e STATISTICS Please show all work Answers alone will be graded wrong Each problem is worth 10 points 1 USA Today (December 13, 1998) reported on a study of the automobilespurchased by women in 1998 The data in the study consisted of a description of the top five automobiles purchased Ford Escort (FE), Honda Accord (HA), Chevrolet Cavalier (CC), Ford Taurus (FT), and Hyundai Excel (HE) The actual study summarized the purchases of several thousand women Let us assume that the data shown below represent a sample of 50 women who purchased one of these five cars Summarize these data with ALL appropriate statistical methods (by hand or any statistical software) and provide verbal statements discussions of the summaries about the model of the cars HAFEFTFTCCHAHAFEFTHAHE HE FTHECCFTFEFE HACCCCFEFECC HAHAHEFTCCCC HAHEHEHAFEFE FEHAHECCCCFT HEFEFECCHAFTFTFE 2 A mathematics achievement test consisting of 100 questions was given to 50 sixth grade students at maple Elementary School The following data show the number of questions answered correct by each student 7548466571496151574984857985835569888955617264676177516168546394545371847975655045657771636757637177 a Using the following classes as given below, complete the table Class frequency relative freq Cumulative freq Cumul Relat Freq 40 49 50 59 60 69 70 79 80 89 90 99 b)draw a relative frequency histogram and discuss the shape of the distribution c)how many classes are there d)What percent of the data values are at least 70 e) Calculate the 37 th percentile and interpret it f)Calculate the 80 th percentile and interpret it g Calculate the IQR and interpret it 3 Christian D'Angelo has scores of 68, 65, 75, and 78 on his statistics tests Find the scores he can make on his final exam to receive a C in the course The final exam counts as two test scores and C is received if the final course grade is from 70 to 79 4 The mean annual salary of 10 employees is $45,000 and the median salary is 36,000 The highest paid employee got a raise of $ $5,000 a What is the new mean salary b What is the new median salary 5 If the z score for an observation is 1 25, the mean of the data set is 80, and the variance is 85, what is the value of the observation 6 Todd Booth, an avid jogger, kept detailed records of the number of miles he ran per week during the past year The frequency distribution in figure below summarizes his records Find the mean , median , and mode of the number of miles per week that Todd ran Miles Run per WeekNumber of Weeks 04 15 210 39 410 57 64 73 a Mean number of miles b Median number of miles c Mode number of miles 7 The Arizona State University Statistical Summary provides information on various characteristics of ASU faculty Data from one year on the variables age and rank of ASU faculty members yielded the contingency table shown below RANK AGE Full Prof, R1 Associate Prof, R2 Assistant Prof, R3 Instructor, R4 TOTAL Under 30,Y 2 3 57 6 68 30 39,G 52 170 163 17 402 40 49 ,M 156 125 61 6 348 50 59,R 145 68 36 4 253 60 over ,O 75 15 3 0 93 TOTAL 430 381 320 33 1164 Suppose an ASU faculty member is selected at random, answer the following questions, using the letters representing the events a What is the probability that the member is neither a full professor nor a an associate professor b Wat is the probability that the selected member is an assistant professor or the member is between 40 49 years of age c If the selected member is an associate professor , what is the probability that the member is older than 49 8 If P(A) 0 60,P(B) 055,and ,find the following a b 8 At a raffle, 1500 tickets are sold at $2 each for 4 prizes of $500, $250, $150, and $75 You bought one of the tickets What is the expected value of your gain 9 It is estimated that out of ten vouchers examined by the audit staff employed by a branch of the Department of Health and Human Resources, one will contain an error Define X to be the number of vouchers in error out of 20 randomly selected vouchers a What is the probability that more than four vouchers will contain an error b What is the probability that at least two vouchers will contain an error c Determine the mean and standard deviation of X 9 The test scores of a college admissions test are normally distributed with a mean of 450 and variance of 10000 If a particular university will not admit anyone scoring below 480, what percentage of the applicants would be acceptable to the university 10 The weights bags of carrots are normally distributed with a mean of 32 ounces and standard deviation of 0 36 ounce Bags in the upper 5 5 are too heavy and must be repackaged What is the least a bag of baby carrots must weigh if it has to be repackaged 11 A production process is working normally if the average weight of manufactured steel is at least 1 3 pounds A sample of 50 steel bars yields a mean of 1 26 pounds and standard deviation of 0 10 pounds Is there any evidence to indicate that the production process needs adjustment Use a 0 05 level of significance Interpret your conclusion in the context of the problem

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e: _STATISTICS________ Please show all work : Answers alone will be graded wrong. Each problem is worth 10 points. 1. USA Today (December 13, 1998)

e: _____STATISTICS____________

Please show all work: Answers alone will be graded wrong. Each problem is worth 10 points.

