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FAMILY NAME

FIRST NAME

STUDENT ID

Test 1, Semester 3, 2011

Introductory Statistics

Unit Code: STAT170 Examination Time: 50 Minutes

Instructions

Using 2B pencil, write your name and student number in the appropriate space on the answer sheet, starting from the left-hand corner.

For each question, decide which of the answers is most appropriate and mark in pencil the corresponding letter on your answer sheet.

All questions are of equal value.

There are 37 questions.

Tables and formulas are provided at the end of this booklet.

Write your name and student number on this booklet, which must be handed in, together with your answer sheet.

This test consists of 11 pages, including the cover page, excluding tables and formulas.

NO PART OF THIS EXAMINATION PAPER IS TO BE TAKEN FROM THE EXAMINATION ROOM.

DO NOT START UNTIL INSTRUCTED TO DO SO

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Unless stated otherwise, all questions in this test are based on the information obtained from a study described below.

A survey was done on a random sample of 112 Macquarie University students taking STAT170, and information was collected on the following variables:

Sex: 0=female, 1=male Level: Students perception of the difficulty level of STAT170:

0=difficult , 1=appropriate Study: Average number of hours studying STAT170 per week (collected from Week 2- Week 11 only) TV: Average number of hour watching TV per week Grade: Grade expected in STAT170: 1=HD, 2=D, 3=Cr, 4=P, 5=F

Question 1 In a statistical study, y is an example of which of the following?

A. sample parameter #B. sample statistic C. population parameter D. population statistic E. an area of study called statistics, for example STAT170 Introductory Statistics.

Question 2 A representative sample is one which:

A. should give unbiased results B. should look like the population from which it arises

C. should always be selected for data analysis

#D. all of the above E. none of the above

Question 3 In a statistical study, which of the following about target population is FALSE?

A. There are many possible target populations for a selected sample. B. Target population must be well defined. C. Target population must include the sample chosen. #D. Statisticians calculate statistics from target population. E. None of the above.

Question 4 What is the difference between parameters and statistics?

A. Statistics describe populations, whereas parameters describe samples #B. Statistics describe characteristics of samples, whereas parameters describe

characteristics of populations. C. Statistics can be estimated, but parameters are calculated. D. Both statistics and parameters are estimated. E. Statistics have fixed values, but parameters have a range of values.

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Question 5 What is the type of the variable Grade?

A. numerical and discrete B. categorical and nominal #C. categorical and ordinal D. categorical and discrete E. categorical and numerical

Question 6 What is the type of the variable TV?

#A. numerical and continuous B. categorical and nominal C. categorical and ordinal D. numerical and discrete E. normal

Question 7 In Week 13 when the examination draws near, it is known from past history that the number of hours students study for STAT170 is 1.5 times their usual number of hours per week in Week 2 Week 11. Define a new variable, Study13 to be the number of hours of study for STAT170 undertaken in Week 13. Indicate how the mean and standard deviation (SD) of Study13 compare to those of Study.

A. Both mean and SD are unchanged. #B. Both mean and SD of Study13 are 1.5 times the mean and SD of Study

respectively. C. Mean of Study13 is 1.5 times the mean of Study, while SD is unchanged. D. Mean is unchanged, but SD of Study13 is 1.5 times the SD of Study. E. None of the above.

Question 8 What is the appropriate visual display (graphic) which could help you answer the Research question: Do male and female STAT170 students have the same expectation of their Grades?

A. histogram B. bar chart C. pie chart #D. clustered bar chart E. stem-and-leaf plot

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Question 9 What is the appropriate visual display (graphic) which could help you answer the Research question: Is there a difference between the average number of hours of study between the two groups who think the level of STAT170 is appropriate or difficult?

A. histogram #B. comparative boxplots C. stem-and-leaf plot D. clustered barchart E. scatter plot

Question 10 In a certain sample, the values of Study are:

0 1 2 3 4 4 5 5 6 8 (hours) What is the 80% percentile of this sample?

