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STAT 252 Department of Mathematical and Statistical Sciences

创建日期：2024-07-19 17:53:37

所属分类：统计学statistics

标签： STAT 252

Department of Mathematical and Statistical Sciences

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Department of Mathematical and Statistical Sciences STAT 252 – PRACTICE MIDTERM

The density of the gastropod Terebralia palutris was investigated in four mangrove forests by throwing a quadrat at random points on the sediment.

Instructions: (READ ALL INSTRUCTIONS CAREFULLY.)

This is a closed bookexam.
You are permitted to use a NON-PROGRAMMABLE calculator, and the formula sheets and tables provided.
Please turn off your cellular phones or pagers.
You have 50 minutes to complete the exam.
The exam is out of a total of 33marks.
This exam has 9 pages (including this cover page and all computer output tables). Please ensure that you have all pages.
Make sure your name and signature are on this cover page and your student ID number is at the top of page two.
For questions that state you should show all steps, be sure that you do this in order to obtain full credit. Conclusions must also be clearly stated. Your answers must have adequate justification.
For other questions that say you do notneed to show all steps, read the question carefully and follow the exact instructions regarding what is required.
If you run out of space in the blank area provided for each question, use the back of the page to complete your answers as needed and label such answers so that is clear which question they belong to.
You may also use the reverse sides of the pages for allrough work.
When referring to “log”, I am always referring to the natural log.

BEST WISHES!!

Student ID Number:

Question 1 (5 marks)

The owner of a fishing camp wanted to test the effectiveness of two brands of mosquito repellents (A and B). From the population of visitors he randomly allocated 12 visitors to use Repellent A and another 12 visitors to use Repellent B. All wore short-sleeved shirts and shorts. The table below shows the summary statistics for the number of bites each visitor had after fishing for 4 hours on the lake. Assume that the data are normally distributed. Note: You might not need all of the statistics shown. At the 5% significance level, carry out the most appropriate test to determine whether there is a difference in the mean number of bites between people who used the two brands. Show all steps of the hypothesis test.

Summary statistics	Brand A	Brand B	Difference
Average	25.08	21.42	3.67
Standard Deviation	8.51	6.68	14.37

There is no indication that the two samples are paired or related, therefore the two-mean test for independent samples should be used

H0: mBrand _ A – mBrand _ B = 0 Parameter: mBrand _ A – mBrand _ B

(There is no difference in the mean number of bites between people who used the two brands)

(There is a difference in the mean number of bites between people who used the two brands)

df = n1 + n2 – 2 = 12 +12 – 2 = 22 Thus, (0.15 > P > 0.10) x 2 ==> 0.30 > P-value > 0.20

There is weak evidence against H0. Since P-value > α (0.05), do not reject H0.

At the 5% significance level, the data do not provide sufficient evidence to conclude that there is a difference in the mean number of bites between people who used the two brands.

Question 2 (3 marks in total)

Suppose that analysis of log transformed data results in the estimate of the difference between the logged means of Treatment A and Treatment B to be 0.746 and a 95% confidence interval for the additive effect of treatment is between 0.218 and 1.278.

Define the parameter as: mLnB – mLnA .

(a)(2 marks) Back transform the estimate and the confidence interval to the original scale. Interpretthe meaning of this confidence interval on the original scale.

Back Transformation of the estimate and confidence interval to the original data gives the following: Estimate of the difference = e0.746 = 2.109

Lower endpoint of the confidence interval = e0.218 = 1.244

Upper endpoint of the confidence interval = e1.278 = 3.589

Therefore, a 95% confidence interval for the ratio of the medians on the original scale is: (e0.218, e1.278 ) = (1.244,3.589)

It is estimated with 95% confidence that the median effectiveness of Treatment B is between 1.244 and 3.589 times the median effectiveness of Treatment A.

(b)(1 mark) Based on the confidence interval you found in part (a), after back transformation, would you conclude that there is a difference between the medians for Treatment A and Treatment B (with 95% confidence)? Explain the logic of your answer.

Since the confidence interval after back transformation, which is (1.244, 3.589), does not contain 1, that means we can be 95% confident that there is a difference between the medians for Treatment A and Treatment B.

Question 3 (7 marks in total)

Based on a random sample of graduates who had just completed 4 different degree programmes (Bachelor’s degree in Civil Engineering, Bachelor’s degree in Mechanical Engineering, Master’s degree in Civil Engineering, and Master’s degree in Mechanical Engineering), information was gathered concerning their starting salaries. Assume that all required assumptions are satisfied for applying the analyses needed to answer parts (a) and (b) below. Use the parameters defined below and the computer output in Tables 1 – 4.

The parameters are already defined for you as follows:

mB–Civil = Bachelor’s degree in Civil Engineering

mB–Mech = Bachelor’s degree in Mechanical Engineering

mM –Civil = Master’s degree in Civil Engineering

mM –Mech = Master’s degree in Mechanical Engineering

Table 1: Summary statistics of the salaries of the 4 groups.

