A direct mail company wishes to estimate the proportion of people on a large mailing list that will purchase a product. Suppose the true proportion is 0.07.

If 402 are sampled, what is the probability that the sample proportion will be less than 0.04? Round your answer to four decimal places.

Hospital records show that 12% of all patients are admitted for surgical treatment (ST), 16% are admitted for obstetrical treatment (OT), and 2% receive both obstetrical and surgical treatment.

(a) Describe in terms of ST and OT the event that a newly admitted patient will receive at least one of these treatments and then compute its probability.

(b) Describe in terms of ST and OT the event that a newly admitted patient will receive surgical treatment but not obstetrical treatment and then compute its probability.

(c) Describe in terms of ST and OT the event that a newly admitted patient receives neither of these treatments and then compute its probability.

(d) If a newly admitted patient receives obstetrical treatment, what is the probability that the patient also receives surgical treatment?

(e) Are OT and ST independent events? Explain.

MPG
36.3
41
36.9
37.1
44.9
36.8
30
37.2
42.1
36.7
32.7
37.3
41.2
36.6
32.9
36.5
33.2
37.4
37.5
33.6

1. The EPA collects data on 20 cars and calculates their gas mileage in miles per gallon (MPG).

a) Make a histogram for the data with the first class of [30, 32).

b) Find the mean, the median and the standard deviation of the data.

c) Find the Q1, Q3, IQR and fences.

d) Using the modified box-plot methodology determine if there are any outliers and justify. You do not have to make the box-plot!

e) Create a new variable by subtracting the mean from each observation and then dividing the difference by the standard deviation.

f) Find the mean, median and standard deviation of the new variable.

g) In one or two sentences, describe the original data.

A community youth group is having a raffle to raise funds. Several community businesses have donated prizes. The prizes and their retail values are listed in the table below. Each prize will be given away, regardless of the number of raffle tickets sold. Tickets are sold for $16 each. Determine the expected value of a ticket, and discuss whether it would be to your financial advantage to buy a ticket under the given circumstances. (Enter your answers to two decimal places.)

(a) 1000 tickets are sold.
$   

Should you buy a ticket?

Yes No     

(b) 2000 tickets are sold.
$  

Should you buy a ticket?

YesNo     

(c) 3000 tickets are sold.
$  

Should you buy a ticket?

YesNo    

Question 5 (1 point)

A student at a university wants to determine if the proportion of students that use iPhones is less than 0.46. The hypotheses for this scenario are as follows. Null Hypothesis: p ≥ 0.46, Alternative Hypothesis: p < 0.46. If the student takes a random sample of students and calculates a p-value of 0.8906 based on the data, what is the appropriate conclusion? Conclude at the 5% level of significance.

Question 5 options:

Question 6 (1 point)

You hear on the local news that for the city of Kalamazoo, the proportion of people who support President Trump is 0.37. However, you think it is greater than 0.37. The hypotheses you want to test are Null Hypothesis: p ≤ 0.37, Alternative Hypothesis: p > 0.37. You take a random sample around town and calculate a p-value for your hypothesis test of 0.9793. What is the appropriate conclusion? Conclude at the 5% level of significance.

Question 6 options:

Question 7 (1 point)

A medical researcher wants to determine if the average number of days spent in the hospital after a certain procedure is different from 9.8 days. If the researcher conducts a hypothesis test, what will the null and alternative hypotheses be?

Question 7 options:

Question 8 (1 point)

Consumers Energy states that the average electric bill across the state is $39.09. You want to test the claim that the average bill amount is actually different from $39.09. What are the appropriate hypotheses for this test?

Question 8 options:

The life of light bulbs is distributed normally. The standard deviation of the lifetime is 20 hours and the mean lifetime of a bulb is 590 hours. Find the probability of a bulb lasting for at most 626 hours. Round your answer to four decimal places.

Use a table of cumulative areas under the normal curve to find the​ z-score that corresponds to the given cumulative area. If the area is not in the​ table, use the entry closest to the area. If the area is halfway between two​ entries, use the​ z-score halfway between the corresponding​ z-scores. If​ convenient, use technology to find the​ z-score.

0.054

Find the mean for the following frequency tables. (Round your answers to one decimal place.)

In a maze running study, a rat is run in a T maze and the result of each run recorded. A reward in the form of food is always placed at the right exit. If learning is taking place, the rat will choose the right exit more often than the left. If no learning is taking place, the rat should randomly choose either exit. Suppose that the rat is given n = 100 runs in the maze and that he chooses the right exit x = 63 times. Would you conclude that learning is taking place? (Use α = 0.01.)

State the null and alternative hypotheses.

H₀: p ≠ 0.63 versus H_a: p = 0.63H₀: p = 0.63 versus H_a: p ≠ 0.63    H₀: p = 0.5 versus H_a: p > 0.5H₀: p = 0.5 versus H_a: p ≠ 0.5H₀: p < 0.5 versus H_a: p > 0.5

Find the test statistic and the p-value. (Round your test statistic to two decimal places and your p-value to four decimal places.)