A. 80% B. 5 #C. 5.5 D. 6 E. 8

Questions 11 to 13 are based on the following information: The variable Study is known to be normally distributed with a mean of 6 hours and standard deviation of 3 hours.

Question 11 If 16 students were randomly selected, how many of them would you expect to study more than 7 hours per week? Round your result to the nearest integer.

A. 2 B. 5 #C. 6 D. 10 E. Cannot be calculated, since 16

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Question 13 What is the 30th percentile of Study in the population?

A. 30% B. 0.3 #C. 4.44 hours D. 7.56 hours E. Cannot be found because n is unknown in the equation n*p/100.

Questions 14 to 25 are based on the following information: In the survey of 112 students, 92 students thought that the level of STAT170 was appropriate, while 20 students thought it was difficult. Past history indicates that the percentage of students who thought the level of STAT170 was appropriate was 70%. Research question: Is the proportion of all STAT170 students who think the level of STAT170 is appropriate equal to 70%?

Question 14 What are the assumptions to be checked before the appropriate hypothesis test is performed?

A. n 25 B. np 25 and n(1-p) 25 C. n 25 and n(1- ) 25 D. np 5 and n(1-p) 5 #E. n 5 and n(1- ) 5

Question 15 Which of the following is a correct statement of the null hypothesis?

#A. H0: = 0.7 B. H0: = 0.8214 C. H0: p = 0.7 D. H0: p = 0.8214 E. H0: y = 92

Question 16 What is the meaning of the null hypothesis in words?

A. The sample proportion of STAT170 students who think the level of STAT170 is appropriate is 0.7.

B. The sample proportion of STAT170 students who think the level of STAT170 is appropriate is 0.8214.

#C. The population proportion of STAT170 students who think the level of STAT170 is appropriate is 0.7.

D. The population proportion of STAT170 students who think the level of STAT170 is appropriate is 0.8214.

E. The number of students who think the level of STAT170 is appropriate is 92.

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Question 17 What is the appropriate test statistic to test the claim?

#A. z = 2.80 B. z = -2.80 C. z = 3.35 D. z = -3.35 E. None of the above.

Question 18 What is the p-value for the test?

A. p-val = 0.0026 #B. p-val = 0.0051 C. p-val = 0.00081 D. p-val = 0.00041 E. p-val > 0.05

Question 19 What is the conclusion of the test?

A. The population proportion of STAT170 who think the level of STAT170 is appropriate is less than 0.7.

#B. The population proportion of STAT170 who think the level of STAT170 is appropriate is more than 0.7.

C. The population proportion of STAT170 who think the level of STAT170 is appropriate could be 0.7.

D. The sample proportion of STAT170 who think the level of STAT170 is appropriate is less than 0.7.

E. The sample proportion of STAT170 who think the level of STAT170 is appropriate is more than 0.7.

Question 20 What is the correct expression in order to calculate a 95% C.I. for the population proportion of STAT170 who think the level of STAT170 is appropriate?

A. 112

3.07.096.18214.0

B. 92

1786.08214.096.18214.0

#C. 112

1786.08214.096.18214.0

D. 112

3.07.096.17.0

E. 92

3.07.096.17.0 .

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Question 21 What is the interpretation of the 95% CI above?

A. 95% chance the sample proportion is equal to population proportion. B. We are 95% confident that the sample proportion lies between 0.75 and 0.89 #C. We are 95% confident that the population proportion lies between 0.75 and 0.89 D. We are 95% confident that the population proportion lies between 0.73 and 0.91 E. None of the above.

Question 22 Does this 95% C.I contain the sample proportion?

#A. Definitely yes (100% certain) B. Definitely no C. 95% chance containing the sample proportion D. 5% chance containing the sample proportion E. Unable to determine

Question 23 Does this 95% C.I contain the true population proportion?

