Here are my Statistics assignment

STAT

: Introduction to Statistics Final Examination, Fall 20

Page 1 of

Refer to the following frequency distribution for Questions 1, 2,

, and 4.

The frequency distribution below shows the distribution for suspended solid concentration (in ppm) in river water of 50 different waters collected in September 2011.

Concentration (ppm)	Frequency
20 – 29	1
30 – 39			8
40 – 49
50 – 59		10
60 – 69	12
7 0 – 79	7
80 – 89			2
90 – 99

1. What percentage of the rivers had suspended solid concentration greater than or equal to 70?

2. Calculate the mean of this frequency distribution.

3. In what class interval must the median lie? Explain your answer. (You don’t have to find the median)

4. Assume that the smallest observation in this dataset is 20. Suppose this observation were incorrectly recorded as 2 instead of 20. Will the mean increase, decrease, or remain the same? Will the median increase, decrease or remain the same? Explain your answers.

Refer to the following information for Questions 5 and 6.

A coin is tossed 4 times. Let A be the event that the first toss is heads. Let B be the event that the third toss is heads.

5. What is the probability that the third toss is heads, given that the first toss is heads?

6. Are A and B independent? Why or why not?

Refer to the following data to answer questions 7 and 8. Show all work. Just the answer, without supporting work, will receive no credit.

A random sample of song playing times in seconds is as follows:

242 231 220 213 230 293

7. Find the standard deviation.

8. Are any of these playing times considered unusual in the sense of our textbook? Explain. Does this differ with your intuition? Explain.

Refer to the following situation for Questions 9, 10, and 11.

The boxplots below show the real estate values of single family homes in two neighboring cities, in thousands of dollars.

For each question, give your answer as one of the following: (a) Tinytown; (b) BigBurg; (c) Both cities have the same value requested; (d) It is impossible to tell using only the given information. Then explain your answer in each case.

9. Which city has greater variability in real estate values?

10. Which city has the greater percentage of households with values $85,000 and over?

11. Which city has a greater percentage of homes with real estate values between $55,000 and $85,000?

12. A random sample of the lifetime of 49 UltraIllum light bulbs has a mean of 3,960 hours and a standard deviation of 200 hours. Construct a 95% confidence interval estimate of the mean lifetime for all UltraIllum light bulbs.

Refer to the following information for Questions 13 and 14.

There are 500 students in the senior class at a certain high school. The high school offers two Advanced Placement math / stat classes to seniors only: AP Calculus and AP Statistics. The roster of the Calculus class shows 95 people; the roster of the Statistics class shows 86 people. There are 43 overachieving seniors on both rosters.

13. What is the probability that a randomly selected senior is in exactly one of the two classes (but not both)?

14. If the student is in the Statistics class, what is the probability the student is also in the Calculus class?

Refer to the following information for Questions 15, 16, and 17.

A box contains 10 chips. The chips are numbered 1 through 10. Otherwise, the chips are identical. From this box, we draw one chip at random, and record its value. We then put the chip back in the box. We repeat this process two more times, making three draws in all from this box.

15. How many elements are in the sample space of this experiment?

16. What is the probability that the three numbers drawn are all different?

17. What is the probability that the three numbers drawn are all even numbers?

Questions 18 and 19 involve the random variable x with probability distribution given below.

0.1

3	5
		0.1	0.3	0.4

18. Determine the expected value of x.

19. Determine the standard deviation of x.

Consider the following situation for Questions 20 and 21.

Airline overbooking is a common practice. Due to uncertain plans, many people cancel at the last minute or simply fail to show up. Air Eagle is a small commuter airline. Its past records indicate that 80% of the people who make a reservation will show up for the flight. The other 20% do not show up. Air Eagle decided to book 12 people for today’s flight. Today’s flight has just 10 seats.

20. Find the probability that there are enough seats for all the passengers who show up. (Hint: Find the probability that in 12 people, 10 or less show up.)

21. How many passengers are expected to show up?

22. Given a sample size of 65, with sample mean 726.2 and sample standard deviation 85.3, we perform the following hypothesis test.

What is the conclusion of the test at the level? Explain your answer.

