The proportion of deaths due to lung cancer in males ages 15–64 in England and Wales during the period 1970–1972 was 12%. Suppose that of 20 deaths that occur among male workers in this age group who have worked for at least 1 year in a chemical plant, 5 are due to lung cancer. We wish to determine whether there is a difference between the proportion of deaths from lung cancer in this plant and the proportion in the general population. a) State the hypotheses to use in answering this question. b)Is a one-sided or two-sided test appropriate here? c)Perform the hypothesis test, and report a p-value.

You are a researcher working for an educational research firm. Your firm was asked to conduct a satisfaction survey among the parents of students attending the School District public schools. Your boss has asked you to develop a sampling design for this survey.

For this survey, you are asked to select a representative sample of parents. When you answer the questions, keep the following in mind:

• Assume that you have unlimited authority to access all the information you may need and remember that your task is to select the most representative sample of the parent population.
• There are 10,000 households with children at public schools in the school district.
• One parent will be interviewed for each household in the sample. (Remember that multiple children from the same household may attend public schools, and there may be more than one parent in each household. Regardless of these variations, only one parent will be interviewed from each household selected for the sample.)

1. Describe your population. Elaborate on the specifics of your population.

2. Describe your sampling frame. Be specific in your descriptions. Where would you find the information to define it? Remember that you have full authority to access all the information available, (You just need to know whom to ask and what to ask for.)

3. If you use a simple random sampling design, what is the minimum sample size you will need to determine the percentage (proportion) of those parents who are satisfied with the public schools at the 4% accuracy level, with the 95% confidence level? Explain how you determined your sample size.

4. If you use a multistage cluster sampling design, would your minimum sample size be larger or smaller than the previous simple random sampling design? Why?

5. If you use a proportionate stratified sampling design, would your minimum sample size be larger or smaller than the simple random sampling design. Why?

The eigenvalue is a measure of how much of the variance of the observed variables a factor explains. Any factor with an eigenvalue ≥1 explains more variance than a single observed variable, so if the factor for socioeconomic status had an eigenvalue of 2.3 it would explain as much variance as 2.3 of the three variables. This factor, which captures most of the variance in those three variables, could then be used in another analysis. The factors that explain the least amount of variance are generally discarded. How do we determine how many factors are useful to retain?

What is the relationship between the simple two-sample t-test and the Bonferroni method of multiple comparisons?

13.50 The owner of a moving company typically has his most experienced manager predict the total number of labor hours that will be required to complete an upcoming move. This approach has proved useful in the past, but the owner has the business ob-jective of developing a more accurate method of predicting labor hours. In a preliminary effort to provide a more accurate method, the owner has decided to use the number of cubic feet moved and the number of pieces of large furniture as the independent vari-ables and has collected data for 36 moves in which the origin and destination were within the borough of Manhattan in New York City and the travel time was an insignificant portion of the hours worked. The data are organized and stored in Moving .a. State the multiple regression equation.b. Interpret the meaning of the slopes in this equation.c. Predict the mean labor hours for moving 500 cubic feet with two large pieces of furniture.d. Perform a residual analysis on your results and determine whether the regression assumptions are valid.e. Determine whether there is a significant relationship between labor hours and the two independent variables (the number of cubic feet moved and the number of pieces of large furniture) at the 0.05 level of significance.f. Determine the p-value in (e) and interpret its meaning.g. Interpret the meaning of the coefficient of multiple determina-tion in this problem.h. Determine the adjusted r2.i. At the 0.05 level of significance, determine whether each inde-pendent variable makes a significant contribution to the regres-sion model. Indicate the most appropriate regression model for this set of data.j. Determine the p-values in (i) and interpret their meaning.k. Construct a 95% confidence interval estimate of the population slope between labor hours and the number of cubic feet moved. How does the interpretation of the slope here differ from that in Problem 12.44 on page 443?l. What conclusions can you reach concerning labor hours?

Many people purchase SUV because they think they are sturdier and hence safer than regular cars. However data have indicated that the costs of repair of SUV are higher that midsize cars when both cars are in an accident. A random sample of 8 new SUV and midsize cars is tested for front impact resistance. The amount of damage in hundreds of dollars to the vehicles when crashed at 20mph are recorded below.

Questions: 1. Is this an independent data or paired?