A. Definitely yes (100% certain) B. Definitely no #C. 95% chance containing the true population proportion D. 5% chance containing the true population proportion E. Unable to determine

Question 24 If the sample size is increased, what is the effect on the 95% CI?

A. The 95% CI will not change. B. The 95% CI will become longer. #C. The 95% CI will become shorter. D. The CI will become longer, the name 95% CI has to be changed to something like

98% CI. E. The CI will become shorter, the name 95% CI has to be changed to something

like 92% CI.

Question 25 Suppose the University Council claims that the percentage of students who think the level of STAT170 is appropriate is 80% (instead of 70%). Using 95% CI you found earlier, what can you say about the University Councils claim about the proportion of STAT170 students who think the level of STAT170 is appropriate?

A. The population proportion is equal to 0.7. B. The population proportion could be equal to 0.7. C. The population proportion is equal to 0.8. #D. The population proportion could be equal to 0.8. E. The population proportion is not equal to 0.8.

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Questions 26 to 31 are based on the following information: In the table below, there were 7 students who failed STAT170 in the previous semester and had to re-do the unit. The following shows the average number of hours per week each of these students spent in the previous semester and in this current semester.

Name No. of hours (previous semester)

No. of hours (current semester)

Rose 1 3.5 Mathew 3 5 Julian 5 7 Bill 3 3 Peter 3 4 Petra 2 3.5 Adam 3 5

Research question: Is there a difference between the average number of hours per week studying STAT170 in the previous semester and in this semester?

Question 26 What is the sample standard deviation which may be used for the appropriate test statistic to investigate the research question?

A. 0.776 B. 1.829 #C. 0.838 D. 1.291 E. None of the above.

Question 27 What is the appropriate statement of the null hypothesis?

#A. H0: d = 0 B. H0: 1 = 2 C. H0: 21 yy = D. H0: 0=dy E. None of the above.

Question 28 What is the absolute value (i.e. disregard the + or sign) of the test statistic?

A. t = 5.35 B. t = 2.28 #C. t = 4.96 D. z = 4.96 E. None of the above

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Question 29 What is the p-value for the test?

A. 0.02 < p-val < 0.05 #B. 0.002 < p-val < 0.005 C. p-val > 0.05 D. 0.00063 E. None of the above

Question 30 What is the conclusion of the test?

A. There could be a difference, on average, between the average number of hours per week studying STAT170 in the previous semester and in this semester. B. There is no difference, on average, between the average number of hours per week studying STAT170 in the previous semester and in this semester. C. There could be no difference, on average, between the average number of hours per week studying STAT170 in the previous semester and in this semester. #D. The number of hours per week studying STAT170 in the previous semester is less than that in this semester, on average. E. None of the above.

Question 31 What is the correct expression in order to calculate a 95% C.I. for the population mean of the difference in the number of hours per week spent in the previous semester and in the current semester?

A. 71

7129.196.1571.1 +

B. 71

7129.1179.2571.1 +

C. 7

838.096.1571.1

#D. 7

838.0447.2571.1

E. None of the above

Questions 32-37 refer to the following information. Summary statistics were obtained on Study for male and female students separately. The results are given in the table below.

Study Sex n Mean St Dev

Male 56 4.8 2.6 Female 56 5.5 2.0

Research question: Is there a difference in the average number of hours of Study per week between male and female students?

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Question 32 What is the sample standard deviation which may be used for the appropriate test statistic to investigate the research question?

A. 2.3 #B. 2.32 C. 5.38 D. 0.6 E. 0.221

Question 33 What is the appropriate statement of the null hypothesis?

#A. H0: 1 = 2 B. H0: d = 0 C. H0: 21 yy = D. H0: 0=dy E. None of the above.

Question 34 What is the absolute value (i.e. disregard the + or sign) of the test statistic?

A. z = 1.60 #B. t = 1.60 C. t = 8.73 D. t = 2.28 E. t = 0.30

Question 35 What is the p-value of the test?

