Describe 5 different types of data distributions. You may include jpegs or bitmaps. Provide 2 example of a variable that is representative for each distribution. You may not use the standard normal. t-distribution, F-distribution, Chi-Square distribution, Binomial distribution, or uniform distribution. These distributions are all covered in the course.

Data from the Framingham Study allow us to compare the distributions of initial serum cholesterol levels for two populations of males: those who go on to develop coronary heart disease and those who do not. The mean serum cholesterol level of the population of men who do not develop heart disease is µ = 206mg/10ml and the standard deviation is σ = 36mg/100ml. Suppose, however, that you do not know the true population mean; instead, you hypothesize that µ is equal to 230mg/100ml. This is the mean initial serum cholesterol level of men who eventually develop the disease. Since it is believed that the mean serum cholesterol level for the men who do not develop heart disease cannot be higher than the mean level for men who do, a one-sided test conducted at the α = 0.05 level of significance is appropriate.

a. How could you increase the power?

b. You wish to test the null hypothesis H0: µ ≥ 230mg/100ml against the alternative HA: µ < 230mg/100ml at the alpha = 0.05 level of significance. If the true population mean is as low as 206mg/100ml, you want to risk only a 5% chance of failing to reject H0. How large a sample would be required?

c. How would the sample size change if you were willing to risk a 10% chance of failing to reject a false null hypothesis?

To test whether extracurricular activity is a good predictor of college success, a college administrator records whether students participated in extracurricular activities during high school and their subsequent college freshman GPA.

(a) Code the dichotomous variable and then compute a point-biserial correlation coefficient. (Round your answer to three decimal places.)

Randomly selected students participated in an experiment to test their ability to determine when one minute​ (or sixty​ seconds) has passed. Forty students yielded a sample mean of 61.6 seconds. Assuming that sigma equals8.7 ​seconds, construct and interpret a 90 ​% confidence interval estimate of the population mean of all students. Click here to view a t distribution table. LOADING... Click here to view page 1 of the standard normal distribution table. LOADING... Click here to view page 2 of the standard normal distribution table. LOADING... What is the 90 ​% confidence interval for the population mean mu ​? nothing less thanmuless thannothing ​(Type integers or decimals rounded to one decimal place as​ needed.)

Instructions:  Read the information below.  Provide a print screen of your work when using a software tool.

Adbul is the new maintenance supervisor at a local manufacturing plant. He is responsible for the maintenance of machinery for production line processes.  Abdul is interested in the level of machine failures. He would like to simulate the number of machine failures each month.  Using historical date, Abdul established the probability of failures during a month as follows:

Simulate Abdul’s monthly machine failures for a period of 3 years.  Replicate the failures 300 times.  Provide the following information:

A copy of the completed Excel spreadsheet                                       

The average number of failures per month for one replication         (1 mark)

The average number of failures per month for 300 replications       (1 mark)

Explain any difference(s) between the simulated average failures and the expected value of failures (long run value).                 

You have 8 collected prices for a textbook (assume that the prices are normally distributed) from various websites and found the mean price to be $214 and sample standard deviation = $26.10. Based on a 90% confidence interval for the population mean, could you can you say that the $200 you paid for a good copy of the book was about the average cost of the textbook or a bargain?

Confidence Interval - _________________________

Conclusion - __________________________________________________

Claudia Maurva, manufacturer of CM denim skirts, has pitched her advertising to develop a "stylish yet affordable" image for her brand. She is concerned, however, that retailers are undermining this image, and cutting her market share, by pricing them above her recommended retail price of $49.95. A random sample of thirty-two fashion outlets who stock her skirts finds that the average price charged is $52.05 with the standard deviation being $4.68.

1. State the direction of the alternative hypothesis used to test the company's claim. Type the letters gt (greater than), ge (greater than or equal to), lt (less than), le (less than or equal to) or ne (not equal to) as appropriate in the box.
2. Use the tables in the text to determine the critical value used to conduct the test, assuming a 1% level of significance. If there are two critical values, state only the positive value.
3. Calculate the test statistic (two decimal places).
4. Is the null hypothesis rejected at the 1% level of significance? Type yes or no.
5. If in fact the retailers are charging $52.95 on average, determine the nature of the decision made in the test. Type cd (correct decision), 1 (a Type I error was made) or 2 (a Type II error was made) as appropriate.

