Use the sample data and confidence level given below to complete parts​ (a) through​ (d). A research institute poll asked respondents if they felt vulnerable to identity theft. In the​ poll, n equals n=1065 and x equals 548 who said​ "yes." Use a 95 confidence level.

a) Find the best point estimate of the population proportion p. Round to three decimal places as​ needed.)

b) Identify the value of the margin of error E. E = (Round to three decimal places as​ needed.)​

​c) Construct the confidence interval < p <. ​(Round to three decimal places as​ needed.)

​d) Write a statement that correctly interprets the confidence interval. Choose the correct answer below.

A.One has 9999​% confidence that the sample proportion is equal to the population proportion.

B.There is a 9999​% chance that the true value of the population proportion will fall between the lower bound and the upper bound.

C.One has 9999​% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.Your answer is correct.

D. 9999​% of sample proportions will fall between the lower bound and the upper bound.

How to calculate the P(A|B) of a 8 sided die that is rolled one time?

Event A occurs whenever a less than 2 is rolled. Event B occurs whenever an even number is rolled. Event C occurs whenever a 1 or 3 is rolled. What are the complements, probabilities, the intersections and the unions and are they statistically independent?

what are the P(A|B) and the P(C|A)?

Using R Studio

Use the two iid samples. (You can copy and paste the code into R). They both come from the same normal distribution.

X = c(-0.06, 1.930, 0.608 -0.133,0.657, -1.284, 0.166, 0.963, 0.719, -0.896)

Y = c(0.396, 0.687, 0.809, 0.939, -0.381, -0.042, -1.529, -0.543, 0.758, -2.574, -0.160, -0.713, 0.311, -0.515, -2.332, -0.844, -0.942, 0.053, 0.066, 0.942, -0.861, -0.186, -0.947, -0.110, 0.634, 2.357, 0.201, -0.428, -1.661, 0.395)

(a) Report 95% confidence interval for the mean of X. Should we use t-CI or z-CI?

(b) Report 95% confidence interval for the mean of X, if we have already known the population variance is 1. Should we use t-CI or z-CI?

(c) Report 90% confidence interval (t-CI) for the mean of Y .

(d) Report 95% confidence interval (t-interval) for the mean of Y and compare the result with the result in part (c). Describe the relationship between the confidence level and the width of the CI.

(e) Assuming the CIs reported in (a) and (c) are valid, compare the result of (a) and (c) and describe the relationship between the sample size and the width of the CI.

There was a certain class in which students had completed the work load assigned was very heavy. The instructor knew that the amount learned was directly related to that work load. The instructor surveyed 40 former students and asked if they would have been willing to actually learn less if that had meant less work. The instructor hoped that the ultimate goal of a student was to learn and so that less than 25 % of students would agree to learn less. The results of the survey showed 7 students would have been willing to actually learn less if that had meant less wor.

Is there sufficient evidence at the alpha = .05 level of significance to support the instructors hope and what do you conclude? What is the p-value of your test statistic.

9.13

Using the SHHS data in Table 2.10,fit all possible multiple regression models (without interactions) that predict the y variable serum total cholesterol from diastolic blood pressure,systolic blood pressure,alcohol,carbon monoxide and cotinine. Scrutinize your results to understand how the x variables act in conjuction.For these data,which is the "best " multiple regression model for cholesterol? What percentage of variation does it explain?

Find the expected count and the contribution to the chi-square statistic for the (Group 1, Yes) cell in the two-way table below. Yes No Group 1 711 263 Group 2 1159 313 Round your answer for the excepted count to one decimal place, and your answer for the contribution to the chi-square statistic to three decimal places. Expected count= contribution to the chi-square statistic=

Raw scores on behavioral tests are often transformed for easier comparison. A test of reading ability has mean 55 and standard deviation 5 when given to third graders. Sixth graders have mean score 77 and standard deviation 7 on the same test. To provide separate "norms" for each grade, we want scores in each grade to have mean 100 and standard deviation 20. (Round your answers to two decimal places.)

(a) What linear transformation will change third-grade scores x into new scores xnew = a + bx that have the desired mean and standard deviation? (Use b > 0 to preserve the order of the scores.)

(b) Do the same for the sixth-grade scores.

(c) David is a third-grade student who scores 75 on the test. Find David's transformed score.


Nancy is a sixth-grade student who scores 75. What is her transformed score?


Who scores higher within his or her grade?

The administrators of the city's Stormwater Program are interested in evaluating the public's knowledge of the causes and effects of stormwater pollution. They set up an information booth at the city's Earth Day celebration, and people who visit the booth are offered the opportunity to complete a survey on their knowledge of stormwater pollution.

(a.) If the population of interest is adult residents of the city, discuss any sources of bias that might limit the usefulness in using this survey to draw conclusions about this population.

(b.) The survey at the Earth Day celebration was intended to be used as a pilot study to make sure the questions were not ambiguous. The full survey is to be an online survey. Residents are to be made aware of the survey through information mailed with their utility bills, and asked to go online to complete the survey. Discuss any sources of bias that might be contained in the full survey.

(c.) Suppose we select a random sample of utility customers. Only the residents in the sample are to be made aware of the survey through information mailed with their utility bills, and asked to go online to complete the survey. Does this have any advantages or disadvantages over the full survey in part (b) in terms of possible bias? Explain.

The community bank survey asked about net income and reported the percent change in net income between the first half of last year and the first half of this year. The mean change for the 120 banks in the sample is 7.6%. Because the sample size is large, we are willing to use the sample standard deviation s = 20.5% as if it were the population standard deviation σ. Does the 7.6% mean increase provide evidence that the net income for all banks has changed? Assumeα= 0.05. You must show all steps as outlined in class to receive full credit.

