The Human Resource department of a multi-national bank is preparing a survey about workplace equality. The survey will target employees of three departments: retail banking, commercial banking, and global banking. There are 1800, 2300, and 900 employees in these departments respectively. A total of 200 employees will be selected randomly for the survey.

The following table shows the number of weekly working hours of 14 employees in a sample dataset: 38 41 41 43 46 48 49 51 54 54 57 64 64 64

(d) Find the 30th percentile and third quartile of the data.

(e) Write a simple report about the weekly working hours of the employees by referring to your findings in part (c) and part (d).

(f) The standard working hour per week is 40 hours. Every extra working hour would have an hourly allowance of $35. Use X to denote the weekly working hour of an employee and Y to denote the weekly allowance of that employee. Express Y in terms of X. Hence, find the sample mean and sample standard deviation of the weekly allowance of an employee.

247247

261261

269269

272272

275275

279279

280280

284284

285285

285285

285285

288288

289289

292292

292292

295295

295295

300300

311311

504504

A.

The​ outlier(s) is/are

nothing

pounds.

​(Type a whole number. Use a comma to separate answers as​ needed.)

B.

There are no outliers.

The median is

nothing

pounds.

​(Type an integer or decimal rounded to one decimal place as​ needed.)

The untrimmed mean is

nothing

pounds.

​(Type an integer or decimal rounded to one decimal place as​ needed.)

The​ 10% trimmed mean is

nothing

pounds.

​(Type an integer or decimal rounded to one decimal place as​ needed.)

The​ 20% trimmed mean is

nothing

pounds.

​(Type an integer or decimal rounded to one decimal place as​ needed.)

Compare the values. Choose the correct answer below.

A.

The​ median, untrimmed​ mean, and​ 10% trimmed mean are close to each other.​ However, the​ 20% trimmed mean is significantly different from those values.

B.

The​ median, untrimmed​ mean, and​ 20% trimmed mean are close to each other.​ However, the​ 10% trimmed mean is significantly different from those values.

C.

All of the values are close to each other.

D.

The untrimmed​ mean, 10% trimmed​ mean, and​ 20% trimmed mean are close to each other.​ However, the median is significantly different from those values.

E.

The​ median, 10% trimmed​ mean, and​ 20% trimmed mean are close to each other.​ However, the untrimmed mean is significant

In a simple random sample of 1600 young​ people, 86​% had earned a high school diploma. Complete parts a through d below. a. What is the standard error for this estimate of the percentage of all young people who earned a high school​ diploma? .0096 nothing ​(Round to four decimal places as​ needed.) b. Find the margin of​ error, using a​ 95% confidence​ level, for estimating the percentage of all young people who earned a high school diploma. nothing​% ​(Round to one decimal place as​ needed.) c. Report the​ 95% confidence interval for the percentage of all young people who earned a high school diploma. left parenthesis nothing % comma nothing % right parenthesis ​(Round to one decimal place as​ needed.) d. Suppose that in the​ past, 80% of all young people earned high school diplomas. Does the confidence interval you found in part c support or refute the claim that the percentage of young people who earn high school diplomas has​ increased? Explain. A. The interval does not support this claim. This is because​ 80% is not in the​ interval, and all values are above​ 80%. B. The interval supports this claim. This is because​ 80% is not in the​ interval, and all values are above​ 80%. C. The interval does not support this claim. This is because​ 80% is in the interval. D. The interval supports this claim. This is because​ 80% is in the interva

The National Study of the Changing Work Force has just completed an extensive survey of 2958 wage and salaried workers on issues ranging from relationships with their bosses to household chores. The data were gathered through hour-long telephone interviews with a nationally representative sample (The Wall Street Journal). In response to the question “What does success mean to you?” 1538 responded, “Personal satisfaction from doing a good job.”

Based on your professional skills in statistical analysis, you have just been hired to help with an analysis and interpretation of this survey.

If p be the population proportion of all wage and salaried workers who would respond the same way to the stated question, what would be the 80% (or 90% or 95% or 99%) confidence interval for p.

Make sure that you show your computations.

Complete the following table:

A study was done using a treatment group and a placebo group. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed​ populations, and do not assume that the population standard deviations are equal. Complete parts​ (a) and​ (b) below. Use a 0.10 significance level for both parts

    Treatment                Placebo

μ          μ1                    μ2

n          27                    40

x          2.38                 2.61

s           0.68                 0.99

a. Test the claim that the two samples are from populations with the same mean.

What are the null and alternative​ hypotheses?

A. H0​: μ1≠μ2

H1​: μ1<μ2

B. H0​: μ1=μ2

H1​: μ1≠μ2

C. H0​: μ1<μ2

H1​: μ1≥μ2

D. H0​: μ1=μ2

H1​: μ1>μ2

The test​ statistic, t, is _____. ​(Round to two decimal places as​ needed.)

The​ P-value is _____. ​(Round to three decimal places as​ needed.)

State the conclusion for the test.

A. Fail to reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean.

B. Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean.

C. Reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean.

D. Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean.

b. Construct a confidence interval suitable for testing the claim that the two samples are from populations with the same mean.

_____<μ1−μ2< _____

​(Round to three decimal places as​ needed.)

Mitchell and Cameron have two adopted children. We are interested in the biological sex (Male/Female) of their children.

