(a) Do not reject since .39

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Stats 2B03 Test #2

(Version 1)

November 19th, 2013

Name:___________________________________________

(Last Name) (First Name)

Student Number:_____________________

Day Class

Duration: 75 Minutes Instructor: Childs

Maximum Mark: 20

This test paper consists of 19 multiple choice questions worth 1 mark each, and one question worth 1 mark on proper computer card filling. Marks will NOT be deducted for wrong answers (i.e., there is no penalty for guessing). QUESTIONS MUST BE ANSWERED ON THE COMPUTER CARD with an HB PENCIL. Answer all questions. You are responsible for ensuring that your copy of this paper is complete. Bring any discrepancy to the attention of your invigilator. Only the McMaster standard Calculator Casio fx-991 is allowed.

1. Researchers wished to know if they could conclude that two populations of infants differ with respect to mean age at which they walked alone. The following data (ages in months) were collected and are summarized in Minitab output #1 below:

Sample from Population A: 9.5, 10.5, 10.4, 9.75, 10.0, 13.0, 10.3,10.0 10.0, 13.5, 10.0, 11.1, 10.0, 9.75, 11.1,11.6 Sample from Population B: 12.5, 9.5, 13.5, 13.75, 8.75, 13.75

12.5, 9.5, 12.0, 9.8, 12.0, 12.0,14.25

Test the hypothesis that the population variances are equal using αœ Þ"! (i.e., test the hypothesis L À! 5"# œ5## vs L ÀE 5"# Á5##.

Minitab Output #1

---Descriptive Statistics: A, B

Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 A 16 0 10.656 0.290 1.161 9.500 10.000 10.150 11.100 B 13 0 11.831 0.516 1.859 8.750 9.650 12.000 13.625

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2. A sample of 36 hospital patients were administered a certain anesthetic, and these patients slept an average of 9.5 hours, with standard deviation 3 hours. Find the -vaue for the:

hypothesis test that the average time slept following the administration of this anasthetic is different than 9 hours for the sampled population.

(a) .3174 (b) .1667 (c) .4325 (d) .1587 (e) .8413

3. Suppose that we were interested in testing whether marital status(" œ married,

# œnever married, $ œdivorced) has an effect on exercise level (0 = none, =1

light, = moderate, = heavy).2 3 What method could be used? (a) F-test for variances

(b) Contingency table (Chi-Square test) (c) > test for comparing two means (d) one-sample D-test for a proportion (e) Analysis of variance

4. A researcher is interested in testing whether there is a difference in mean IQ level among people with varying levels of education (ed-level). For the ed-level variable, 0œno high school degree, 1œhigh school graduate, 2œcollege graduate, 3œgraduate degree. Suppose that the following data is collected.

101 105 118 115 96 106 115 129 103 111 108 131

99 126

0 1 2 3

For this data set the sum of squares for treatments is equal to WWX < œ "$#$, and the total sum of squares is WWX œ1627.2. Find the value of the -statistic for testing the hypothesisJ

L À! ." œ.# œ .$ œ.% vs L ÀE .3 Á .4 for at least one pair Ð3ß 4Ñ

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5. Researchers wished to know if they could conclude that two populations of infants differ with respect to mean age at which they walked alone. The following data (ages in months) were collected and are summarized in the Minitab outputbelow:

Sample from Population A: 9.5, 10.5, 10.4, 9.75, 10.0, 13.0, 10.3,10.0 10.0, 13.5, 10.0, 11.1, 10.0, 9.75, 11.1,11.6 Sample from Population B: 12.5, 9.5, 13.5, 13.75, 8.75, 13.75

12.5, 9.5, 12.0, 9.8, 12.0, 12.0,14.25

Assuming that 5_"# _Á5_##, find the critical value for testing the hypothesis that the mean walking time for Population A is less than for Population B, using αœ Þ!&Þ

Minitab Output

-

--Descriptive Statistics: A, B

Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 A 16 0 10.656 0.290 1.161 9.500 10.000 10.150 11.100 B 13 0 11.831 0.516 1.859 8.750 9.650 12.000 13.625 -

(a)Þ!)%#>  Þ#'&)> (b)Þ!(#'>  Þ"%$>

Þ!)%#  Þ#'&) Þ!(#'  Þ"%$

"#ßÞ*& "&ßÞ*& "&ßÞ*& "#ßÞ*&

(c)Þ!(#'>  Þ"%$> (d)Þ!)%#>  Þ#'&)>

Þ!(#'  Þ"%$ Þ!)%#  Þ#'&)

"&ßÞ*(& "#ßÞ*(& "&ßÞ*& "#ßÞ*&

(e)Þ!)%#>  Þ#'&)>

Þ!)%#  Þ#'&)

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6. A researcher is interested in testing whether there is a difference in mean IQ level among people with varying levels of education (ed-level). For the ed-level variable, 0œno high school degree, 1œhigh school graduate, 2œcollege graduate, 3œgraduate degree. Suppose that the following data is collected.

101 105 118 115 98 106 115 129 103 111 108 131

99 126

0 1 2 3

Which of the following is a correct normal probability plot of the residuals?

Residual Pe rc e n t 20 10 0 -10 -20 99 95 90 80 70 60 50 40 30 20 10 5 1

Normal Probability Plot of the Residuals

(response is C1)

(response is C1) (a) (b) Residual Pe rc e n t 20 10 0 -10 -20 99 95 90 80 70 60 50 40 30 20 10 5 1

(response is C1)

(c) (d) Residual Pe rc e n t 30 20 10 0 -10 -20 -30 99 95 90 80 70 60 50 40 30 20 10 5 1

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7. Suppose we wish to test the relative effects of three drugs, A, B, C, on the reduction of fever. The drugs are prescribed to children aged 5-14 with a fever of 100.0°F to 100.9°F, and the reduction in fever after four hours is noted as follows:

Drug A Drug B Drug C

2.0 0.5 1.1

1.6 1.2 1.0

2.1 0.3 0.2

0.4

 

Some Minitab output for this data is given below.

