what is the difference between mutually exclusive, independent and conditional probabilities?

Part 1. Suppose you are told that a 95% confidence interval for the average price of a gallon of regular gasoline in your state is from $2.99 to $3.99. Use the fact that the confidence interval for the mean is in the form x − E to x + E to compute the sample mean and the maximal margin of error E. (Round your answers to two decimal places.)

Part 2. Anystate Auto Insurance Company took a random sample of 380 insurance claims paid out during a 1-year period. The average claim paid was $1510. Assume σ = $254.

Find a 0.90 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

Lower Limit

Upper limit

Find a 0.99 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

Lower Limit

Upper limit

Anystate Auto Insurance Company took a random sample of 364 insurance claims paid out during a 1-year period. The average claim paid was $1525. Assume σ = $258.

Find a 0.90 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

Find a 0.99 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

The normal monthly precipitation (in inches) for September is listed for 20 different U.S. Cities.

3.5       1.6       2.4       3.7       4.1       3.9       1.0       3.6       4.2       3.4       3.7       2.2       1.5       4.2 3.4       2.7       0.4       3.7       2.0       3.6

Find

Mean of the data

Median of the data

Range of the data

Interquartile range of the data.   

A political scientist hypothesize that a political ad will increase attitudes about a particular issue. The scientist randomly asks 21 individuals walking by to see the ad and then take a quiz on the issue. The general public that knows little to nothing about the issue, on average, scores 50 on the quiz. The individuals that saw the ad scored an average of 51.8 with a variance of 29.05. What can the political scientist conclude with α = 0.05?

a) What is the appropriate test statistic?
---Select--- na z-test one-sample t-test independent-samples t-test related-samples t-test

b)
Population:
---Select--- the particular issue the political ad individuals walking by general public the ad
Sample:
---Select--- the particular issue the political ad individuals walking by general public the ad

c) Compute the appropriate test statistic(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
critical value =  ; test statistic =
Decision:  ---Select--- Reject H0 Fail to reject H0

d) If appropriate, compute the CI. If not appropriate, input "na" for both spaces below.
[  ,  ]

e) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
d =  ;   ---Select--- na trivial effect small effect medium effect large effect
r² =  ;   ---Select--- na trivial effect small effect medium effect large effect

f) Make an interpretation based on the results.

Individuals that watched the political ad scored significantly higher on the quiz than the general public

.Individuals that watched the political ad scored significantly lower on the quiz than the general public.    

Individuals that watched the political ad did not score significantly different on the quiz than the general public.

Consider that you toss a fair 6-sided die containing the numbers 1-2-3-4-5-6 and also toss a fair 4-sided die containing the numbers 1-2-3-4. Find the probability distribution for the sum of the values on the two dice. Also, find the mean and the variance of this probability distribution.

Please provide a well written and well explained answer.

James Madison, president of Madison Manufacturing, inc,. is considering whether to build more manufacturing plants in Madison Wisconsin. He is considering three sizes of plant: Small, Medium, or Large. At the same time, an uncertain economy makes ascertaining the demand for the new plants difficult. His management team has prepared the following cost payoff table (in thousands of dollars).

Decision Alternatives States of Nature

Good Economy Fair Economy Poor Economy Expected Value

Small plant d1 $650 $650 $600 ?

Medium plant d2 $900 $600 $300 ?

Large plant d3 $800 $650 $500 ?

Probability Factor 40% 35% 25% ?

Best decision Alternative= ?

1. Calculate the expected value for each decision alternative using Expected Value Strategy in Excel Spread Sheet.

2. Specify the best decision alternative to minimize cost.

Consider an automated plagiarism detection software that is used to evaluate essay submissions. Four sections of a writing course use the software to check for plagarism, with 30% of the students in section 1, 16% in section 2, 30% in section 3, and 24% in section 4. In section 1 of a course, 20% of the essays are flagged, in section 2, 23%, section 3, 15% and section 4, 8%. (a) What percentage of total students committed plagiarism overall? (b) Given that a particular student committed plagiarism, what in the probability that they were registered for section 1 of the course. (c) Given that a particular student committed plagiarism, what in the probability that they were registered for section 2 of the course. (d) If there are 200 students registered between these 4 sections, how many students in section 3 cheated?

