The null and alternate hypotheses are:

H₀ : μ₁ = μ₂
H₁ : μ₁ ≠ μ₂

A random sample of 9 observations from one population revealed a sample mean of 24 and a sample standard deviation of 3.7. A random sample of 6 observations from another population revealed a sample mean of 28 and a sample standard deviation of 4.6.

At the 0.01 significance level, is there a difference between the population means?

a. State the decision rule. (Negative values should be indicated by a minus sign. Round your answers to 3 decimal places.)

b. Compute the pooled estimate of the population variance. (Round your answer to 3 decimal places.)

c. Compute the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)

d. State your decision about the null hypothesis.​

e.The  p-value is​

• How, do you think, the music industry can benefit from the application of Big Data technology?

Professor X travels from Houston to Istanbul with stop overs in New York and Londa. At each stop he luggage is transferred from one plane to another. In each airport, including Houston, chances are that with probability p her luggage is not placed in the right plane. Professor X finds that his suitcase has not reached Istanbul. What are the chances that the mishap took place in Houston, New York, and London, respectively?

Problem 3: A Corporate Perceptions Study surveyed 200 readers and asked them on how they would rate XYZ Corporation on the “Quality of Management” and the “Reputation of the Company”. The two variables of the study were rated on a categorical scale as excellent, good, and fair. The sample data on 200 responses for the study is summarized as follows. Conduct an appropriate hypothesis test for this problem to check if the variables are independent of each other. Reputation of Company Quality of Management Excellent Good Fair Excellent 39 26 5 Good 36 34 10 Fair 25 10 15 Problem 3d) Calculate and show the chi-square components in a table. What is the test statistic value? Problem 3e) Type in the Excel function with inputs to be used to determine p-value. What is the p-value? Conduct Hypothesis test using p-value approach (at .004 level of significance). What is the decision on the hypothesis test? Problem 3f) Type in the Excel function with inputs to be used to determine Critical-value. What is the Critical-value? Conduct Hypothesis test using Critical-Value approach (at .008 level of significance). What is the decision on the hypothesis test? Problem 3g) Are the decisions under the p-value and critical-value approaches different? If they are different, why are they different? If they are not different, why are they not different? Problem 3h) Based on test decisions under parts 3e) and 3f), what conclusion would you draw? Does your conclusion sound meaningful?

Identify the population, variables, types of variables, type of sampling plan used, and any potential sources of bias in the following situation. Researchers spend one Saturday night waiting outside of a bar to conduct a survey on attitudes towards drinking and driving. They ask every 5th person who comes out of the bar the number of drinks they had that night, their age, and if they believe that drinking and driving is a serious problem.

• What new Big Data trends in the field of sports do you think will impact the sport and audiences the most? why?

A researcher recruited a sample of 5 women who were interested in trying a new six-week program of diet and exercise designed to promote healthy weight loss. She plans to use the .01 significance level to test whether weight decreases (on average) for women using this program. The table below gives the starting and end weights (in pounds) for each of the five women.

a. Should these samples be considered paired or independent? Why?

b. Chose the appropriate formula for the test statistic and finds its value.

c. Describe the rejection region for this test.

d. What should the researcher conclude?

e. Find a 95% confidence interval for the mean weight-loss of women using this program. What mean weightless would you predict for women who follow this program?

An independently selected sample of five men also participated in the same study. The table below shows results for the number of pounds lost by the five men and the five women in the study. The researcher will use the .01 significance level to test whether (on average) the program produces different weight loss results for men and women. You may assume the population variances are equal (although the sample variances are not).

f. Formulate the hypothesis for this test.

g. Should the pooled-sample variance be used in this situation? Why?

h. Choose the appropriate formula for the test statistic and find its value.

i. What is the rejection region for this test?

j. What should the researcher conclude?

Propose the key factors in designing a questionnaire.

Plug-in estimates: Unbiased estimates are not transformation invariant, Show that:

a.) In N(μ, σ²), x̄² is not an unbiased estimate of μ²

b.) In Exponential(λ), e^(-x̄ ) is not an unbiased estimate of λ.

c.) In Poisson(λ), e^(-x̄ ) is not an unbiased estimate of e^λ.

d.) s is not an unbiased estimate of σ

Annual revenues are used to predict the value of a baseball franchise. A sample of 32 franchises was used. An analysis of variance of these data showed that b1= 5.0785 and Sb1 = 0.2357.

a. At the 0.05 level of​ significance, is there evidence of a linear relationship between annual revenue and franchise​ value?

b. Construct a​ 95% confidence interval estimate of the population​ slope, β1.

a: Compute the test statistic. tSTAT= ​(Round to four decimal places as​ needed.)

The critical​ value(s) is(are) ​(Round to four decimal places as​ needed.)

b: The​ 95% confidence interval is ____ ≤ β1 ≤ ____ ​(Round to four decimal places as​ needed.)

A researcher conducts a study of white and black attitudes toward the police in her community.

