Define 2 different measures of correlation of 2 data sets to each other.

List all basic distributions for which:

a) MLE is unbiased, but Method of Moments (MM) estimator is biased

b) MLE is biased, but MM estimator is unbiased

An industrial plant discharges water into a river. An environmental protection agency has studied the discharged water and found the lead concentration in the water (in micrograms per litre) has a normal distribution with population standard deviation σ = 0.7 μg/l. The industrial plant claims that the mean value of the lead concentration is 2.0 μg/l. However, the environmental protection agency took 10 water samples and found that the mean is 2.56 μg/l. A hypothesis test is carried out to determine whether the lead concentration population mean is higher than the industrial plant claims. (Use 1% level of significance). An appropriate test for this one population hypothesis problem is to use the _______.

A random sample of 20 observations results in 11 successes. [You may find it useful to reference the z table.]

a. Construct the an 90% confidence interval for the population proportion of successes. (Round intermediate calculations to at least 4 decimal places. Round "z" value and final answers to 3 decimal places.)  

Construct the an 90% confidence interval for the population proportion of failures. (Round intermediate calculations to at least 4 decimal places. Round "z" value and final answers to 3 decimal places.)

Many consumer groups feel that the U.S. Food and Drug Administration (FDA) drug approval process is too easy and, as a result, too many drugs are approved that are later found to be pushed for a more lenient approval process so that pharmaceutical companies can get new drugs approved more easily and quickly. Consider a null hypothesis that a new, unapproved drug is unsafe and an alternative hypothesis that a new, unapproved drug is safe.

1. Differentiate Type 1 and Type 2 errors.
2. Given the case scenario, explain the risks of committing a Type 1 or Type 2 error.
3. Which type of error are consumer groups trying to avoid?
4. Which type of error are industry lobbyists trying to avoid?

One state lottery game has contestants select 5 different numbers from 1 to 45. The prize, if all numbers are matched is 2 million dollars. The tickets are $2 each.

1) How many different ticket possibilities are there?

2) If a person purchases one ticket, what is the probability of winning? What is the probability of losing?

3) Occasionally, you will hear of a group of people going in together to purchase a large amount of tickets. Suppose a group of 30 purchases 6,000 tickets. a) How much would each person have to contribute? b) What is the probability of the group winning? Losing?

4) How much would it cost to “buy the lottery”, that is, buy a ticket to cover every possibility? Is it worth it?

5) Create a probability distribution table for the random variable x = the amount won/lost when purchasing one ticket.

6) In fair games, the expected value will be $0. This means that if the game is played many…many times, then one is expected to break even eventually. This is never true for Casino and Lottery games. Find the expected value of x = the amount won/lost when purchasing one ticket.

7) Interpret the expected value. See section 4.2 in the textbook for an example on how to interpret the expected value.

8) Fill in the following table using the expected value.

Please answer all questions! I will rate you!

QUESTION 5

From a sample of 500 college students it was found that 300 of them had taken a statistics course.

Construct a 95% confidence interval for the proportion of college students who have taken a statistics course. What is the LOWER BOUND on the interval? Round your answer to three decimal places (i.e. 0.123).

4 points   

QUESTION 6

From a sample of 500 college students it was found that 300 of them had taken a statistics course.

Construct a 95% confidence interval for the proportion of college students who have taken a statistics course. What is the UPPER BOUND on the interval? Round your answer to three decimal places (i.e. 0.123).

If I toss a fair coin 50,000 times which of the following is true?

a) the number of heads should be between 15,000 and 25,000.

b) the proportion of heads should be close to 50%.

c) the proportion of heads in these tosses is a parameter.

d) the number of heads should be exactly 25,000.

e) the proportion of heads will be close to 1.

When looking at statistics in criminal justice, how do you feel the mean, median, and mode are useful? Do you feel that there are times when one is more valuable than another? How can these be used to help deter crime?

Suppose you are working for a regional residential natural gas utility. For a sample of 95 customer visits, the staff time per reported gas leak has a mean of 219 minutes and standard deviation 34 minutes. The VP of network maintenance hypothesizes that the average staff time devoted to reported gas leaks is 226 minutes. At a 5 percent level of significance, what is the upper bound of the interval for determining whether to accept or reject the VP's hypothesis? Note that the correct answer will be evaluated based on the z-values in the summary table in the Teaching Materials section. Please round your answer to the nearest tenth.

A particular fruit's weights are normally distributed, with a mean of 718 grams and a standard deviation of 27 grams.

If you pick 12 fruits at random, then 16% of the time, their mean weight will be greater than how many grams?

Give your answer to the nearest gram.

1) You test a new drug to reduce blood pressure. A group of 15 patients with high blood pressure report the following systolic pressures (measured in mm Hg): ̄y s before medication: 187 120 151 143 160 168 181 197 133 128 130 195 130 147 193 157.53 27.409 after medication: 187 118 147 145 158 166 177 196 134 124 133 196 130 146 189 156.40 27.060 change: 0 2 4 -2 2 2 4 1 -1 4 -3 -1 0 1 4 1.133 2.295 a) Calculate a 90% CI for the change in blood pressure. b) Calculate a 99% CI for the change in blood pressure. c) Does either interval (the one you calculated in (a) or (b)) include 0? Why is this important? d) Now conduct a one sample t-test using μ = 0, and α = .10. Are the results consistent with (a)? e) Finally, conduct a one sample t-test using μ = 0, and α = .01. Are the results consistent with (b)? PLEASE TELL HOW TO GET ALPHA I USE .05 AND GOT VALUE 2.145

The professors who teach the Introduction to Psychology course at State University pride themselves on the normal distributions of exam scores. After the first exam, the current professor reports to the class that the mean for the exam was 73, with a standard deviation of 7.

a. What proportion of student would be expected to score above 80?

b What proportion of students would be expected to score between 55 and 75?

c. What proportion of students would be expected to score less than 65?

d. If the top 10% of the class receive an A for the exam, what score would be required for a student to receive an A?

e. If the bottom 10% of the class fail the exam, what score would earn a student a failing grade?

using chapter 13 data set 2, the researchers want to find out whether there is a difference among the graduation rates (and these are percentages) of five high schools over a 10-year period. Is there? (hint: are the years a factor?)

To study the effect the ecological impact of malaria, researchers in California measured the effect of malaria on what distance an animal could run in 2 minutes. They used a sample of a local lizard species, Sceloporis occidentalis, collected in the field. They selected 15 lizards from those found to be infected with the malarial parasite Plasmodium mexicanum and 15 lizards found not infected.

The distance each lizard could run in a time limit of 2 minutes was recorded in a controlled environment. The data (below) is also in an Excel file, “Malaria effect”

a) Does this design use paired data or independent samples? Explain.

b) Compute a 95% confidence interval for the difference in distance ran between the two malarial infections of the lizards. Show all of your working.

c) Based on this confidence interval, can you conclude there is a difference in mean distance ran between the infected and uninfected lizards?

d) Conduct a test of significance (at a significance level of 5%) on the difference between infected and uninfected lizards to decide whether the uninfected lizards can run a further distance on average. Follow all steps clearly and write a clear conclusion.

e) Do you have the same conclusion from the confidence interval calculation in c) as that concluded by the test done in d) above? Explain why or why not.