A. p-val < 0.05 B. p-val = 0.1096 C. 0.02 < p-val < 0.05 #D. 0.1 < p-val < 0.2 E. 0.2

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Question 37 What is the correct expression in order to calculate a 95% C.I. for the difference of population means in the number of hours of Study per week between male and female students?

A. 561

56132.296.17.0 + or 56156132.296.17.0 +

#B. 561

56132.2984.17.0 + or 56156132.2984.17.0 +

C. 566.096.17.0 or

566.096.17.0

D. 566.0009.27.0 or

566.0009.27.0

E. None of the above

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TABLES

0 z

p

|z| 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 .5000 .4960 .4920 .4880 .4840 .4801 .4761 .4721 .4681 .4641

0.1 .4602 .4562 .4522 .4483 .4443 .4404 .4364 .4325 .4286 .4247 0.2 .4207 .4168 .4129 .4090 .4052 .4013 .3974 .3936 .3897 .3859 0.3 .3821 .3783 .3745 .3707 .3669 .3632 .3594 .3557 .3520 .3483 0.4 .3446 .3409 .3372 .3336 .3300 .3264 .3228 .3192 .3156 .3121

0.5 .3085 .3050 .3015 .2981 .2946 .2912 .2877 .2843 .2810 .2776 0.6 .2743 .2709 .2676 .2643 .2611 .2578 .2546 .2514 .2483 .2451 0.7 .2420 .2389 .2358 .2327 .2296 .2266 .2236 .2206 .2177 .2148 0.8 .2119 .2090 .2061 .2033 .2005 .1977 .1949 .1922 .1894 .1867 0.9 .1841 .1814 .1788 .1762 .1736 .1711 .1685 .1660 .1635 .1611

1.0 .1587 .1562 .1539 .1515 .1492 .1469 .1446 .1423 .1401 .1379 1.1 .1357 .1335 .1314 .1292 .1271 .1251 .1230 .1210 .1190 .1170 1.2 .1151 .1131 .1112 .1093 .1075 .1056 .1038 .1020 .1003 .0985 1.3 .0968 .0951 .0934 .0918 .0901 .0885 .0869 .0853 .0838 .0823 1.4 .0808 .0793 .0778 .0764 .0749 .0735 .0721 .0708 .0694 .0681

. 1.5 .0668 .0655 .0643 .0630 .0618 .0606 .0594 .0582 .0571 .0559 1.6 .0548 .0537 .0526 .0516 .0505 .0495 .0485 .0475 .0465 .0455 1.7 .0446 .0436 .0427 .0418 .0409 .0401 .0392 .0384 .0375 .0367 1.8 .0359 .0351 .0344 .0336 .0329 .0322 .0314 .0307 .0301 .0294 1.9 .0287 .0281 .0274 .0268 .0262 .0256 .0250 .0244 .0239 .0233

2.0 .0228 .0222 .0217 .0212 .0207 .0202 .0197 .0192 .0188 .0183 2.1 .0179 .0174 .0170 .0166 .0162 .0158 .0154 .0150 .0146 .0143 2.2 .0139 .0136 .0132 .0129 .0125 .0122 .0119 .0116 .0113 .0110 2.3 .0107 .0104 .0102 .0099 .0096 .0094 .0091 .0089 .0087 .0084 2.4 .0082 .0080 .0078 .0075 .0073 .0071 .0069 .0068 .0066 .0064

2.5 .0062 .0060 .0059 .0057 .0055 .0054 .0052 .0051 .0049 .0048 2.6 .0047 .0045 .0044 .0043 .0041 .0040 .0039 .0038 .0037 .0036 2.7 .0035 .0034 .0033 .0032 .0031 .0030 .0029 .0028 .0027 .0026 2.8 .0026 .0025 .0024 .0023 .0023 .0022 .0021 .0021 .0020 .0019 2.9 .0019 .0018 .0018 .0017 .0016 .0016 .0015 .0015 .0014 .0014

