A researcher wishes to estimate the proportion of adults who have​ high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.03 with 95​% confidence if ​

(a) she uses a previous estimate of 0.36? (round up to the nearest integer) ​(b) she does not use any prior​ estimates? (round up to the nearest integer)

Scores: 57, 49, 53, 60, 58, 59, 48,

1. What is the mean of these scores?   (round your answer to 2 decimal places)
2. What is the median?
3. What is the estimated standard deviation of the population based on this sample?   (round your answer to 2 decimal places)

4.

A simple random sample of 800 elements generates a sample proportion j5 =

.70.

a.

Provide a 90% confidence interval for the population proportion.

b.

Provide a 95% confidence interval for the population proportion.

We assume that our wages will increase as we gain experience and become more valuable to our employers. Wages also increase because of inflation. By examining a sample of employees at a given point in time, we can look at part of the picture. How does length of service (LOS) relate to wages? The data here (data336.dat) is the LOS in months and wages for 60 women who work in Indiana banks. Wages are yearly total income divided by the number of weeks worked. We have multiplied wages by a constant for reasons of confidentiality.

(a) Plot wages versus LOS. Consider the relationship and whether or not linear regression might be appropriate. (Do this on paper. Your instructor may ask you to turn in this graph.)

(b) Find the least-squares line. Summarize the significance test for the slope. What do you conclude?

(c) State carefully what the slope tells you about the relationship between wages and length of service.

This answer has not been graded yet.

(d) Give a 95% confidence interval for the slope.
(  ,  )

worker  wages   los     size
1       44.898  39      Large
2       85.8585 122     Small
3       37.6708 100     Small
4       44.1095 168     Small
5       47.756  25      Large
6       40.8481 22      Small
7       50.5179 27      Large
8       63.4659 70      Large
9       37.2126 86      Large
10      66.0707 95      Small
11      53.5897 56      Large
12      42.5586 18      Small
13      50.3493 129     Small
14      60.3041 75      Large
15      46.2348 93      Large
16      56.1494 23      Large
17      45.4136 15      Large
18      40.9541 44      Small
19      55.3183 26      Large
20      50.7934 58      Large
21      41.2603 79      Large
22      37.3516 19      Small
23      42.1137 30      Large
24      60.4141 88      Small
25      51.9331 119     Large
26      49.6191 20      Small
27      53.1292 116     Small
28      60.8961 62      Large
29      51.3743 31      Large
30      52.4964 42      Large
31      47.748  102     Small
32      47.1194 90      Large
33      60.6775 99      Large
34      70.5214 21      Small
35      39.4673 164     Large
36      50.4703 83      Large
37      66.2801 100     Large
38      62.3078 185     Small
39      43.79   18      Large
40      54.1258 56      Small
41      39.0053 174     Small
42      52.4289 59      Small
43      57.6612 89      Large
44      51.6591 17      Small
45      50.383  73      Large
46      38.2104 40      Small
47      52.421  78      Large
48      45.5227 55      Large
49      62.5477 53      Small
50      43.9493 58      Large
51      76.2546 87      Large
52      56.4322 110     Large
53      37.8525 64      Large
54      37.132  47      Small
55      50.4954 84      Small
56      49.1702 54      Large
57      41.8979 16      Small
58      45.3906 40      Large
59      57.8986 41      Small
60      40.3537 34      Large

The Consumer Reports Restaurant Customer Satisfaction Survey is based upon 148,599 visits to full-service restaurant chains.† One of the variables in the study is meal price, the average amount paid per person for dinner and drinks, minus the tip. Suppose a reporter for a local newspaper thought that it would be of interest to her readers to conduct a similar study for restaurants located in her city. The reporter selected a sample of 8 seafood restaurants, 8 Italian restaurants, and 8 steakhouses. The following data show the meal prices ($) obtained for the 24 restaurants sampled.

Use α = 0.05 to test whether there is a significant difference among the mean meal price for the three types of restaurants.

State the null and alternative hypotheses.

H₀: At least two of the population means are equal.
H_a: At least two of the population means are different.H₀: μ_Italian ≠ μ_Seafood ≠ μ_Steakhouse
H_a: μ_Italian = μ_Seafood = μ_Steakhouse    H₀: μ_Italian = μ_Seafood = μ_Steakhouse
H_a: μ_Italian ≠ μ_Seafood ≠ μ_SteakhouseH₀: μ_Italian = μ_Seafood = μ_Steakhouse
H_a: Not all the population means are equal.H₀: Not all the population means are equal.
H_a: μ_Italian = μ_Seafood = μ_Steakhouse

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to four decimal places.)

p-value =

What is your conclusion?

Reject H₀. There is sufficient evidence to conclude that the mean meal prices are not all the same for the three types of restaurants.Reject H₀. There is not sufficient evidence to conclude that the mean meal prices are not all the same for the three types of restaurants.    Do not reject H₀. There is not sufficient evidence to conclude that the mean meal prices are not all the same for the three types of restaurants.Do not reject H₀. There is sufficient evidence to conclude that the mean meal prices are not all the same for the three types of restaurants.

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%)?