scale? Convert back the two values in your confidence interval.

(Data below) (to be done with EVIEWS or any data processor)

Millions of investors buy mutual funds, choosing from thousands of possibilities. Some funds can be purchased directly from banks or other financial institutions (direct) whereas others must be purchased through brokers (broker), who charge a fee for this service. A group of researchers randomly sampled 50 annual returns from mutual funds that can be acquired directly and 50 from mutual funds that are bought through brokers and recorded their net annual returns (NAR, %), which are the returns on investment after deducting all relevant fees.1

(a) In general, we can conduct hypothesis tests on a population central location with EViews by performing the (one sample) t-test, the sign test or the Wilcoxon signed ranks test.2 Suppose we would like to know whether there is evidence at the 5% level of significance that the population central location of NAR is larger than 5%. Which test(s) offered by EViews would be the most appropriate this time? Explain your answer by considering the conditions required by these tests.

(b) Perform the test you selected in part (e) above with EViews. Do not forget to specify the null and alternative hypotheses, to identify the test statistic, to make a statistical decision based on the p-value, and to draw an appropriate conclusion. If the test relies on normal approximation, also discuss whether this approximation is reasonable this time.

(c) Perform the other tests mentioned in part (a). Again, do not forget to specify the null and alternative hypotheses, to identify the test statistics, to make statistical decisions based on the p-values, and to draw appropriate conclusions. Also, if the tests rely on normal approximation, discuss whether these approximations are reasonable this time.

(d) Compare your answers in parts (b) and (c) to each other. Does it matter in this case whether the population of net returns is normally, or at least symmetrically distributed or not? Explain your answer.