3.0 .00135 .00131 .00126 .00122 .00118 .00114 .00111 .00107 .00104 .00100 3.1 .00097 .00094 .00090 .00087 .00084 .00082 .00079 .00076 .00074 .00071 3.2 .00069 .00066 .00064 .00062 .00060 .00058 .00056 .00054 .00052 .00050 3.3 .00048 .00047 .00045 .00043 .00042 .00040 .00039 .00038 .00036 .00035 3.4 .00034 .00032 .00031 .00030 .00029 .00028 .00027 .00026 .00025 .00024

3.5 .00023 .00022 .00022 .00021 .00020 .00019 .00019 .00018 .00017 .00017 3.6 .00016 .00015 .00015 .00014 .00014 .00013 .00013 .00012 .00012 .00011 3.7 .00011 .00010 .00010 .00010 .00009 .00009 .00008 .00008 .00008 .00008 3.8 .00007 .00007 .00007 .00006 .00006 .00006 .00006 .00005 .00005 .00005 3.9 .00005 .00005 .00004 .00004 .00004 .00004 .00004 .00004 .00003 .00003 4.0 .000032

Table A1: Single tail areas corresponding to z-values for the standardised normal curve

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0-z z

p/2 p/2

|z| 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 1.000 .9920 .9840 .9761 .9681 .9601 .9522 .9442 .9362 .9283

0.1 .9203 .9124 .9045 .8966 .8887 .8808 .8729 .8650 .8572 .8493 0.2 .8415 .8337 .8259 .8181 .8103 .8026 .7949 .7872 .7795 .7718 0.3 .7642 .7566 .7490 .7414 .7339 .7263 .7188 .7114 .7039 .6965 0.4 .6892 .6818 .6745 .6672 .6599 .6527 .6455 .6384 .6312 .6241

0.5 .6171 .6101 .6031 .5961 .5892 .5823 .5755 .5687 .5619 .5552 0.6 .5485 .5419 .5353 .5287 .5222 .5157 .5093 .5029 .4965 .4902 0.7 .4839 .4777 .4715 .4654 .4593 .4533 .4473 .4413 .4354 .4395 0.8 .4237 .4179 .4122 .4065 .4009 .3953 .3898 .3843 .3789 .3735 0.9 .3681 .3628 .3576 .3524 .3472 .3421 .3371 .3320 .3271 .3222

1.0 .3173 .3125 .3077 .3030 .2983 .2937 .2891 .2846 .2801 .2757 1.1 .2713 .2670 .2627 .2585 .2543 .2501 .2460 .2420 .2380 .2340 1.2 .2301 .2263 .2225 .2187 .2150 .2113 .2077 .2041 .2005 .1971 1.3 .1936 .1902 .1868 .1835 .1802 .1770 .1738 .1707 .1676 .1645 1.4 .1615 .1585 .1556 .1527 .1499 .1471 .1443 .1416 .1389 .1362

. 1.5 .1336 .1310 .1285 .1260 .1236 .1211 .1188 .1164 .1141 .1118 1.6 .1096 .1074 .1052 .1031 .1010 .0989 .0969 .0949 .0930 .0910 1.7 .0891 .0873 .0854 .0836 .0819 .0801 .0784 .0767 .0751 .0735 1.8 .0719 .0703 .0688 .0672 .0658 .0643 .0629 .0615 .0601 .0588 1.9 .0574 .0561 .0549 .0536 .0524 .0512 .0500 .0488 .0477 .0466

2.0 .0455 .0444 .0434 .0424 .0414 .0404 .0394 .0385 .0375 .0366 2.1 .0357 .0349 .0340 .0332 .0324 .0316 .0308 .0300 .0293 .0285 2.2 .0278 .0271 .0264 .0257 .0251 .0244 .0238 .0232 .0226 .0220 2.3 .0214 .0209 .0203 .0198 .0193 .0188 .0183 .0178 .0173 .0168 2.4 .0164 .0160 .0155 .0151 .0147 .0143 .0139 .0135 .0131 .0128