Question 1: You will receive a prize if both a fair coin lands "heads" AND a fair die lands "6". After the coin is flipped and the die is rolled you ask if AT LEAST ONE of these events has occurred and you are told "yes."

a) Use an event tree to help calculate the probability of winning the prize

b) Formally calculate the probability of you winning the prize, whilst answering these questions in each step of your answer

i. Specify the joint distribution, ?(?,?,?,?), in terms of its constituent conditional distributions

ii. Specify the full prior probabilities for the coin, ?(?) and the dice, ?(?), events

iii. Specify the full conditional distribution for the event that the coin is heads or dice is six, ?=?∪?

iv. Specify the full conditional distribution for the event that the coin is heads and dice is six, ?=?∩?

v. Use the fundamental rule to derive the distribution for the coin and dice events given the event that the coin is heads or dice is six, ?(?,?|?=????)

vi. Calculate the probability of observing that the coin is heads or dice is six, ?(?=????)

vii. Specify and calculate the posterior distribution for the joint probability of the coin and dice events given the event that the coin is heads or dice is six, ?(?,?|?=????)

viii. Derive the marginal distribution for the event that coin is heads and dice is six given we know the event heads or six, ?=???? | ?=???? , has occurred

ix. Calculate the marginal probability that the coin is heads and dice is six given we know the event heads or six, ?(?=????|?=????)

x. Calculate the probability of you winning the prize

Note: Your formal calculation must include mathematical notation and the derivation of every step in the calculation without ambiguity. Your model must include these variables: ? for the coin, ? for the dice, ? for the event that coin is heads or dice is six and ? for the event that coin is heads and dice is six. Correct answer that take short cuts or ignore the full set of variables will be penalised. Note, also by ‘full’ distributions above it is meant that all relevant states for the variables are used in the calculations.

As part of the study on ongoing fright symptoms due to exposure to horror movies at a young age, the following table was presented to describe the lasting impact these movies have had during bedtime and waking life:

(a) What percent of the students have lasting waking-life symptoms? (Round your answer to two decimal places.)
%

(b) What percent of the students have both waking-life and bedtime symptoms? (Round your answer to two decimal places.)
%

(c) Test whether there is an association between waking-life and bedtime symptoms. State the null and alternative hypotheses. (Use α = 0.01.)

Null Hypothesis:

H₀: Bedtime symptoms cause waking symptoms.H₀: Waking symptoms cause bedtime symptoms.     H₀: There is a relationship between waking and bedtime symptoms.H₀: There is no relationship between waking and bedtime symptoms.

Alternative Hypothesis:

H_a: Bedtime symptoms cause waking symptoms.H_a: There is no relationship between waking and bedtime symptoms.     H_a: There is a relationship between waking and bedtime symptoms.H_a: Waking symptoms cause bedtime symptoms.

State the χ² statistic and the P-value. (Round your answers for χ² and the P-value to three decimal places.)

Conclusion:

We do not have enough evidence to conclude that there is a relationship.

We have enough evidence to conclude that there is a relationship.    

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 (data197.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.


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

worker  wages   los     size
1       55.2228 62      Large
2       72.6471 43      Small
3       64.7938 28      Small
4       83.1899 52      Small
5       74.6722 77      Large
6       45.3301 156     Small
7       43.6869 16      Large
8       54.4083 253     Large
9       41.5534 134     Large
10      43.4756 79      Small
11      64.5044 105     Large
12      51.4939 172     Small
13      46.8273 39      Small
14      61.5737 59      Large
15      40.4888 192     Large
16      42.5272 77      Large
17      44.0275 98      Large
18      49.1887 45      Small
19      41.9127 110     Large
20      44.5922 59      Large
21      45.2959 41      Large
22      67.5828 63      Small
23      49.1524 119     Large
24      49.6111 26      Small
25      41.2403 62      Large
26      64.3923 114     Small
27      48.8709 73      Small
28      53.2818 55      Large
29      52.4652 26      Large
30      38.5335 65      Large
31      42.8304 56      Small
32      62.9239 25      Large
33      37.9765 42      Large
34      60.7783 105     Small
35      64.4702 78      Large
36      63.7232 89      Large
37      56.527  41      Large
38      50.0613 188     Small
39      40.3449 59      Large
40      48.4422 37      Small
41      72.214  55      Small
42      44.3634 79      Small
43      68.0063 81      Large
44      52.1295 120     Small
45      40.9163 72      Large
46      54.7163 24      Small
47      42.0233 35      Large
48      115.9302        24      Large
49      39.8092 127     Small
50      40.779  40      Large
51      37.6496 65      Large
52      49.833  121     Large
53      53.0945 143     Large
54      76.8681 34      Small
55      53.227  24      Small
56      44.4872 136     Large
57      59.3171 111     Small
58      59.3403 79      Large
59      44.9148 19      Small
60      45.3378 72      Large

Using the correlation coefficient of the normal probability​ plot, is it reasonable to conclude that the population is normally​ distributed? Select the correct choice below and fill in the answer boxes within your choice.

A. No. The correlation between the expected​ z-scores and the observed​ data, _____ does not exceed does not exceed

the critical ​value, _______.​Therefore, it is not reasonable to conclude that the data come from a normal population.

B. Yes. The correlation between the expected​ z-scores and the observed​ data, _______ exceeds the critical​ value, ______. ​Therefore, it is reasonable to conclude that the data come from a normal population.

C. Yes. The correlation between the expected​ z-scores and the observed​ data, _______ exceeds the critical value _____. ​Therefore, it is not reasonable to conclude that the data come from a normal population.

D. No. The correlation between the expected​ z-scores and the observed​ data, _______ does not exceed the critical​value, ______. ​Therefore, it is reasonable to conclude that the data come from a normal population.