6. Regardless of your answer for 4, if the null hypothesis was rejected, could we conclude that fashion outlets seem to be charging more than the recommended retail price? Type yes or no.

Suppose that 1/2 of all cars sold at a Nissan dealer in a given year are Altimas, 1/3 are Maximas, and the rest are Sentras. Suppose that 3/4 of the Altimas, 1/2 of the Maximas, and 1/2 of the Sentras have a moon roof. Answer the following questions. For each question, first decide whether the probability is a conditional probability or not.

1. What is the probability a randomly selected car has a moon roof?

2. What is the probability that a randomly selected car has a moon roof given it is a Sentra?

3. What is the probability a randomly selected car is a Maxima if it has a moon roof?

A large snack company claims that children enjoy their whole wheat snack equally as much as normal snacks. A study testing this claim on a SRS of 86 children were given both snack alternatives and then each child was asked which snack they preferred. The whole wheat snack was chosen by 48 children.

a) Using the 68-95-99.7 rule, if the snack company claims were true, you would expect ?̂ to fall between what two percent about 95% of the time?

b) Using your answer from a, is the snack company's claim correct?

c) Perform a significance test for α = 0.5

The local bakery bakes more than a thousand 1-pound loaves of bread daily, and the weights of these loaves varies. The mean weight is 1.7 lb. and 3 oz., or 856 grams. Assume the standard deviation of the weights is 25 grams and a sample of 32 loaves is to be randomly selected.

(A) This sample of 32 has a mean value of x, which belongs to a sampling distribution. Find the shape of this sampling distribution.

a) skewed right

b) approximately normal   

c) skewed left

d) chi-square

(b) Find the mean of this sampling distribution. (Give your answer correct to nearest whole number.)
_____ grams

(c) Find the standard error of this sampling distribution. (Give your answer correct to two decimal places.) ______


(d) What is the probability that this sample mean will be between 846 and 866? (Give your answer correct to four decimal places.) _______


(e) What is the probability that the sample mean will have a value less than 847? (Give your answer correct to four decimal places.) _______


(f) What is the probability that the sample mean will be within 4 grams of the mean? (Give your answer correct to four decimal places.) _______

A box contains 1 fair coin and 1 2-Headed coin. A coin is drawn and flipped several times.

(a) The first flip results in Heads. What is the probability that the coin is fair?

(b) 3 flips result in all Heads. What is the probability that the coin is fair?

(c) 5 flips result in all Heads. What is the probability that the coin is fair?

(d) How many flips of all Heads are required to know with 99.9% accuracy that the coin is not fair?

An economist wonders if corporate productivity in some countries is more volatile than in other countries. One measure of a company's productivity is annual percentage yield based on total company assets.

A random sample of leading companies in France gave the following percentage yields based on assets.

Use a calculator to verify that the sample variance is s² ≈ 1.982 for this sample of French companies.

Another random sample of leading companies in Germany gave the following percentage yields based on assets.

Use a calculator to verify that s² ≈ 1.108 for this sample of German companies.

Test the claim that there is a difference (either way) in the population variance of percentage yields for leading companies in France and Germany. Use a 5% level of significance. How could your test conclusion relate to the economist's question regarding volatility (data spread) of corporate productivity of large companies in France compared with companies in Germany?

(a) What is the level of significance?

State the null and alternate hypotheses.

H_o: σ₁² = σ₂²; H₁: σ₁² > σ₂²H_o: σ₁² > σ₂²; H₁: σ₁² = σ₂²     H_o: σ₂² = σ₁²; H₁: σ₂² > σ₁²H_o: σ₁² = σ₂²; H₁: σ₁² ≠ σ₂²

(b) Find the value of the sample F statistic. (Use 2 decimal places.)


What are the degrees of freedom?

What assumptions are you making about the original distribution?

The populations follow dependent normal distributions. We have random samples from each population.The populations follow independent normal distributions.     The populations follow independent normal distributions. We have random samples from each population.The populations follow independent chi-square distributions. We have random samples from each population.

