2. We are interested in analyzing data related to the Olympics from one decade. We are looking at individuals and if they participated in the summer or winter Olympics and whether or not they won a medal. Use S to denote summer and M to denote if a medal was won. The probability that someone participated in the summer Olympics is 72%. The probability that they won a medal is 13%. The probability that they won a medal and it was in the summer Olympics is 10%. ( please show steps)

a. What percentage of people participated in the summer Olympics or won a medal?

b. What percentage of people participated in the winter Olympics?

c. Given someone won a medal, what is the probability that they participated in the summer Olympics?

d. What percentage of people did NOT participate in the summer games NOR won a medal?

e. Are M and S mutually exclusive events? Why or why not? f. Are M and S independent events? Explain, using probabilities.

g. If we know someone participated in the summer Olympics, what is the probability that they also won a medal?

A) Find the upper limit for the mean at the 90% confidence level.

B) Find the lower limit for the mean at the 90% confidence level.

C) Find the width of the confidence interval at the 90% confidence level.

D) Find the score from the appropriate probability table (standard normal distribution, t distribution, chi-square) to construct a 99% confidence interval.

If you use Excel, please list what Excel functions would allow me to get this answers for future reference

Question 1:

Eight measurements were made on the inside diameter of forged piston rings used in an automobile engine. The data (in millimeters) are 74.001, 74.003, 74.015, 74.000, 74.005, 74.002, 74.005, and 74.004.

1. Compute the sample mean and sample standard deviation of the temperature data.
2. Graph a histogram of the data.
3. Graph a normal probability plot of the data.
4. Comment on the data.

Question 2:

The April 22, 1991 issue of Aviation Week and Space Technology reports that during Operation Desert Storm, U.S. Airforce F-117A pilots flew 1270 combat sorties for a total of 6905 hours. What is the mean duration of an F-117A mission during this operation? Why is the parameter you have calculated a population mean?

14.- A sociologist asserts that only 5% of all seniors in high school, capable of performing work at the university level, actually attend university. Find the probabilities that among 180 students capable of performing work at university level:
a) exactly 10 attend college using the binomial
b) Using the normal distribution
c) at least 10 go to university using binomial T.I or excel
d) Using the normal distribution
e) when many eight go to university using binomial or excel
f) Using the normal distribution

The mean of a population is 77 and the standard deviation is 12. The shape of the population is unknown. Determine the probability of each of the following occurring from this population. a. A random sample of size 35 yielding a sample mean of 81 or more

b. A random sample of size 150 yielding a sample mean of between 76 and 80

c. A random sample of size 221 yielding a sample mean of less than 77.2

(Round all the values of z to 2 decimal places and final answers to 4 decimal places.)

A laboratory tested 12 chicken eggs and found that the mean amount of cholesterol was 183 milligrams with s=12.7. Construct a 95% confidence interval for the true mean cholesterol content of all such eggs and demonstrate two methods for finding margin of error.

A random sample of 121 observations produced a sample proportion of 0.4. An approximate 95% confidence interval for the population proportion p is between

Use the population of ages {56, 49, 58, 46} of the four U.S. presidents (Lincoln, Garfield, McKinley, Kennedy) when they were assassinated in office. Assume that random samples of size n = 2 are selected with replacement.

1. List the 16 different samples. For example, the samples for age 56 would be

56, 56

56, 49

56, 58

56, 46.

2. After listing all 16 samples, find the mean of each sample, then construct a table representing the sampling distribution of the sample mean. In the table, combine values of the sample mean that are the same.

3. Compare the mean of the population {56, 49, 58, 46} to the mean of the sampling distribution of the sample mean.

4. Do the sample means target the value of the population mean? In general, do sample means make good estimators of population means? Why or why not?

1) The PDF of a Gaussian random variable is given by fx(x).

fx(x)= (1/(3*sqrt(2pi) )*e^((x-4)^2)/18

determine

a.) P(X > 4) b). P(X > 0). c). P(X < -2).

