Sociology/Criminology/Economics: Records comparing unemployment rates, violent crime rates (per 1,000) and property crime rates (per 1,000) were gathered in a state for the years 1975 - 2005 (n = 31). Below are the scatterplots, regression lines, and corresponding statistics for these 31 years.

Answer the following questions regarding the relationship between unemployment and these two types of crime rates.

(a) Is there a significant linear correlation between unemployment and violent crime rates?

YesNo    

(b) Is there a significant linear correlation between unemployment and property crime rates?

YesNo    

(c) Choose the most valid concluding statement.

There is no correlation between unemployment and crime rates.While there is a significant correlation between unemployment and property crime rates, there is no such correlation between unemployment and violent crime rates.     There is a significant correlation between unemployment and all types of crime rates.

AM -vs- PM sections of Stats - Significance test (Raw Data, Software Required):
There are two sections of statistics, one in the afternoon (PM) with 30 students and one in the morning (AM) with 22 students. Each section takes the identical test. The PM section, on average, scored higher than the AM section. The scores from each section are given in the table below. Test the claim that the PM section did significantly better than the AM section, i.e., is the difference in mean scores large enough to believe that something more than random variation produced this difference. Use a 0.01 significance level.

An article in IEEE International Symposium on Electromagnetic Compatibility (Vol. 2, 2002, pp. 667–670) describes the quantification of the absorption of electromagnetic energy and the resulting thermal effect from cellular phones. The experimental results were obtained from in vivo experiments conducted on rats. The arterial blood pressure values (mmHg) for the control group (8 rats) during the experiment are X1 = 90, s₁ = 5 and for the test group (9 rats) are X2 = 115,s₂ = 10.

(a) Is there evidence to support the claim that the test group has higher mean blood pressure? Assume that both populations are normally distributed but the variances are not equal. Answer this question by finding the P-value for this test.

The test group has ( higher OR the same OR smaller)  mean blood pressure, since P-value ( > 0.05 OR < 0.05)

(b) Calculate 95% one sided CI to answer the claim in (a). Round your answer to 1 decimal place.

μ₁ - μ₂ ≤ -------

Applying the Central Limit Theorem: The amount of contaminants that are allowed in food products is determined by the FDA (Food and Drug Administration). Common contaminants in cow milk include feces, blood, hormones, and antibiotics. Suppose you work for the FDA and are told that the current amount of somatic cells (common name "pus") in 1 cc of cow milk is currently 750,000 (note: this is the actual allowed amount in the US!). You are also told the standard deviation is 111000 cells. The FDA then tasks you with checking to see if this is accurate. You collect a random sample of 40 specimens (1 cc each) which results in a sample mean of 784399 pus cells. Use this sample data to create a sampling distribution.

a. Why is the sampling distribution approximately normal?

d. Assuming that the population mean is 750,000, what is the probability that a simple random sample of 40 1 cc specimens has a mean of at least 784399 pus cells?

e. Is this unusual? Use the rule of thumb that events with probability less than 5% are considered unusual. No Yes

f. Explain your results above and use them to make an argument that the assumed population mean is incorrect. (6 points) Structure your essay as follows: Describe the population and parameter for this situation. Describe the sample and statistic for this situation. Give a brief explanation of what a sampling distribution is.

Describe the sampling distribution for this situation.

Explain why the Central Limit Theorem applies in this situation.

Interpret the answer to part d. Use the answer to part e. to argue that the assumed population mean is either correct or incorrect. If incorrect, indicate whether you think the actual population mean is greater or less than the assumed value.

Explain what the FDA should do with this information.

Create frequency table (including  include class interval, frequency, relative frequency and cumulative relative frequency. ) and frequency polygon.

Please explain HOW for a thumbs up!! TY

An elevator has a placard stating that the maximum capacity is 1328 lblong dash8 passengers.​ So, 8 adult male passengers can have a mean weight of up to 1328 divided by 8 equals 166 pounds. If the elevator is loaded with 8 adult male​ passengers, find the probability that it is overloaded because they have a mean weight greater than 166 lb.​ (Assume that weights of males are normally distributed with a mean of 170 lb and a standard deviation of 28 lb​.) Does this elevator appear to be​ safe?

The probability the elevator is overloaded is?

(Round to four decimal places as​ needed.

