Assume that 80% of people are left-handed. If we select 5 people at random, find the probability of each outcome described below, rounded to four decimal places:

a. There are some lefties (≥ 1) among the 5 people.

b. There are exactly 3 lefties in the group.

c. There are at least 4 lefties in the group.

d. There are no more than 2 lefties in the group

. e. How many lefties do you expect?

f. With what standard deviation?

1. Major television networks have never seemed to have issues showing commercials for beer and other alcoholic beverages. Even though adult viewers tend to enjoy the commercials, most adults seem to think that the commercials target teenagers and young adults (those under 21 years old). To study this belief, the networks conducted a joint poll of viewers and asked them if they felt that beer and other alcoholic beverage commercials targeted teenagers and young adults. The results of the survey are as follows

a. Are the sample sizes large enough such that inferences about the differences between two population proportion can be made? If so, calculate a 99% confidence interval for the difference in the proportions of those older than 30 and those 30 or younger that believe alcoholic beverage commercials targeted teenagers and young adults. Interpret the interval.

b. Based on the data, can the networks conclude that the percentage of viewers who believe beer and alcoholic beverage commercials target teenagers and young adults is significantly higher in the over 30 age group than in the 30 or younger age group? Construct the 10 steps of hypothesis testing using α = 0.01 to answer the question.

Step 1 (Define the hypotheses to be tested in plain English)

Step 2 (Select the appropriate statistical measure, such as the population mean, proportion, or
              variance.)

Step 3 (Determine whether the alternative hypothesis should be one-sided or two-sided.)

Step 4 (State the hypotheses using the statistical measure found in Step 2)

Step 5 (Specify α, the level of the test.)

Step 6 (Select the appropriate test statistic based on the information at hand and the
              assumptions you willing to make.)

Step 7 (Determine the critical value of the test statistic.)

Step 8 (Collect sample data and compute the value of the test statistic.)

Step 9 (Make the decision.)

Step 10 (State the conclusion in terms of the original question.)

For a study, 375 patients were randomly assigned tor eceive a daily dose of levvofloxacin, and 363 were given placebo. In the group receiving treatment, fever was present in 243 patients for the duration of neutroenia, whereas feverw as experienced by 308 patients in the placebo group. Using this information, determine whether or not the proportion of patients with fever differed between the two groups at the 1% level of significance. State the null and alternative hypothesis, manually calculate the test statistic and determine its p-value. Then state your decision and conclusion.

A doctor wants to estimate the mean HDL cholesterol of all​ 20- to​ 29-year-old females. How many subjects are needed to estimate the mean HDL cholesterol within 4 points with 99 % confidence assuming s equals 13.9 based on earlier​ studies? Suppose the doctor would be content with 90 % confidence. How does the decrease in confidence affect the sample size​ required? A​ 99% confidence level requires nothing subjects. ​(Round up to the nearest​ subject.) A 90 % confidence level requires nothing subjects. ​(Round up to the nearest​ subject.)

99 % confidence is

90 confidence is

How does the decrease in confidence affect the sample size​ required?

A. Decreasing the confidence level increases the sample size needed.

B. Decreasing the confidence level decreases the sample size needed.

C. The sample size is the same for all levels of confidence.

Consider a binomial experiment with 16 trials and probability 0.60 of success on a single trial.

(a) Use the binomial distribution to find the probability of exactly 10 successes.

(b) Use the normal distribution to approximate the probability of exactly 10 successes.

(c) Compare the results of parts (a) and (b).

Group 1: 4.2, 4.2, 3.4

Group 2: 4.5, 2.1, 2.3

Group 3: 1.2, 0.3, -0.3, 2.3

Use the Bonferronni method to test each of the 3 possible hypotheses at the 3% significance level.

(a) Find the value of the test statistic for each of the 3 possible hypotheses.

(b) Which pairs of means are significantly different (using the Bonferronni method at the 3% significance level?

M&M'S MILK CHOCOLATE: 24% cyan blue, 20% orange, 16% green, 14% bright yellow, 13% red, 13% brown.

Confidence Interval for Small n

Choose the color of M&M’s you will be working with for this project

Color:

Using the collected data below from a single fun-sized bag, provide the frequency and proportion of M&M’s in your color of choice.

Number of M&M's in your color:

Total number of M&M's:

            Proportion of M&M's in your color:

Construct a 95% confidence interval for the proportion of M&M’s one can expect to find in the color of your choice.

Check the requirements for constructing a confidence interval for the proportion are satisfied. Show your work.

The conditions might not be satisfied, depending on how many candies were in your bag. If the conditions are not met, what could you do?

Part 2: Confidence Interval for Larger n

Now, use the data collected below from a collection of fun-sized bags to provide the frequency and proportion of M&M’s in your original color of choice.