State your conclusion.

The p-value is less than alpha, so H₀ is rejected. There is insufficient evidence to indicate that learning is taking place.The p-value is greater than alpha, so H₀ is not rejected. There is sufficient evidence to indicate that learning is taking place.    The p-value is less than alpha, so H₀ is rejected. There is sufficient evidence to indicate that learning is taking place.The p-value is greater than alpha, so H₀ is not rejected. There is insufficient evidence to indicate that learning is taking place.

please answer step by step

In a survey of 1010 Canadian adults, 780 say that the energy situation in Canada is very or fairly serious.

1. Find the point estimate for the population proportion

2. Construct a 95% confidence interval for the population proportion.

a) The critical value

b) The margin of error

c) The lower limit of the interval

d) The upper limit of the interval

3. Find the minimum sample size needed to estimate the population proportion at the 99% confidence level in order to ensure that the estimate is accurate within 5 % of the population proportion.

a) The critical value

b) The margin of error

c) The sample size

A manager of unknown ability is managing an investment fund. Well-managed funds rise in value in 60% of time periods, while badly managed funds only rise in value 40% of the time. It is observed that a particular fund rises in value on four consecutive occasions. Assuming that there is a prior probability of 0.5 that the fund is well-managed:

3.1 (10 points) What would be the rational investor’s estimate of the probability of the fund being well managed, after observing four consecutive rises?
3.2 (5 points) If the investor suffers from one of the ”Law of Small Numbers” biases, how would her estimate be different from the rational investor? Which bias does she potentially suffer from?

(3) Logistic regression

A financial institution that issues credit cards for subprime borrowers wants to identify its credit card applicants who do not exceed a default chance threshhold of 30% to approve an application. It randomly selected 41 past credit card holders and investigated their monthly salary, monthly debt, and marital status at the time of issuance of its credit card and whether they defaulted after taking the credit card. The data is available as DefaultRate.txt (In the data, DEFAULT = 1 means the customer defaulted and 0 otherwise; MARITAL=1 means married and 0 otherwise).

Please use R program to answer this (NO EXCEL or HANDWRITTEN), I really want to know the codes to answer these. Thank you so much in advance and be safe during these times!

(a) Identify the response variable and the predictor variables.

(b) Determine the logistic regression model for the purpose of the institution.

(c) Does the institution issue its credit card to a married customer with monthly salary of 2000 and monthly debt of 1400.

(d) Does the institution issue its credit card to a married customer with monthly salary of 3208 and monthly debt of 2200.

(e) Does the institution issue its credit card to a single customer with monthly salary of 3408 and monthly debt of 1700.

DefaultRate.txt:

DEFAULT   SALARY   DEBT   MARITAL
0   3200   1370   0
0   5230   2700   1
1    2220    1571   0
0    2789    1100   0
0    3310    1700   1
0    3512    2670    1
0    4930    3180    1
1    2220    1571    0
0    3759    1450    0
1    4310    1905    1
0    7050    4023    1
0    5230    2310    0
1    2220    1571    0
0    2789    1100    0
0    6310    3130    0
0    2260    1420    1
0    4280    2810    1
1    2020    1571    1
0    2789    1810    1
1    2310    1300    0
0    3690    2370    1
0    5230    3020    1
1    2220    1571    0
0    2789    1170    0
0    3619    1700    1
0    6290    2207    0
0    5230    2700    1
1    2220    1571    0
0    2789    1130    0
1    3310    2100    1
0    2509    1120    0
0    6230    4420    1
0    2020    971    0
0    2789    1800   1
1    4310    3500   1
0    2503    1424    1
0    5775    2912    0
0    3057    1683    1
1    5412    3705    0
0    3180    2212    1
1    6082    3200    0

Students in a statistics class are conducting a survey to estimate the mean number of units students at their college are enrolled in. The students collect a random sample of 46 students. The mean of the sample is 12.5 units. The sample has a standard deviation of 1.8 units.

What is the 95% confidence interval for the average number of units that students in their college are enrolled in? Assume that the distribution of individual student enrollment units at this college is approximately normal.

( , )

Your answer should be rounded to 2 decimal places.

How can you resolve this case study by using R studio from chapter 10 , book business statistics written by Jaggia/Kelly third edition.can you please resolve for me

Case study 10.1

Chad perrone is a financial analyst Boston studying the annual return data for the health and information technology industries. He randomly samples 20 firms in each industry and notes each firm’s annual return. A portion of the data is shown in the accompanying table.

Data for Case Study 10.1 Annual Returns (in percent) for Firms in Health and Information Technology Industries

In a report, use the sample information to

1. Provide descriptive statistic and comment on the reward and risk in each industry.
2. Determine whether the average returns in each industry differ at the 5% significance level. Assume that the population variances are not equal

Using your own words, create a simple single-subject study using a reversal design to answer a question about a behavior of interest. Describe hypothetical results.