Refer to the following information for Questions 23, 24, and 25.
The BestEver credit scores are normally distributed with a mean of 600 and a standard deviation of 100.

23. What is the probability that a randomly person has a BestEver credit score between 500 and 700?
24. Find the 90th percentile of the BestEver credit score distribution.
25. If a random sample of 100 people is selected, what is the standard deviation of the sample mean BestEver credit scores?

26. Consider the hypothesis test given by

In a random sample of 81 subjects, the sample mean is found to be Also, the population standard deviation is

Determine the P-value for this test. Is there sufficient evidence to justify the rejection of at the level? Explain.

27. A certain researcher thinks that the proportion of women who say that female bosses are harshly critical is greater than the proportion of men.
In a random sample of 200 women, 27% said that female bosses are harshly critical.
In a random sample of 220 men, 25% said that female bosses are harshly critical.

At the 0.05 significance level, is there sufficient evidence to support the claim that the proportion of women saying female bosses are harshly critical is higher than the proportion of men saying female bosses are harshly critical? Show all work and justify your answer.

28. Randomly selected nonfatal occupational injuries and illnesses are categorized according to the day of the week that they first occurred, and the results are listed below. Use a 0.05 significance level to test the claim that such injuries and illnesses occur with equal frequency on the different days of the week. Show all work and justify your answer.

Day

Mon

Tue

Wed

Thu

Fri

Number

Refer to the following data for Questions 29 and 30.
:

– 1

– 2

29. Is there a linear correlation between x and y at the 0.01 significance level? Justify your answer.

30. Find an equation of the least squares regression line. Show all work; writing the correct equation, without supporting work, will receive no credit.

______________________________________________________________________________

()
Px
0
:750
H
m
=
1
:750
H
m
< 0.10 a = 0 1 :530 :530. H H m m = ¹ 524. x = 27 s = 0 H 0.01 a = x

The Project

The infamous company,

Jordan & Associates, is in trouble again. The Deputy Director has just resigned in the midst of rumors going around the departments about discrimination, lawsuits, and even the company picnic has been canceled.

I would like to seek your help in putting together an Ad hoc Statistics Report to be submitted to the CEO so that he can make the appropriate corrective, proactive, and retroactive decisions for the troubled company.

The Report Format
As you might have known already, my brother, the Jordan & Associates CEO is a very difficult person: his way or the highway. He is also insistence on proper report format. Nonetheless, we have to address quite a few issues, which are listed in the later section. Meanwhile, please follow the standard Jordan & Associates report format as follow:

Make a cover page entitled:
Ad-hoc
Statistics Report submitted to the CEO. Then skip a few lines
     By (Your Name)
     Skip one or two more line and put the date.
     This should be the first page, the cover. Then after the cover page, make a table of contents.
     Write Table of Contents at the top center.
   The table of contents should be listed as such:

Title Page ……………………………………………………………………………………………………………………………..i
Table of Contents ………………………………………………………………………………………………………………….iii
Vacation Histogram ……………………………………………………………………………………………………………….1

Means …………………………………………………………………………………………………………………………………2
Promotion Recommendation ……………………………………………………………………………………………………3

Bonus Recommendation …………………………………………………………………………………………………………4

Grievance Board …………………………………………………………………………………………………………………..5
Probability Table …………………………………………………………………………………………………………………..6
Promotions Committee …………………………………………………………………………………………………………..7
Evaluation Confidence Interval …………………………………………………………………………………………………8
T-shirt Order ………………………………………………………………………………………………………………………..

The Issues to be Addressed
Issue 1
Nine employees need to be chosen randomly to serve on the Grievance Board from the Employee Roster so that no one will say that we chose employees based on popularity. You may use any method, including with the aid of a random number table, to accomplish this task. However, you have to explain your method, whichever you choose to use.
Please list the employees ID# after selecting them.
Issue 2
Please complete the following two conditional probability tables. There have been complaints that there is skewness in certain departments as it relates to ethnicity and gender. It seems that certain supervisors are hiring only females or only Asians. Please complete this accurately so that the CEO can see if there are hiring trends in his agency.
Table I

Total

White

Black

Hispanic

Asian

Foreign

Total

Dept. 1

Dept. 2

Dept. 3

Dept. 4

Dept. 5

Table II

Total

Black

White

Hispanic

Asian

Foreign

Total

Female

Male

Issue 3
Please create a histogram for vacation hours for employees in Department 1, 3, and 5. Please exclude any vacation hours over 320 as a person cannot accumulate vacation over that amount.
After you have created this histogram, please indicate the distribution’s shape.
Issue 4
Find the Mean weight for Departments 4 and 5 combined.