2.5 .0124 .0121 .0117 .0114 .0111 .0108 .0105 .0102 .0099 .0096 2.6 .0093 .0091 .0088 .0085 .0083 .0080 .0078 .0076 .0074 .0071 2.7 .0069 .0067 .0065 .0063 .0061 .0060 .0058 .0056 .0054 .0053 2.8 .0051 .0050 .0048 .0047 .0045 .0044 .0042 .0041 .0040 .0039 2.9 .0037 .0036 .0035 .0034 .0033 .0032 .0031 .0030 .0029 .0028

3.0 .00270 .00261 .00253 .00245 .00237 .00229 .00221 .00214 .00207 .00200 3.1 .00194 .00187 .00181 .00175 .00169 .00163 .00158 .00152 .00147 .00142 3.2 .00137 .00133 .00128 .00124 .00120 .00115 .00111 .00108 .00104 .00100 3.3 .00097 .00093 .00090 .00087 .00084 .00081 .00078 .00075 .00072 .00070 3.4 .00067 .00065 .00063 .00060 .00058 .00056 .00054 .00052 .00050 .00048

3.5 .00047 .00045 .00043 .00042 .00040 .00039 .00037 .00036 .00034 .00033 3.6 .00032 .00031 .00029 .00028 .00027 .00026 .00025 .00024 .00023 .00022 3.7 .00022 .00021 .00020 .00019 .00018 .00018 .00017 .00016 .00016 .00015 3.8 .00014 .00014 .00013 .00013 .00012 .00012 .00011 .00011 .00010 .00010 3.9 .00010 .00009 .00009 .00008 .00008 .00008 .00007 .00007 .00007 .00007 4.0 .000063

Table A2: Two-tailed p-values corresponding to z-values for the standardised normal curve

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0-t t

p/2 p/2

p distribu

0.0005 0.001 0.002 0.005 0.01 0.02 0.05 0.1 0.2 0.5

=1 1273. 636.6 318.3 127.3 63.66 31.82 12.71 6.314 3.078 1.000 2 44.70 31.60 22.33 14.09 9.925 6.965 4.303 2.920 1.886 0.816 3 16.33 12.92 10.22 7.453 5.841 4.541 3.182 2.353 1.638 0.765 4 10.31 8.610 7.173 5.598 4.604 3.747 2.776 2.132 1.533 0.741

5 7.976 6.869 5.893 4.773 4.032 3.365 2.571 2.015 1.476 0.727 6 6.788 5.959 5.208 4.317 3.707 3.143 2.447 1.943 1.440 0.718 7 6.082 5.408 4.785 4.029 3.499 2.998 2.365 1.895 1.415 0.711 8 5.617 5.041 4.501 3.833 3.355 2.896 2.306 1.860 1.397 0.706 9 5.291 4.781 4.297 3.690 3.250 2.821 2.262 1.833 1.383 0.703 10 5.049 4.587 4.144 3.581 3.169 2.764 2.228 1.812 1.372 0.700

11 4.863 4.437 4.025 3.497 3.106 2.718 2.201 1.796 1.363 0.697 12 4.716 4.318 3.930 3.428 3.055 2.681 2.179 1.782 1.356 0.696 13 4.597 4.221 3.852 3.372 3.012 2.650 2.160 1.771 1.350 0.694 14 4.499 4.140 3.787 3.326 2.977 2.624 2.145 1.761 1.345 0.692

15 4.417 4.073 3.733 3.286 2.947 2.602 2.131 1.753 1.341 0.691 16 4.346 4.015 3.686 3.252 2.921 2.583 2.120 1.746 1.337 0.690 17 4.286 3.965 3.646 3.222 2.898 2.567 2.110 1.740 1.333 0.689 18 4.233 3.922 3.610 3.197 2.878 2.552 2.101 1.734 1.330 0.688 19 4.187 3.883 3.579 3.174 2.861 2.539 2.093 1.729 1.328 0.688