2. Which non-parametric test will be appropriate. Rank the data using table

3. formally test to determine if there is a difference in the distribution of cost of repairs for the cars use nonparametric test critical rejection region and alpha =0.5

4.what is the p-value compared to the test statistics

car         1           2         3          4           5          6          7       8

SUv     14.23 12.47 14.00   13.17   27.48   12.42   32.58   12.98

midsize 11.97   11.42 13. 27   9.87 10.12   10.36   12.65   25.23

Please provide details. thank you

1. A psychology researcher who does work in creativity wants to determine whether her sample of 50-year-old adults (N = 150) differs statistically from the population of 50-year-olds in intelligence. For her sample, she calculates the following: Mean = 109, SD = 10. (Hint: By definition, the mean IQ of this population is 100 and the population standard deviation is 15. Another hint: Use the z-test here!)
   1. Null hypothesis:
   2. Alternative hypothesis:
   3. Statistical test (You can’t miss this one!):
   4. Significance level (I’ll pick it for you; alpha = .05)
   5. Critical region for rejecting null hypothesis:
   6. Calculate the statistic (please show your work):
   7. Decision:

1.There are 15 teams in the NBA west- ern conference. Warriors are rst. Lakers are right above the Kings in standings. The Thunder is higher than Clippers which is higher than Mavericks in standings. San Anto- nio is lower than the Nuggets. How many possible standings of these 15 teams can there be that satises all conditions mentioned?

2.John and Gina are playing a chess
match. Each game ends with a clear
winner. After 30 games John has
4 more wins than Gina. After 50
games they are tied. What is the pos-
sible number of outcomes (just look-
ing at who won each game) of those
50 games?

When bonding teeth, orthodontists must maintain a dry field. A new bonding adhesive has been developed to eliminate the necessity of a dry field. However, there is a concern that the new bonding adhesive is not as strong as the current standard, a composite adhesive. Tests on a sample of 26 extracted teeth bonded with the new adhesive resulted in a mean breaking strength (after 24 hours) of 2.33 MPa, and a standard deviation of 4 MPa. Orthodontists want to know if the true mean breaking strength is less than 4.06 MPa, the mean breaking strength of the composite adhesive. Assume normal distribution for breaking strength of the new adhesive.

1. What are the appropriate hypotheses one should test?
H₀: μ = 4.06 against   H_a: μ > 4.06.
H₀: μ = 4.06 against   H_a: μ ≠ 4.06.
H₀: μ = 2.33 against   H_a: μ ≠ 2.33.
H₀: μ = 2.33 against   H_a: μ > 2.33.
H₀: μ = 2.33 against   H_a: μ < 2.33.
H₀: μ = 4.06 against   H_a: μ < 4.06.

2. The formula of the test-statistic to use here is
\dfrac[(x)] − μ₀σ/√n.
\dfrac[(x)] − μ₀s/√n.
\dfrac[^(p)] − p₀√{p₀(1−p₀)/n}.
None of the above.

3. Rejection region: We should reject H₀ at 2.5% level of significance if:
test statistic < −1.960.
|test statistic| > 2.241.
test statistic < −2.060.
test statistic > 1.960.
|test statistic| > 2.385.
test statistic > 2.060.

4. The value of the test-statistic is (answer to 3 decimal places):

5. If α = 0.025, what will be your conclusion?
Do not reject H₀.
Reject H₀.
There is not information to conclude.

6. The p-value of the test is (answer to 4 decimal places):

7. We should reject H₀ for all significance level which are
not equal to p-value.
larger than p-value.
smaller than p-value.

Are medical students more motivated than law students? A randomly selected group of each were administered a survey of attitudes toward Life, which measures motivation for upward mobility. The scores are summarized below. The researchers suggest that there are occupational differences in mean testosterone level. Medical doctors and university professors are two of the occupational groups for which means and standard deviations are recorded and listed in the following table.

Let us denote:

• μ₁: population mean testosterone among medical doctors,
• μ₂: population mean testosterone among university professors,
• σ₁: population standard deviation of testosterone among medical doctors,
• σ₂: population standard deviation of testosterone among university professors.