The percentage of a random sample of white respondents (N = 200) who say they have a favorable attitude toward the police is 53%. The percentage of a random sample of black respondents (N = 200) who say they have a favorable attitude toward the police is 45%.

You are asked if there is a real difference between the percentage of whites and blacks who have a positive attitude toward the police in the larger population, or is this sample difference likely to have occurred by random chance or sampling error.

How do you respond? Explain your answer.

Construct a 95% confidence interval for the proportion of Blacks in the population who have a favorable attitude toward the police

A​ gender-selection technique is designed to increase the likelihood that a baby will be a girl. In the results of the​ gender-selection technique,

861861

births consisted of

443443

baby girls and

418418

baby boys. In analyzing these​ results, assume that boys and girls are equally likely.

a. Find the probability of getting exactly

443443

girls in

861861

births.

b. Find the probability of getting

443443

or more girls in

861861

births. If boys and girls are equally​ likely, is

443443

girls in

861861

births unusually​ high?

c. Which probability is relevant for trying to determine whether the technique is​ effective: the result from part​ (a) or the result from part​ (b)?

d. Based on the​ results, does it appear that the​ gender-selection technique is​ effective?

In 2014, a group of students was interested in investigating prices of rental accommodation in suburbs of Brisbane that are close to the CBD and collected information on a total of 200 randomly chosen dwellings in four inner western suburbs. A subset of this data, relating to rental apartments in these suburbs is included below. The variables are:

Per week: weekly rental price for the apartment ($);

Bedrooms: number of bedrooms in the apartment;

Sqm: size of the apartment (m²)

Furnished: whether the apartment was furnished or not (yes/no).

The values are;

265,2,59,No

305,2,70,No

300,1,72,No

320,3,66,No

340,2,113,Yes

330,2,58,Yes

355,2,63,No

345,2,57,Yes

355,2,61,No

360,2,114,Yes

355,2,75,Yes

360,2,68,No

365,2,64,No

370,1,69,No

390,2,73,Yes

380,2,85,Yes

390,2,56,Yes

370,2,56,Yes

385,2,59,Yes

380,2,65,Yes

385,2,62,Yes

400,2,65,No

415,2,69,Yes

400,3,63,No

405,3,70,No

420,2,77,No

435,2,84,Yes

435,2,83,Yes

455,2,73,Yes

450,2,72,Yes

485,2,68,No

500,2,76,Yes

535,2,97,No

290,1,60,No

305,1,63,Yes

330,2,65,No

310,2,70,No

335,2,64,No

330,2,62,No

345,2,79,No

355,1,81,No

340,2,66,No

345,1,60,No

345,2,64,No

355,2,73,No

385,2,61,No

380,2,78,No

405,2,81,No

410,2,76,Yes

430,2,80,No

440,2,61,No

450,3,86,No

485,3,91,No

500,1,87,No

545,1,97,Yes

345,3,86,No

400,2,72,No

400,2,74,No

480,2,73,Yes

755,3,87,No

760,3,77,No

770,3,113,No

824,2,109,No

860,3,104,No

295,1,70,No

290,1,54,No

295,1,61,No

325,1,61,No

340,2,56,No

355,2,61,No

365,2,95,No

420,1,75,No

420,2,66,No

440,2,74,No

480,3,72,No

465,3,87,No

470,1,87,Yes

490,1,81,Yes

495,2,76,No

505,2,97,No

530,2,77,No

545,2,97,No

560,2,79,No

550,2,78,No

560,3,75,No

565,1,96,Yes

580,2,85,Yes

605,3,84,No

605,2,93,Yes

610,2,78,Yes

620,2,87,No

665,2,88,No

700,2,80,No

750,3,97,Yes

740,3,124,No

805,3,101,No

860,3,98,No

960,3,123,Yes

990,3,102,Yes

1195,3,133,No

1190,3,137,No

1405,3,148,Yes

1490,3,154,No

Q1)

The students were interested in exploring the relationship between apartment size and weekly rent. Using R, fit a linear regression relating weekly rent to apartment size; that is, a model of the form:

per. week = β0 + β1 sqm + ε,

and answer the following questions:

(a) What is the MSE (mean-squared error) for this regression? What are the degrees of freedom associated with this value?

(b) Find a 95% confidence interval for the intercept parameter in this model. You may take relevant statistics from the R output for your regression, but please show full working.

(c) Another group of students suggest that apartment pricing is known to increase with apartment size at an average rate of $12 per square metre. Carry out a formal test of this hypothesis and interpret the resulting p-value, using α = 0.05.

(d) You intend to use your research to help inform fair weekly rent for a friend, who is looking at renting an apartment of size 60 m2 . Using R, find a 95% prediction interval for the weekly rent of this apartment.

(e) Construct a residual and normal quantile plot for this analysis. Are there any issues with the underlying assumptions of linearity and/or homoscedasticity?

Please answer this question by using R code !!!!!!! it is very important