1. USA Today (December 13, 1998) reported on a study of the automobilespurchased by women in 1998. The data in the study consisted of a description of the top five automobiles purchased: Ford Escort (FE), Honda Accord (HA), Chevrolet Cavalier (CC), Ford Taurus (FT), and Hyundai Excel (HE). The actual study summarized the purchases of several thousand women. Let us assume that the data shown below represent a sample of 50 women who purchased one of these five cars.

Summarize these data with ALL appropriate statistical methods (by hand or any statistical software) and provide verbal statements/discussions of the summaries about the model of the cars.

HAFEFTFTCCHAHAFEFTHAHE HE

FTHECCFTFEFE

HACCCCFEFECC

HAHAHEFTCCCC

HAHEHEHAFEFE

FEHAHECCCCFT

HEFEFECCHAFTFTFE

2.A mathematics achievement test consisting of 100 questions was given to 50 sixth grade students at maple Elementary School. The following data show the number of questions answered correct by each student.

7548466571496151574984857985835569888955617264676177516168546394545371847975655045657771636757637177

a.Using the following classes as given below, complete the table

Class frequencyrelative freq.Cumulative freq.Cumul. Relat. Freq.

40-49

50-59

60-69

70-79

80-89

90-99

________________________________________________________________

b)draw a relative frequency histogram and discuss the shape of the distribution.

c)how many classes are there?

d)What percent of the data values are at least 70?

e) Calculate the 37^th percentile and interpret it.

f)Calculate the 80^th percentile and interpret it.

g. Calculate the IQR and interpret it.

3.Christian D'Angelo has scores of 68, 65, 75, and 78 on his statistics tests. Find the scores he can make on his final exam to receive a C in the course .The final exam counts as two test scores and C is received if the final course grade is from 70 to 79.

4.The mean annual salary of 10 employees is $45,000 and the median salary is 36,000. The highest paid employee got a raise of $ $5,000.

a.What is the new mean salary?

b.What is the new median salary?

5.If the z-score for an observation is -1.25, the mean of the data set is 80, and the variance is 85, what is the value of the observation?

6.Todd Booth, an avid jogger, kept detailed records of the number of miles he ran per week during the past year. The frequency distribution in figure below summarizes his records. Find the mean, median, and mode of the number of miles per week that Todd ran.

Miles Run per WeekNumber of Weeks

210

410

----------------------------------------------------------------------

a.Mean number of miles=

b.Median number of miles=

c.Mode number of miles =

7.The Arizona State University Statistical Summary provides information on various characteristics of ASU faculty. Data from one year on the variables age and rank of ASU faculty members yielded the contingency table shown below.

RANK

AGE

Full Prof, R1

Associate Prof, R2

Assistant Prof, R3

Instructor,

TOTAL

Under 30,Y

30-39,G

170

163

402

40-49 ,M

156

125

348

50-59,R

145

253

60 & over ,O

TOTAL

430

381

320

1164

Suppose an ASU faculty member is selected at random, answer the following questions, using the letters representing the events.

a.What is the probability that the member is neither a full professor nor a an associate professor?

b. Wat is the probability that the selected member is an assistant professor or the member is between 40 - 49 years of age?

c.If the selected member is an associate professor , what is the probability that the member is older than 49?

8.If P(A) = 0.60,P(B)=055,and ,find the following:

8. At a raffle, 1500 tickets are sold at $2 each for 4 prizes of $500, $250, $150, and $75. You bought one of the tickets. What is the expected value of your gain?

9.It is estimated that out of ten vouchers examined by the audit staff employed by a branch of the Department of Health and Human Resources, one will contain an error. Define X to be the number of vouchers in error out of 20 randomly selected vouchers.

a. What is the probability that more than four vouchers will contain an error?

b.What is the probability that at least two vouchers will contain an error?

c.Determine the mean and standard deviation of X

9.The test scores of a college admissions test are normally distributed with a mean of 450 and variance of 10000. If a particular university will not admit anyone scoring below 480, what percentage of the applicants would be acceptable to the university?

10.The weights bags of carrots are normally distributed with a mean of 32 ounces and standard deviation of 0.36 ounce. Bags in the upper 5.5% are too heavy and must be repackaged. What is the least a bag of baby carrots must weigh if it has to be repackaged?

11.A production process is working normally if the average weight of manufactured steel is at least 1.3 pounds. A sample of 50 steel bars yields a mean of 1.26 pounds and standard deviation of 0.10 pounds. Is there any evidence to indicate that the production process needs adjustment? Use a 0.05 level of significance. Interpret your conclusion in the context of the problem.