(c) Find or estimate the P-value of the sample test statistic. (Use 4 decimal places.)

p-value > 0.2000.100 < p-value < 0.200     0.050 < p-value < 0.1000.020 < p-value < 0.0500.002 < p-value < 0.020p-value < 0.002

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.     At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(e) Interpret your conclusion in the context of the application.

Fail to reject the null hypothesis, there is sufficient evidence that the variance in percentage yields on assets is greater in the French companies.Reject the null hypothesis, there is insufficient evidence that the variance in percentage yields on assets is greater in the French companies.     Reject the null hypothesis, there is sufficient evidence that the variance in percentage yields on assets is different in both companies.Fail to reject the null hypothesis, there is insufficient evidence that the variance in percentage yields on assets is different in both companies.

From the list shown below, for each of the following hypothesis testing situations indicate the type of test you would use. Unless indicated otherwise, the significance level for all the tests is .05

One-sample t test

One sample Wilcoxon signed-ranked test

McNemar Test

Two samples t test for independent means with equal variances

Paired samples t-test

F test

Mann-Whitney U test

Chi-square test

Paired Sample Wilcoxon Signed Ranked test

Two samples t test for independent means with unequal variances

A financial aid advisor wants to see if students are overly optimistic about their future salaries. He knows that the distribution of starting salaries for public health majors graduating from the school is normally distributed with a mean of $ 48,000 or u = $4,000 a month. To determine if public health students are overly optimistic about their potential salaries, the counselor obtains a random sample of 15 MPH students from UWF and asks each one of them individually what they expect their monthly salary will be in their first job after graduation. The 15 students' expected starting monthly salaries had a mean of 4,200. The counselor chooses a one-tailed test and alpha of 0.05. The research question is: Is the student's mean estimated starting salary significantly higher than the actual starting salary for nurse’s students?

Researchers want to find a better way of encouraging children to read more and discovered two possible approaches. To decide which to implement, they randomly select two libraries. In library a they enhanced the children's reading area and shelving as suggested in one plan, and in library B, they enhanced the children's reading area according to the other plan. After a year, they collected data on how many books each member of the two borrowed over the period. The researchers assessed the amount of reading in a Likert scale; therefore, the variable reading was an ordinal variable, and although the distribution was symmetric, the researchers could not assume the data is normally distributed.

Researchers wanted to assess if children living in the far north grow more slowly than those who live in sunnier regions. Their null hypothesis was that there would be no significant difference in height between two samples of 14-year-olds chosen from northern Finland and southern Italy. The randomly selected 50 children aged 14 from two different schools and their heights were measured and recorded in centimeters. It is assumed the test variable “height” was normally distributed in each of the populations; the cases represent a random sample from the population, and the scores on the test variable are independent of each other; and the variances of the normally distributed test variable for the populations are equal

A nurse is leading a smoking cessation group and wants to determine the effectiveness of the intervention. The research question is: will providing a 1-hour smoking cessation workshop help to reduce smoking among the participants? Ho= the smoking cessation workshop is not effective in reducing smoking; Ha: the smoking cessation workshop is effective in reducing smoking. The nurse selects 40 participants. The data is assumed to be normally distributed

An investigator read that there is an antibiotic often tested, well documented, and known to help information stored in memory. This experimenter also knows through scientific reports and guidelines that behavioral therapy has an established efficacy for the treatment of the social phobia. In addition, he knows that behavioral therapy requires the learning of new behaviors which implies information storage.   The number of symptoms of social phobia after two types of therapy was investigated. Two groups of individuals with social phobia were compared. The first group (10 participants) received the behavioral therapy; the second group (15 participants) received the behavioral therapy combined with the antibiotic. After each therapy, both groups showed a decrease in the number of symptoms of social phobia. The number of these symptoms was measured and a test was run to decide whether the combined therapy had more effect on the symptoms than the behavioral therapy alone.

For each exercise, find the equation of the regression line and find the y’ value for the specified x value. Remember that no regression should be done when r is not significant.

27.Class Size and Grades School administrators wondered whether class size and grade achievement (in percent) were related. A random sample of classes revealed the following data.

Find y′ when x = 12.

Answer: R is not significant no regression should be done. Please show work this is a review for an exam coming up. Please do this by hand. Also, specifically show how you find R. Thank you

A 95% confidence interval for p is given as (0.43,0.77). How large was the sample used to construct this​ interval? (n)