A. Create frequency table (include  include class interval, frequency, relative frequency and cumulative relative frequency. )

B. Create Frequency Polygon

Andy is always looking for ways to make money fast. Lately, he has been trying to make money by gambling. Here is the game he is considering playing: The game costs 2 dollars to play. He draws a card from a deck. If he gets a number card (2-10), he wins nothing. For any face card (jack, queen or king), he wins 3 dollars. For any ace, he wins 5 dollars and he wins an extra $20 if he draws the ace of clubs.

a) if x = money gained, write down the pmf for this game.

b) What are the E(X) and V(X)?

C) Find and sketch the cdf, F(x)

Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. Assume a production process produces items with a mean weight of 10 ounces.

(a)

The process standard deviation is 0.21, and the process control is set at plus or minus one standard deviation. Units with weights less than 9.79 or greater than 10.21 ounces will be classified as defects. (Round your answer to the nearest integer.)

Calculate the probability of a defect. (Round your answer to four decimal places.)

Calculate the expected number of defects for a 1,000-unit production run. (Round your answer to the nearest integer.)

defects

(b)

Through process design improvements, the process standard deviation can be reduced to 0.07. Assume the process control remains the same, with weights less than 9.79 or greater than 10.21 ounces being classified as defects.

Calculate the probability of a defect. (Round your answer to four decimal places.)

Calculate the expected number of defects for a 1,000-unit production run. (Round your answer to the nearest integer.)

defects

(c)

What is the advantage of reducing process variation, thereby causing process control limits to be at a greater number of standard deviations from the mean?

Reducing the process standard deviation causes no change in the number of defects.Reducing the process standard deviation causes a substantial increase in the number of defects.     Reducing the process standard deviation causes a substantial reduction in the number of defects.

A teacher is comparing the mean study time of his freshmen and senior students. he believes that his senior students spend more time studying per week than his freshmen students and decides to perform a hypotheses test on this belief.

a. suppose the decision of the hypothesis test is to reject the null hypothesis. If in reality freshmen study for a mean of 10 hours per week and seniors study for a mean of 15 hours per week, was an error made? If so, what type?

b. Suppose the decision of the hypothesis test is to fail to reject the null hypothesis. If in reality the freshmen study for a mean of 15 hours per week and seniors study for a mean of 15 hours per week, was an error made? If so, what type?

Q4. Human blood is grouped into four types: A, B, AB & O. Type O blood can be transfused to anyone (the universal donor) while people with Type AB blood can receive any blood type (the universal recipient). A country is recruiting soldiers but unsuccessful applicants accuse there exists discrimination on their blood type—too many Type A & B applicants are rejected while too many Type O & AB applicants are accepted. Use goodness-of-fit test, test whether the number of recruited soldiers in each blood type are different from the country’s national proportion significantly at the level of significance of 5%.

The following sample of weights was taken from 9 cans of soda off the assembly line. Construct the 80% confidence interval for the population standard deviation for all cans of soda that come off the assembly line. Round your answers to two decimal places. 14.5,14.7,14.3,14.3,14.6,15.1,15.3,15.1,14.4

1. You have 4 groups with an overall sample size of n = 20. The F critical value at the alpha = 0.05 level of significance is 3.24. Complete the following 1 factor ANOVA table below:

Is there a significant difference (α=0.05) between at least two of the four groups for the analysis in question 1 (above)? (circle one) YES   NO

2. Use the following data set to complete the ANOVA table and answer the questions.

Is there a significant difference (α=0.05) between at least two of the four groups for the analysis in question 1 (above)? (circle one) YES   NO

Confidence interval for Group 1 ( _________ , _________)

Confidence interval for Group 2 ( _________ , _________)

Confidence interval for Group 3 ( _________ , _________)

Is Group 1 significantly different from Group 2 at the α=0.05 level of significance YES NO

            Is Group 1 significantly different from Group 3 at the α=0.05 level of significance YES NO

            Is Group 2 significantly different from Group 3 at the α=0.05 level of significance YES NO

Conduct a test at the alpha equals 0.01 level of significance by determining ​(a) the null and alternative​ hypotheses, ​(b) the test​ statistic, and​ (c) the​ P-value. Assume the samples were obtained independently from a large population using simple random sampling. Test whether p 1 greater than p 2. The sample data are x 1 equals 125​, n 1 equals 253​, x 2 equals 135​, and n 2 equals 309.