(a)[3 pts] Give the sample space for thesex of their two children.1 full point out of the 3will be for using the correct format.

(b)[2 pts] What is the probability that both children are girls, given that the first child is a girl? You do not have to show a lot of mathematical work for this, but the more work you show, the more partial credit you may get if your answer is wrong.

(c)[3 pts] We ask Mitchell: “Do you guys have at least one daughter?”He responds: “Yes!” Knowing that Mitch & Cam have at least one daughter, what is the probability now that both children are girls?

Thank u

Is it possible to predict the annual number of business bankruptcies by the number of firm births (business starts)? The following table shows the number of business bankruptcies (1,000s) and the number of firm births (10,000s) for a six-year period. Use these data to develop the equation of the regression model to predict the number of business bankruptcies by the number of firm births. Discuss the meaning of the slope.

r =

The r value represents a relatively :

strong positive, strong negative , moderate positive or moderate negative. (choose one)

relationship between the number of firm births and the number of business bankruptcies.

Y is ________________ + X is _______________________

The slope of the line means that for every 10,000 increase of firm births, the number of business bankruptcies is predicted to increase by ______________

.

Data from a recent year showed that 72​% of the tens of thousands of applicants to a certain program were accepted. A company that trains applicants claimed that 216 of the 280 students it trained that year were accepted. Assume these trainees were representative of the population of applicants. Has the company demonstrated a real improvement over the​ average? Find z score

Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 146 minutes with a standard deviation of 12minutes. Consider 49 of the races.

Let X = the average of the 49 races.

a)Give the distribution of X. (Round your standard deviation to two decimal places.)

X~___(___,___)

b)Find the probability that the average of the sample will be between 145 and 148 minutes in these 49 marathons. (Round your answer to four decimal places.)

_________

c) Find the 70th percentile for the average of these 49 marathons. (Round your answer to two decimal places.)

_____min

d) Find the median of the average running times.

____min

Heine Brothers’, a coffee shop chain from Louisville, Kentucky, wants to determine if the amount of time customers spend in the “Germantown” coffee shop is different from the “Crescent Hill” coffee shop. An employee at each location times the amount of time 20 customers spends in each coffee shop. For the “Germantown” location the sample mean is 56.70 minutes with a sample standard deviation of 13.48 minutes. For the “Crescent Hill” location, the sample mean is 77.25 minutes with a standard deviation of 37.06 minutes.

• (a) Determine a 90% confidence interval for the difference in the mean time customers spend in each location.
• (b) Determine if there is evidence that the average time customers spend in each location is different (use ). What is the p-value or level of significance of this test?

a1) If a researcher wanted to test which fever reducer between Tylenol and ibuprofen work faster. What should they do? Describe very clearly the process all the way down to what the p-value would tell you.

a2) Describe very clearly what pooling the variance assumes.

2. To study the effect of caffeine on cognitive ability, a cognitive ability test was administered to 8 students under two conditions on different days: Condition A) Without caffeine, and Condition B) after the students enjoyed a pumpkin spice latte. The students were randomized to determine if they did Condition A first or Condition B first (on separate days). The following are the results from the test:

• (a) Estimate a 90% confidence interval for the change in test score between Condition A and condition B.
• (b) Determine if there is evidence that caffeine improved performance on the cognitive ability tests at a fixed Type I error rate of 0.05.
• (c) What is the level of significance of the test that you conducted in part (b).

A mango Supply and Demand for a tropical country are given by ;

Demand: P = 50 – (QD) and supply: P = 25 + (QS) where QD = quantity demanded of mangoes and QS = quantity supplied of mangoes

1. Draw the market supply and demand curves. What are the efficient price and efficient quantity? Explain the law of supply and the law of demand.
2. Show on your graph consumer surplus and producer surplus and calculate the values of consumer surplus and producer surplus.
3. Instead of a price ceiling, the government provides a subsidy of $8 to consumers, illustrate graphically the economics effects of this intervention
4. Compute the deadweight loss and the consumer surplus
5. Assume that the government levied a $6 tax on the consumers of mangoes. Illustrate graphically the different economics effects of the tax.

1. Steel Supply and Demand for USA

2. Show on your graph consumer surplus and producer surplus and calculate the values of consumer surplus and producer surplus.
3. The government decides to impose a price ceiling of $200. Illustrate graphically the different economics effects of such intervention in this market.
4. Compute the deadweight loss generated by the government intervention and the new consumer surplus .
5. Instead of a price ceiling the government provides a subsidy of $50 to consumers, illustrate graphically the economics effects of this intervention.
6. Compute the deadweight loss and the consumer surplus
7. Assume that the government levied a $50 tax on the suppliers of steel. Illustrate graphically the different economics effects of the tax ( and compute the DWL and specify the tax burden ).

8. The government decides to impose a price floor of $750. Illustrate graphically the different economics effects of such intervention in this market.

9. Compute the deadweight loss generated by the government intervention and the producer surplus.

10. Assume that the government levied a $25 tax on the consumers of steel. Illustrate graphically the different economics effects of the tax.

Question 2: (Marks: 2)

Intelligence quotients (IQs) on the Stanford-Binet intelligence test are normally distributed with a mean of 100 and a standard deviation of 16. In Exercises a–d, use the 68–95–99.7 Rule to find the percentage of people with IQs

1. between 84 and 116

2. between 84 and 100

3. above 132

4. below 68