The Bureau of Economic Analysisin the U.S. Department of Commerce reported that the mean annual income for a resident of North Carolina is $18,688 (USA Today, August 24, 1995). A researcher for the state of South Carolina wants to see if the mean annual income for a resident of South Carolina is different. A sample of 400 residents of South Carolina shows a sample mean annual income of $16,860 and the population standard deviation is assumed to known, =$14,624. Use a 0.05 level of significance, the researcher wants to test the following hypothesis.H0:= 18,688Ha:18,688a.What are three rejection rules (You have used confidence interval approach in Question 2)? b.Do three rejection rules lead to the same conclusion? What is your conclusion?

Barking deer.

Microhabitat factors associated with forage and bed sites of barking deer in Hainan Island, China were examined from 2001 to 2002. In this region woods make up 4.8% of the land, cultivated grass plot makes up 14.7%, and deciduous forests makes up 39.6%. Of the 426 sites where the deer forage, 4 were categorized as woods, 16 as cultivated grassplot, and 61 as deciduous forests. The table below summarizes these data.

1. Write the hypotheses for testing if barking deer prefer to forage in certain habitats over others.

2. What type of test can we use to answer this research question?
3. Check if the assumptions and conditions required for this test are satisfied.
4. Do these data provide convincing evidence that barking deer prefer to forage in certain habitats over others? Conduct an appro- priate hypothesis test to answer this research question.

Consider a multiple-choice examination with 50 questions. Each question has four possible answers. Assume that a student who has done the homework and attended lectures has a 65% chance of answering any question correctly. (Round your answers to two decimal places.)

(a) A student must answer 44 or more questions correctly to obtain a grade of A. What percentage of the students who have done their homework and attended lectures will obtain a grade of A on this multiple-choice examination? Use the normal approximation of the binomial distribution to answer this question.

(b) A student who answers 34 to 39 questions correctly will receive a grade of C. What percentage of students who have done their homework and attended lectures will obtain a grade of C on this multiple-choice examination? Use the normal approximation of the binomial distribution to answer this question.

(c) A student must answer 30 or more questions correctly to pass the examination. What percentage of the students who have done their homework and attended lectures will pass the examination? Use the normal approximation of the binomial distribution to answer this question.

(d) Assume that a student has not attended class and has not done the homework for the course. Furthermore, assume that the student will simply guess at the answer to each question. What is the probability that this student will answer 30 or more questions correctly and pass the examination? Use the normal approximation of the binomial distribution to answer this question.

20 babies born in one week in a local hospital had the following weights (in pounds): 9.6, 8.8, 5.1, 7.7, 6.1, 8.9, 8, 9.2, 5.7, 9.1, 8.5, 7.3, 9.3, 9.6, 5.2, 9.9, 7.6, 9, 7.2, 8.5 (a) Create a QQ plot and histogram of the weights. Do you think it is reasonable to assume that the population distribution is normal? Explain your answer. (b) Regardless of your answer to (a), use R to perform the bootstrap with 3000 resamplings to create a 98% CI for µ. (Show your R code and its output - you can copy and paste the code given in lecture or discussion.) (c) Now construct a 98% CI for µ by hand using the t-tables, and compare it to your bootstrap-t confidence interval. (e) Compute the power of the test if the true population mean is µA = 15. (f) Using s = 4.88 as our best guess of σ, approximately what sample size would be required to achieve a power of 0.8 if the true population mean is µA = 15? Give your answer as the smallest whole number that meets the criterion.

Problem #1 -- Historically, 20% of graduates of the engineering school at a major university have been women. In a recent, randomly selected graduating class of 210 students, 58 were females. Does the sample data present convincing evidence that the proportion of female graduates from the engineering school has shifted (changed)? Use α = 0.05.

A. Explain what it means to make a Type I error and indicate the probability of it occurring, under the assumption the null hypothesis was true.