Number of M&M's in your color:

Total number of M&M's:

Proportion of M&M's in your color:

Construct a 95% confidence interval for the proportion of M&M’s one can expect to find in the color of your choice.

Write an interpretation of your confidence interval specific to your color.

Check the requirements for constructing a confidence interval for the proportion are satisfied. Show your work. (See the note in the blue box on page 426)

How are confidence intervals affected by sample size?

How does the margin of error for the confidence interval in Part 1 compare to the margin of error for your confidence interval in Part 2? (compute both and compare)

Does the confidence interval you constructed in Part 2 contain the claimed proportion given by Mars Inc?

Do you believe the claims given by Mars Inc?

The following is a payoff table giving profits for various situations.

States of Nature Alternatives A B C D

Alternative 1 120 140 170 160

Alternative 2 210 130 140 120

Alternative 3 120 140 110 190

Do Nothing 0 0 0 0

a. What decision would a pessimist make?

b. What decision would an optimist make?

c. What decision would be made based on the realism criterion, where the coefficient of realism is 0.60?

d. What decision would be made based on the equally likely criterion?

e. What decision would be made based on the minimax regret criterion? Suppose now that the probabilities of the 4 states of nature are known, that is, the probability to observe A is 30%, the probability to observe B is 35%, the probability to observe C is 20%, and the probability to observe D is 15%. Answer the following

f. What decision would be made based on the expected monetary value?

g. What is the EVPI

1) Let X be a continuous random variable. What is true about fX(x)fX(x)?
fX(2) is a probability.
fX(2) is a set.
It can only take values between 0 and 1 as input.
fX(2) is a number.

2) Let X be a continuous random variable. What is true about FX(x)FX(x)?
FX(x) is a strictly increasing function.
It decreases to zero as x→∞x→∞.
FX(2) is a probability.
FX(x) can be any real number.

Engineers concerned about a tower's stability have done extensive studies of its increasing tilt. Measurements of the lean of the tower over time provide much useful information. The following table gives measurements for the years 1975 to 1987. The variable "lean" represents the difference between where a point on the tower would be if the tower were straight and where it actually is. The data are coded as tenths of a millimeter in excess of 2.9 meters, so that the 1975 lean, which was 2.9646 meters, appears in the table as 646. Only the last two digits of the year were entered into the computer.

(a) Plot the data. Consider whether or not the trend in lean over time appears to be linear. (Do this on paper. Your instructor may ask you to turn in this graph.)

(b) What is the equation of the least-squares line? (Round your answers to three decimal places.)
y =  +  x

What percent of the variation in lean is explained by this line? (Round your answer to one decimal place.)
%

(c) Give a 99% confidence interval for the average rate of change (tenths of a millimeter per year) of the lean. (Round your answers to two decimal places.)
( , )

Use technology and the given confidence level and sample data to find the confidence interval for the population mean μ. Assume that the population does not exhibit a normal distribution. Weight lost on a diet: 99% confidence n=41 x overbar =4.0 kg s=6.9 kg What is the confidence interval for the population mean μ? ___ kg<μ<___ kg (Round to one decimal place as needed.) Is the confidence interval affected by the fact that the data appear to be from a population that is not normally distributed? A. No, because the population resembles a normal distribution. B. No, because the sample size is large enough. C. Yes, because the population does not exhibit a normal distribution. D. Yes, because the sample size is not large enough.

Scores on a certain IQ test are known to have a mean of 100. A random sample of 60 students attend a series of coaching classes before taking the test. Let m be the population mean IQ score that would occur if every student took the coaching classes. The classes are successful if m > 100. A test is made of the hypotheses H0: m = 100 vs H1: m > 100.

Consider three possible conclusions:

The classes are successful.

The classes are not successful.

The classes might not be successful.

Answer the following questions:

1.Which of the three conclusions is best if H0 is rejected?

2.Which of the three conclusions is best if H0 is not rejected?

3.Assume that the classes are successful but the conclusion is reached that the classes might not be successful. Which type of error is this?

4.Assume that the classes are not successful. Is it possible to make a Type I error? Explain.

5.Assume that the classes are not successful. Is it possible to make a Type II error? Explain.

I have draw a random sample of 20 of my neighbors. I ask them their income (What can I say? I'm a nosy neighbor). My sample average (x bar) is $41,000. I want to create a 95% confidence interval around x bar.

My estimated standard deviation is $5,000.

What is the 95% confidence internal for the average income in my neighborhood? $38,652 to $43.347, $38,663 to $43,336, $38,809 to $43,191, or not enough information?

What are ALL the possible difficulties with with fitting linear regression? Please explain the reasoning.