2) The joint PDF of random variables X and Y is given by

fxy(x,y)=Ke^-(x+y), x>0 , y>0

Three resistors with resistances R₁, R₂, R₃ are connected in parallel across a battery with voltage V. By Ohm’s law, the current (amps) is

I = V* [ (1/R₁) + (1/R₂) + (1/R₃) ]

Assume that R₁, R₂, R_3, and V are independent random variables

where R₁ ~ Normal (m = 10 ohms, s = 1.5 ohm)

            R₂ ~ Normal (m = 15 ohms, s = 1.5 ohm)

            R₃ ~ Normal (m =20 ohms, s = 1.0 ohms)

            V ~ Normal (m = 120 volts, s = 2.0 volts

(a) Use Monte Carlo Simulation (10,000 random draws from each input random variable) to estimate the mean and standard deviation of the output variable current. (b) Assess whether the output variable current is normally distributed. (c) Assess whether the inverse of current squared (1/ I2 ) is normally distributed. (d) Estimate the probability that the current is less than 25 amps assuming that the inverse of current squared is normally distributed. (e) Compare your answer to (d) with your simulation results – how many of the 10,000 random results for current are below 25 amps via the Stat > Tables > Tally command?

A survey of 2645 consumers by DDB Needham Worldwide of Chicago for public relations agency Porter/Novelli showed that how a company handles a crisis when at fault is one of the top influences in consumer buying decisions,with 73% claiming it is an influence. Quality of product was the number one influence, with 96% of consumers stating that quality influences their buying decisions. How a company handles complaints was number two, with 85% of consumers reporting it as an influence in their buying decisions. Suppose a random sample of 1,100 consumers is taken and each is asked which of these three factors influence their buying decisions.

*a. What is the probability that more than 820 consumers claim that how a company handles a crisis when at fault is an influence in their buying decisions?
**b. What is the probability that fewer than 1,030 consumers claim that quality of product is an influence in their buying decisions?
*c. What is the probability that between 82% and 83% of consumers claim that how a company handles complaints is an influence in their buying decisions?

*(Round the values of z to 2 decimal places. Round the intermediate values to 4 decimal places. Round your answer to 4 decimal places.)
**(Round the values of z to 2 decimal places. Round the intermediate values to 4 decimal places. Round your answer to 5 decimal places.)

A political scientist is interested in the effectiveness of a political ad about a particular issue. The scientist randomly asks 14 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 51 on the quiz. The individuals that saw the ad scored an average of 45.79 with a variance of 26.01. What can the political scientist conclude with an α of 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--- general public the ad the particular issue individuals walking by the political ad
Sample:
---Select--- general public the ad the particular issue individuals walking by the political 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 or  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.

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

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

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

The contents of bottles of beer are Normally distributed with a mean of 300 ml and a standard deviation of 5 ml.

What is the value in which 90% of the six-packs will have a higher average content?

An exponential probability distribution has a mean equal to 6 minutes per customer. Calculate the following probabilities for the distribution. (PLEASE USE EXCEL FUNCTIONS TO CALCULATE)

A) P(X > 8)

B) P(X > 4)

C) P(6 less than or equal to X less than or equal to 16)

D) P(1 less than or equal to X less than or equal to 5)

The following descriptive statistics are calculated from SPSS. Use them to calculate the test statistic.

1. What is the calculated test statistic?

a) 1.228

b) 3.017

c) 3.249

d) 5.786

2. What is the correct conclusion?

a) Males are not significantly better than females at memory recall (p<.05)

b) Males are significantly better than females at memory recall (p<.05)

c) Males are not significantly better than females at memory recall (p>.05)

d) Males are significantly better than females at memory recall (p>.05)

3. What is the margin of error for calculating a 98% confidence interval for the difference of means?

a) 1.077

b) 2.215

c) 2.479

d) 2.670

4. What are the lower and upper bounds of the 98% confidence interval to estimate the differences of means?

a) 2.423 and 4.577

b) 1.285 and 5.715

c) 1.021 and 5.979

d) 0.830 and 6.170