1. If the researcher is interested to know whether the mean testosterone level among medical doctors is higher than that among university professors, what are the appropriate hypotheses he should test?
H₀: μ₁ = μ₂   against   H_a: μ₁ < μ₂.
H₀: μ₁ = μ₂   against   H_a: μ₁ > μ₂.
H₀: [(x)]₁ = [(x)]₂   against   H_a: [(x)]₁ ≠ [(x)]₂.
H₀: [(x)]₁ = [(x)]₂   against   H_a: [(x)]₁ > [(x)]₂.
H₀: [(x)]₁ = [(x)]₂   against   H_a: [(x)]₁ < [(x)]₂.
H₀: μ₁ = μ₂   against   H_a: μ₁ ≠ μ₂.

Case 1: Assume that the population standard deviations are unequal, i.e. σ₁ ≠ σ₂.
1. What is the standard error of the difference in sample mean [(x)]₁ − [(x)]₂? i.e. s.e.([(x)]₁−[(x)]₂) = [answer to 4 decimal places]

2. Rejection region: We reject H₀ at 10% level of significance if:
t < −1.89.
t > 1.41.
t < −1.41.
|t| > 1.89.
t > 1.89.
None of the above.

3. The value of the test-statistic is: Answer to 3 decimal places.

4. If α = 0.1, and the p-value is 0.1965, what will be your conclusion?
Do not reject H₀.
Reject H₀.
There is not enough information to conclude.

Case 2: Now assume that the population standard deviations are equal, i.e. σ₁ = σ₂.
1. Compute the pooled standard deviation, s_pooled [answer to 4 decimal places]

2. Rejection region: We reject H₀ at 10% level of significance if:
t > 1.78.
t < −1.36.
t > 1.36.
|t| > 1.78.
t < −1.78.
None of the above.

3. The value of the test-statistic is: Answer to 3 decimal places.

4. If α = 0.1, , and the p-value is 0.1904, what will be your conclusion?
Reject H₀.
There is not enough information to conclude.
Do not reject H₀.

how is multimodal distribution related to criminal justice?

Suppose we want to estimate the proportion of teenagers (aged 13-18) who are lactose intolerant. If we want to estimate this proportion to within 5% at the 95% confidence level, how many randomly selected teenagers must we survey?

If 15% of adults in a certain country work from home, what is the probability that fewer than 42 out of a random sample of 350 adults will work from home? (Round your answer to 3 decimal places)

Do you use probability in your profession or real life? You most likely do. For example, the chance of rain tomorrow is 27%. We hear similar probabilities in the media all the time. Similar probabilities could be found in other professions. Complete one of the following:

(i) Find an example of probability involving “A or B” that is used in your chosen profession or real life. Explain the example. Are the events A and B in your example mutually exclusive? Which Addition Rule formula for P(A or B) applies? Be sure to cite the source of the information clearly.

(ii) Using a search engine, find an example of probability involving “A and B” that is used in your chosen profession or real life. Explain the example. Are the events A and B in your example independent? Which Multiplication Rule formula for P(A and B) applies? Be sure to cite the source of the information clearly.

(iii) Find an example involving conditional probability that is used in your chosen profession or real life. Explain the example. Be sure to cite the source of the information clearly.

Be sure to support your statements with logic and argument, citing any sources referenced. Post your initial response early, and check back often to continue the discussion. Be sure to respond to your peers’ and instructor’s posts, as well.

Part 1b. Give one example of some practical case where we can use Normal distribution (for instance, IQ scores follow a normal distribution of probabilities with the mean IQ of 100 and a standard deviation around the mean of about 15 IQ points.) In your example,

a) cite the source that claims the variable to be normally distributed (Hint: Look to the examples and exercises in the book)

b) mention the randomly distributed variable

c) provide an estimated value for the mean of the variable

d) provide an estimated value for the standard deviation of the variable

e) provide an estimated range of values for the variable

Thirty small communities in Connecticut (population near 10,000 each) gave an average of x = 138.5 reported cases of larceny per year. Assume that σ is known to be 44.9 cases per year.

(a) Find a 90% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(b) Find a 95% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(c) Find a 99% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(d) Compare the margins of error for parts (a) through (c). As the confidence levels increase, do the margins of error increase?

As the confidence level increases, the margin of error increases.As the confidence level increases, the margin of error remains the same.    As the confidence level increases, the margin of error decreases.

(e) Compare the lengths of the confidence intervals for parts (a) through (c). As the confidence levels increase, do the confidence intervals increase in length?

As the confidence level increases, the confidence interval remains the same length.As the confidence level increases, the confidence interval decreases in length.    As the confidence level increases, the confidence interval increases in length.