B. Explain what it means to make a Type II error and suggest a possible value of the parameter in order for such an error to occur.

1. Tar in cigarettes: Listed below are amounts of tar (mg per cigarette) in sing size cigarettes. 100-mm menthol cigarettes, and 100-mm non menthol cigarettes. The king size cigarettes are nonfiltered, nonmenthol, and nonlight. The 100-mm menthol cigarettes are filtered and nonlight. The 100-mm nonmenthol cigarettes are filtered and nonlight. Use a .05 significance level to test the claim that the three categories of cigarettes yield the same mean amount of tar. Given that only the king-size cigarettes are not filtered, do the filters appear to make a difference?

King 20,27,27,20,20,24,20,23,20,22,20,20,20

       20, 20,10, 24,20,21,25,23,20,22,20,20

Kool 16,13,16,9,14,13,12,14,14,13,13,16,13,

        13, 18, 9, 19, 2, 13, 14, 14, 15,16 6, 8,

Long 5, 16, 17, 13, 13, 14, 15, 15, 15, 9, 13, 13,13,

       15, 2, 15, 15, 13, 14, 15, 16, 15, 7, 17, 15,

Help solve without using computer step by step

• Nine experts rated two brands of Colombian coffee in a taste-testing experiment. A rating on a 7-point scale ( 1=1= 1 equals extremely unpleasing, 7=7= 7 equals extremely pleasing) is given for each of four characteristics: taste, aroma, richness, and acidity. The following data stored in Coffee contain the ratings accumulated over all four characteristics:

  	BRAND
  EXPERT	A	B
  C.C.	24	26
  S.E.	27	27
  E.G.	19	22
  B.L.	24	27
  C.M.	22	25
  C.N.	26	27
  G.N.	27	26
  R.M.	25	27
  P.V.	22	23

  • a. At the 0.05 level of significance, is there evidence of a difference in the mean ratings between the two brands?

  • b. What assumption is necessary about the population distribution in order to perform this test?

  • c. Determine the p-value in (a) and interpret its meaning.

  • d. Construct and interpret a 95% confidence interval estimate of the difference in the mean ratings between the two brands.

An exercise science major wants to try to use body weight to predict how much someone can bench press. He collects the data shown below on 30 male students. Both quantities are measured in pounds.

b) Compute a 95% confidence interval for the average bench press of 150 pound males. What is the lower limit? Give your answer to two decimal places.  

c) Compute a 95% confidence interval for the average bench press of 150 pound males. What is the upper limit? Give your answer to two decimal places.  

d) Compute a 95% prediction interval for the bench press of a 150 pound male. What is the lower limit? Give your answer to two decimal places.  

e) Compute a 95% prediction interval for the bench press of a 150 pound male. What is the upper limit? Give your answer to two decimal places.  

Thoroughly answer the following questions:

Why are adjustments needed in determining risks and rates?

In product design for human use and recommended guideline for the product’s human use, it is important to consider the weights of people so that airplanes or elevators aren’t overloaded. Based on data from the National Health Survey, the weight of adults in the United States has a mean of 181 pound (the average of 195.5 for males and 166.2 for females, assuming, arbitrarily, equal male and female population) with a standard deviation of 30 pounds. An airplane is designed to have a human carrying maximum-capacity 18,500 pounds. An Airline adopts the operation procedure of maximum passenger number (n), based on the concept of the probability of a randomly selected n passengers exceeding the maximum-capacity to be less than 0.01 (i.e., 1%). a) [3 pts] Determine n b) b) [2 pts] What will be the value of n if the probability of exceeding the maximum-capacity is no more than 0.001 (i.e., 0.1%)?

Now suppose Thermata officers want to ascertain employee satisfaction with the company. They randomly sample nine employees and ask them to complete a satisfaction survey under the supervision of an independent testing organisation. As part of this survey, employees are asked to respond to questions on a 5-point scale where 1 is low satisfaction and 5 is high satisfaction. The questions and the results of the survey are shown in the next column. Analyse the data by finding a confidence interval (with =0.05) to estimate the population response to each of these questions. Provide your interpretation and discussions of the results.