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FE 825 IERG 5130 STAT 8178 EE161 ADS2 G54FUZ CS326 113B ECN 226 QBUS6860 ELEC3202 COMP9334 MGT11B MET CS 777 STA238 00099F Python SMM306 CMT206 EC116 SP MAST90084 CS480/680 BCPM0091 CMPT 300 ECON2209 FY20 STAT 432 CVEN9625 MATH1712 CMP9771M CMP3750M CIS 325 AI506 MAT344H1S MGT7180 PSTAT 160B CSYS5010 1D STAT 453/558 ME152B STA304H1F CSCI-128 ME428 CO3002 FINE 7640 COMP3234 ECSE 223 EE497 – 3D MATH5905 ECS648U ENG5009 MATH10242 EC665 A CPI221 ISOM5220 MACE40402 MGT B456F COMP9315 AFM 113 STAT 778 CS 564 MA231 CS 230 CS 124 COMP5511 CSC317 ITEC1010 ELEC207 INFT 3019 7CCMFM06 EE 161 5G ECLT5810 MATH 7349 CS526 O2 COMP90054 ELE00063M ACCT5034 ARC1015 CSCI 40 CSCI E40 FIN 524B CS 462 389COM CMT309 MFIN703 COMP4250 STA304 STA304H1S STA 1003 FIN 448 BUFN 732 CS520 CVEN3701 ECMT6006 PHAS0100 CSIT314 MDIA 5028 CSCI 2134 MAT 451 CMPT 459 STAT 457 INFO20003 COMP4141 IELE8066 F540 ECM9 CSE 6321 FIN 430 MATH3911 BFC5916 COMP1011 EEE 6209 STATS 240 CW3 COMP206 COMP1003 4331W ISE 530 CMPT 295 MATH 239 QF5203 INFR08010 IT114105 FIT2093 ECON3124 ECON1195 MATH 337 STAT 3006 COMP202 COMP3130 MATH3609 COMP 250 CS6140 IEEE ELE00041I FIN40090 CIV 5899 MATH3066 IGNMENT MATH 2009 STAT3405 HIST 101 MATH 3281 CEGE0042 ICT532 LAB 7 LAB 5 MCO455 CSIT214 Q4 IFB104 A1 ECO220Y5Y DA5020 CMPSC473 FIN9007 DSCI553 MSCI534 COMP3308 CSE-112 CMPT 310 EE104 F 2C P20 ALY2010 BUSM060 STA258 ECO00030M R BIOSTAT 274 COS6012-B FIT3155 CMPUT 340 EC421 INFS4205 ECOM135 NATS 1740 COMP809 MBE 6005 STA465 CSSE2310 CIVL2700 DATA4700 CMPSC 473 ISE 529 CS5044 MAST30020 COMP2207 ENGG1001 COMP0046 FIT3165 STAT GR5241 MECH0007 vATHK1001 ANALYTIC ATHK1001 MATH352001 HW3 S1 BMAN 24662 COMP 636 Stat-461 STAT 302 STAT 2132 STAR534 ENG4137 CMP3752M CS3103 BISM3222 STA 135 ME155A IIMT3601 ECON3371 ECON 3371 HW4 FINA 5840 DT211C CTEC3902 MAT005 MATH2148 S261F Econ 332 MATH3734 MIS41270 7CCMFM13 SYST 664 CIS434 CENG10014 MT4111 MT4527 ECMM424 CMT219 Math 136 MATH 3120 COMP10002 MAST20009 MATH0058 BEEM117 ISYE 6420 MGMTMFE 405 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COMP532 MAS275 COMP5318 COMP4002 FIT5086 MAST20004 FIT3152 FIT5129 CIS2380 CS521 COMP 1005 EECMS CITS5501 ECE 462 ECON 6002 ENG 4051 CSC 648 CMT654 MECHENG 713 PHYS1002 AMME 2000 FP0060 DDES3200 MECHENG 743 BINF90002 FIT2081 ISYS90081 ELECTENG 722 BUS 360 ECOS3010 BUS2810 ETF2100 ENG2048 STAT5002 COMP2017 CEME 2003 MATS3004 COMP9319 PHYS1001 COMP5349 AMME2261 COMP-381 FIT3173 COSC2757 ENG4025 QBUS2820 COMP9414 MATH2021 EOSC118 MFIN6690 PMATH 321 CSE-141L MATH575A COMPSCI5002 COMP1511 management comp2123 FINS3616 COMP 3331 COMS30034 DTSC 71 AcF 702 AcF702 DTSC71 MAT021 ELE8083 ACFI213 EG-127J 127J FIT5163 FIT2001 ELE00113M CMT310 CS 245 ENGL 1101 MTH6115 EE497 CS 325 Math 124A MTH5130 MBA502 MGT 5380 ARCH 1261 F033800 20LLP109 ELE4009 FINANCIAL COMP3331 Computer ECE4179 20T3 COMP9311 COMP9311 UNSW MFIN6210 ACCT 5930 EE590 ENG2029 ECO100 SIT315 ACCT3610 COMP3600 STK2100 FIT2004 COMP30020 ACTL1101 Stat 101B BANA 200 COSC2473 ENGG1400 AI COMP90043 MMF 1914H PHYS 127 CS584 CIVL2010 ECMT2150 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