For mallard ducks and Canada geese, what percentage of nests are successful (at least one offspring survives)? Studies in Montana, Illinois, Wyoming, Utah, and California give the following percentages of successful nests (Reference: The Wildlife Society Press, Washington, D.C.). x: Percentage success for mallard duck nests 11 23 44 53 65 y: Percentage success for Canada goose nests 39 15 48 15 39 (a) Use a calculator to verify that Σx = 196; Σx2 = 9,620; Σy = 156; and Σy2 = 5,796. Σx Σx2 Σy Σy2 (b) Use the results of part (a) to compute the sample mean, variance, and standard deviation for x, the percent of successful mallard nests. (Round your answers to two decimal places.) x s2 s (c) Use the results of part (a) to compute the sample mean, variance, and standard deviation for y, the percent of successful Canada goose nests. (Round your answers to two decimal places.) y s2 s (d) Use the results of parts (b) and (c) to compute the coefficient of variation for successful mallard nests and Canada goose nests. (Round your answers to one decimal place.) x y CV % % Write a brief explanation of the meaning of these numbers. What do these results say about the nesting success rates for mallards compared to Canada geese? The CV is the ratio of the standard deviation to the mean; the CV for Canada goose nests is higher. The CV is the ratio of the standard deviation to the mean; the CV for Canada goose nests is equal to the CV for mallard nests. The CV is the ratio of the standard deviation to the mean; the CV for mallard nests is higher. The CV is the ratio of the standard deviation to the variance; the CV for Canada goose nests is higher. The CV is the ratio of the standard deviation to the variance; the CV for Canada goose nests is equal to the CV for mallard nests. The CV is the ratio of the standard deviation to the variance; the CV for mallard nests is higher. Would you say one group of data is more or less consistent than the other? Explain. The x data group is more consistent because the standard deviation is smaller. The two groups are equally consistent because the standard deviations are equal. The y data group is more consistent because the standard deviation is smaller.

Bob reported that the patients suffering from the “Mad Man Disease” who used his “magic dust” elixir properly resulted in an odds-ratio = .6 relative to controls who did not use his elixir, whose probability of suffering from the “Mad Man Disease” was only p = .3.

(a) Describe the meaning of the odds-ratio for elixir users in words.

(b) What was the probability of suffering from the “Mad Man Disease” for the elixir group?

Given the following numbers:   25 16 61 18 15 20 15 20 24 17 19 28, derive the mean, median, mode, variance, standard deviation, skewness, kurtosis, range, minimum, maximum, sum, and count. Interpret your results. What is the empirical rule for two standard deviations of the data?

please do this as simple as you can!

if you flip a fair coin 10 times what is the probability of
a) getting all tails?
b) getting all heads
c) getting atleast 1 tails

1.Time taken for oil change

It is known that the amount of time needed to change the oil on a car is normally distributed with a standard deviation of 5 minutes. The manager of a service shop recorded the amount of time (in minutes) to complete a random sample of 10 oil changes. They are listed below. 11 10 16 15 18 12 25 20 18 24

a. The sample average is: _______ minutes (up to 2 decimal points)

B.The sample standard deviation is: _______ minutes (up to 2 decimal points)

The following information applies to the next two questions:

Compute a 95% interval estimate of the population mean.

1. Lower Confidence Level ___ Minute (up to 2 decimal points)
2. Upper Confidence Level ___ Minutes (up to 2 decimal points)
3. Based on your answer above, if you take your car to this particular shop, your car will be serviced between  and minutes. You are  % certain about this.

4. Suppose that the manager feels that the range of values he obtained above are too wide to attract customers. What can he do to obtain a narrower range of values?

Use a 90% confidence interval

Take a random sample of 100 oil changes

Train his employees well so that the variability in time to change oil reduces

All the above

None of the above

5. A marketing researcher wants to estimate the mean amount spent ($) on Amazon.com by Amazon Prime member shoppers. A random sample of 100 Amazon Prime member shoppers who recently made a purchase on Amazon.com yielded a mean of $1,500 and a standard deviation of $200.

Construct a 90% Confidence Interval estimate for the mean spending for all Amazon Prime shoppers.

What is the Lower Confidence Level $______

What is the Upper Confidence Level $______

8. Based on the above calculation, which one of the following statements is correct

We are 90% confident that an Amazon Prime Member spends $1500

We are 90% confident that an Amazon Prime Member spends between $1467.10 and $1532.90

Both of the above statements are true

An Amazon Prime member spends between $1467.10 and $1532.90

9. The researcher is not happy with the estimate, and she wants tighter interval, i.e., a smaller level of error. If she wants the estimate to be within ±$25 with 90% confidence, what sample size does she need?

Sample size _____ (report the next whole number, 100.2 should be reported as 101)

10. The salaries of graduates from the MBA program of a Big Ten school are NOT normally distributed. In order to get a better understanding of the range of salaries made by the graduates, the marketing director compiles a five-year record of salaries offered to students at campus recruitment events. He randomly selects groups of 120 students graduating in Fall, Summer, and Spring for the past five years (i.e., 15 groups, each with 120 students).

According to the Central Limit Theorem, the salaries within any of these 15 groups will be distributed normally. True or False?

According to the Central Limit Theorem, the average salaries of these 15 groups will be distributed normally. True or False