A local car dealer is attempting to determine which premium will draw the most visitors to its showroom. An individual who visits the showroom and takes a test ride is given a premium with no obligation. The dealer chose four premiums and offered each for one week. The results are as follows:

3(a): Please identify the research question (one sentence).

Here are some examples of the research question:

How/why A is related to B?

Does A cause/equal/bigger/smaller/explain than B?

Whether A is equal/bigger/smaller than B?

3(b) Please generate the appropriate hypothesis

H0:

Ha:

3(c): Find the appropriate statistical test, compute the test statistics. Please give detailed calculation procedures.

3(d): Based on your computed test statistics, draw your conclusions

The age distribution of the Canadian population and the age distribution of a random sample of 455 residents in the Indian community of a village are shown below.

Use a 5% level of significance to test the claim that the age distribution of the general Canadian population fits the age distribution of the residents of Red Lake Village.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: The distributions are different.
H₁: The distributions are the same.H₀: The distributions are the same.
H₁: The distributions are the same.    H₀: The distributions are different.
H₁: The distributions are different.H₀: The distributions are the same.
H₁: The distributions are different.

(b) Find the value of the chi-square statistic for the sample. (Round your answer to three decimal places.)


Are all the expected frequencies greater than 5?

YesNo    

What sampling distribution will you use?

uniformnormal    chi-squareStudent's tbinomial

What are the degrees of freedom?


(c) Estimate the P-value of the sample test statistic.

P-value > 0.1000.050 < P-value < 0.100    0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis that the population fits the specified distribution of categories?

Since the P-value > α, we fail to reject the null hypothesis.Since the P-value > α, we reject the null hypothesis.    Since the P-value ≤ α, we reject the null hypothesis.Since the P-value ≤ α, we fail to reject the null hypothesis.

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

At the 5% level of significance, the evidence is insufficient to conclude that the village population does not fit the general Canadian population.At the 5% level of significance, the evidence is sufficient to conclude that the village population does not fit the general Canadian population.

The data below are the heights of fathers and sons (inches). There are 8 rows in total.

Father Son

1. Which statistical test would you use to determine if there is a tendency for tall fathers to have tall sons and short fathers to have short sons? Test for the statistical significance.

2. Compute the regression equation for predicting sons' heights from fathers' heights.

3. Use the equation from #2 to predict the height of a son whose father is 46 inches tall.

4. Should you use the regression equation to predict the hight of a son whose father had a height of 25" when he was the same age as his son?

5. Which statistical test would you use to determine if generations get taller. The question is, are sons taller than their fathers were at the same age?

You may need to use the appropriate appendix table or technology to answer this question.

Consider a multiple-choice examination with 50 questions. Each question has four possible answers. Assume that a student who has done the homework and attended lectures has a 65% chance of answering any question correctly. (Round your answers to two decimal places.)

(a)

A student must answer 44 or more questions correctly to obtain a grade of A. What percentage of the students who have done their homework and attended lectures will obtain a grade of A on this multiple-choice examination? Use the normal approximation of the binomial distribution to answer this question.

(b)

A student who answers 36 to 39 questions correctly will receive a grade of C. What percentage of students who have done their homework and attended lectures will obtain a grade of C on this multiple-choice examination? Use the normal approximation of the binomial distribution to answer this question.

(c)

A student must answer 30 or more questions correctly to pass the examination. What percentage of the students who have done their homework and attended lectures will pass the examination? Use the normal approximation of the binomial distribution to answer this question.

(d)

Assume that a student has not attended class and has not done the homework for the course. Furthermore, assume that the student will simply guess at the answer to each question. What is the probability that this student will answer 30 or more questions correctly and pass the examination? Use the normal approximation of the binomial distribution to answer this question.