Find the Mean salary for Department 2.

Find Mean age for Department 1.

Find the Mean Placement Score (P. Score) for Department 3.
Issue 5
Find the standard deviation for the evaluation score (E. Score) of Department 5 and Department 2 separately.
The CEO is thinking about giving one of these department a $1000 per person bonus. Based on their means and standard deviation, which department is doing better as it relates to this year’s evaluation? Who should the bonus go to and why?
Issue 6
The Equal Opportunity Commission has cited Jordan & Associates with discrimination against Asian females and Hispanic females. They need to promote either an Asian female or an Hispanic female within the next month. Based on their evaluation scores (E. Score), find the corresponding z -score for each Asian and Hispanic female and make a decision on which person should be promoted. Please list them by their ID # based on the percentile.
Use s = 6.06 and m = 16.

Issue 7
Please refer to the conditional probability table or complete it first before attempting this assignment. The CEO has asked for a committee to be formed to approve and review promotions. Please list all your answers in percentages?
From Table 1, what is the probability of choosing an African American employee?
From Table 2, what is the probability of choosing an Asian female given all females?
From Table 1, what is the probability of choosing a White employee from Dept. 2 and then an Hispanic employee from Dept. 3?
From Table 2, what is the probability of choosing a Black male or Foreign male?
From Table 1, what is the probability of choosing a Foreigner or an Hispanic both from Department 5?
Issue 8
Find the evaluation score (E. Score) confidence intervals for the following two departments: Department 1 and Department 4 combined.
Find the confidence interval at the 95% level. Use s = 6.06 and
= 17.62

Issue 9
We are about to order the annual summer picnic T-shirts. In the past, the mean employee weight is 210 lbs with an s = 67 lbs. Test H a > 210 at 0.05 significance level by combining the weights of departments 2, 3, and 4. If their mean weight is greater than 210, we need to order all extra large T-shirts. Please make a decision.

The Data

138

300

120

138

125

120

159

300

212

204

325

150

155

151

120

110

325

ID #	Dept.	Ethnicity	Gender	Weight	Age	Salary ($)	Vacation Hrs.	Absences	E. Score	P. Score
6 9 4								3																			F	25 2		1 8	69,3 8 0	300	16	24	94
26 1														W	1 78				21	39,9 86		60			22	90
		1 38								2							B	1 32	40,000		34				15	86
222	162	32,000		1 59		32					1 7			76
5 56								5															M	2 19	31,000			1 20	70	19	98
									1	1 92	84,000				80
	58							H		1 10			25	12,7 75					0	14
169	26	25,594		125		72
558	220	27	22,000								85		7		87
7 65								4	2 71		30	22,6 97	330		42	71
7 28	270	97,424	65
901	310					31	18,000	1292		40
6 11	229	98,000	13		84
2 64	189	67,089		81	20
128	127	48,000	4 44			10	91
118	126	37,328	61
101				A	124	66,000	336			47	96
605	226	27,0 82
9 45	399		35	14,000	8	75
721	255	31,4 66	64	9
852	2 88		37	51,2 43
207	54,101	49		79
811	287		38	35,000			325		43
508	217	17,000	45		77
927	315		41	40,718		2 12			97
83,331	534		28		11	88
421	11,000	78	92
327		204	214,000	317			23	74
507	215	44	43,847			12
	1 51	46	80,712		150
198	86,274	82
206		155	15,544
333	210	48	26,400	384
727	262		51	15,155	156
496	214	15,400	39
233	174	53	29,050
971	407	56	43,761
301	195	59	73,582	564
877	290	66	12,484
906	314		73	91,000

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