20 4.146 3.850 3.552 3.153 2.845 2.528 2.086 1.725 1.325 0.687 21 4.110 3.819 3.527 3.135 2.831 2.518 2.080 1.721 1.323 0.686 22 4.077 3.792 3.505 3.119 2.819 2.508 2.074 1.717 1.321 0.686 23 4.047 3.768 3.485 3.104 2.807 2.500 2.069 1.714 1.319 0.685 24 4.021 3.745 3.467 3.091 2.797 2.492 2.064 1.711 1.318 0.685

25 3.996 3.725 3.450 3.078 2.787 2.485 2.060 1.708 1.316 0.684 26 3.974 3.707 3.435 3.067 2.779 2.479 2.056 1.706 1.315 0.684 27 3.954 3.690 3.421 3.057 2.771 2.473 2.052 1.703 1.314 0.684 28 3.935 3.674 3.408 3.047 2.763 2.467 2.048 1.701 1.313 0.683 29 3.918 3.659 3.396 3.038 2.756 2.462 2.045 1.699 1.311 0.683

30 3.902 3.646 3.385 3.030 2.750 2.457 2.042 1.697 1.310 0.683 35 3.836 3.591 3.340 2.996 2.724 2.438 2.030 1.690 1.306 0.682 40 3.788 3.551 3.307 2.971 2.704 2.423 2.021 1.684 1.303 0.681 45 3.752 3.520 3.281 2.952 2.690 2.412 2.014 1.679 1.301 0.680 50 3.723 3.496 3.261 2.937 2.678 2.403 2.009 1.676 1.299 0.679

60 3.681 3.460 3.232 2.915 2.660 2.390 2.000 1.671 1.296 0.679 70 3.651 3.435 3.211 2.899 2.648 2.381 1.994 1.667 1.294 0.678 80 3.629 3.416 3.195 2.887 2.639 2.374 1.990 1.664 1.292 0.678 90 3.612 3.402 3.183 2.879 2.632 2.368 1.987 1.662 1.291 0.677

100 3.598 3.390 3.174 2.871 2.626 2.364 1.984 1.660 1.290 0.676 3.481 3.291 3.090 2.807 2.576 2.326 1.960 1.645 1.282 0.674

Table A3: Values of |t| corresponding to two-tailed p-values for Student's t distribution

15

Statistical Formulas:

=

yz (for data)

n

yz

/

= (for sample mean) n

pz

/)1( pipipi

=

(for sample proportion)

standard error (se) of y = n

, estimated se of y =

n

s

se of p = n

)1( pipi , estimated se of p =

n

pp )1(

n

yz

/0

= 95% CI:

ny 96.1

n/)1(p

z00

0

pipi

pi= 95% CI: p 1.96

n

pp )1(

ns

yt

/0

= , (df: = n1) 95% CI: n

sty

n/sy

td

0d = , ( = nd 1) 95% CI:

n

sty dd

nns

yyt

2

1

1

1p

21

+

= , ( = n1 + n2 2)

95% CI: 21

p21n

1n

1st)yy( +

2nn

s)1n(s)1n(s

21

222

211

p+

+=

$yi = a + b xi bx x y y

x x

i i

i=

( )( )( ) 2 =

SS

XY

XX, a y b x=

95% CI: b tn-2 se (b)

SXX = (nx - 1)sx2 SYY = (ny - 1)sy2

= yxnxyS XY t = )b(seb

, ( = n 2)

r2 =

SS S

XY

XX YY

2

= 1 ( $)( )y y

y yi

i

2

2 rS

S Sx x y y

x x y yXY

XX YY

i i

i i

= =

( )( )( ) ( )2 2

2 =

=

( )O EE

j j

jjc

2

1 = c1 2 =

= = i

r ij ij

ijjc O E

E1

2

1

( ) = (r1)(c1)

w = a c

b d//