---Source DF SS MS F P C2 2 5.873 2.937 7.12 0.021 Error 7 2.887 0.412

Total 9 8.760

---Use Tukey's HSD* test at the 5% significance level to test the hypothesis

L À! ." œ.# vs L ÀE ." Á .# (where ." is the average reduction in fever for the

population taking Drug A, and .# is the corresponding average for Drug B). (a) Do not reject L! since 1.32.94

(b) Do not reject L! since 1.31.442 (c) Reject L! since 3.31.442 (d) Reject L! since 3.32.94

(e) Do not reject L! since 1.31.158

8. A researcher wishes to test the levels of calcium deficiency for three groups of women by taking lumbar spine bone-density measurements for a sample of women from each of the three groups. The following data is obtained

Group 1 Group 2 Group 3

Sample Size Sample Size Sample Size

Mean Mean Mean

Standard Deviation Standard Deviatio

: 10 : 8 : 9

: 20 : 10 : 30

: 2 n: 3 Standard Deviation: 4

If you were to use one-way ANOVA to analyse the above data, what would be the value of the sum of squares error WWI?

(6)

9. Suppose that we were interested in testing whether marital status(" œ married,

# œnever married, $ œdivorced) has an effect on weight (measured in pounds). What method could be used?

(a) > test for comparing two means (b) Analysis of variance

(c) D-test for proportions (d) F-test for variances

(e) Contingency table (Chi-Square test)

10. The serum cholesterol levels of a group of 9 people aged 20-39 who eat a primarily macrobiotic diet were measured (in mg/dL) and summarized in the Minitab output below: ---Descriptive Statistics: cholesterol

Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 cholesterol 9 0 205.22 4.92 14.77 174.00 197.00 207.00 216.00

Variable Maximum cholesterol 223.00

---The mean cholesterol level in the general population in this age group is 230. Test the hypothesis that the average cholesterol level for people in this age group who eat a primarily macrobiotic diet is different than for the general population, using αœ Þ!".

(a) Reject L! since &Þ!$$  $Þ$&&%

(b) Reject L! since &Þ!$$  #Þ)*'

(c) Do not reject L! since &Þ!$$  $Þ$&&%

(d) Reject L! since "*Þ$%  #Þ)*'

(e) Reject L! since "*Þ$%  $Þ$&&%

11. Cross fertilizing a pure strain of red flowers with a pure strain of white flowers produces pink hybrids that have one gene of each type. Crossing these hybrids can lead to any one of four possible gene pairs. Under Mendel's theory, these four are equally likely, so T ÐwhiteÑ œ "_%,

T ÐpinkÑ œ "_#, T ÐredÑ œ "_%. An experiment carried out by Correns, one of Mendel's

followers, resulted in the frequencies 141, 291, and 132 for white, pink, and red flowers respectively. (Source: W. Johannsen, 1909, Elements of the Precise Theory of Heredity, G. Fischer, Jena.) Do these observations appear to contradict the probabilities suggested by Mendel's theory? Use the 5% significance level.

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12. A researcher is interested in testing whether there is a difference in mean IQ level among people with varying levels of education (ed-level). For the ed-level variable, 0œno high school degree, 1œhigh school graduate, 2œcollege graduate, 3œgraduate degree. Suppose that the following data is collected.

101 105 118 115 98 106 115 129 103 111 108 131

99 126

0 1 2 3

Which of the following is NOT an assumption required for the analysis? (a) The population variances must all be equal.

(b) The population variances must be known.

(c) The populations must follow a normal distribution.

(d) All other factors affecting the IQ variable must be kept constant. (e) The samples are independent.

13. A researcher wishes to test whether excercise level (0 = none, = light, = moderate, =1 2 3

heavy) has an effect on systolic blood pressure. So the researcher collects some data and produces Minitab Output #1 which is given with the green sheets of tables and formulas. Test the following hypotheses using Tukey's method with αœ Þ!&,

(i) L À! ." œ.#

(ii) L À! ." œ.$

(iii) L À! ." œ.%

(where ." is the average for the population corresponding to 0 = none, .# is the average for the population corresponding to 1 = light, .$ is the average for the population corresponding to 2 = moderate, and .% is the average for the population corresponding to 3 = heavy). (a) (i) Reject L! (ii) Reject L! (iii) Do not reject L!

(b) (i) Do not reject L! (ii) Reject L! (iii) Reject L!

(c) (i) Reject L! (ii) Reject L! (iii) Reject L!

(d) (i) Do not reject L! (ii) Do not reject L! (iii) Do not reject L!

(8)

14. Consider the data set that is summarized in the Minitab output below. Find the missing -:

value.

-

--Test and CI for One Proportion

Test of p = 0.3 vs p < 0.3

95% Lower

Sample X N Sample p Bound Z-Value P-Value 1 11 50 0.220000 0.123639 ? ?

-

--(a) .218 (b) .034 (c) .068 (d) .891 (e) .109

15. A sociologist wants to determine if the life expectancy of people in Africa is different than the life expectancy of people in Asia. The data obtained is shown in the table below. Africa Asia

B 55.3 58.2

= 8.1 9.3

8 53 42

Find the -value:

(a) .026 (b) .1096 (c)<.0002 (d) .0548 (e) .013

16. Consider the data in the following contingency table.

Biological Offspring Parental Handedness Right-Handed Left-Handed

(father mother) Right Right

Right Left Left Right

‚

‚ $!$ $(

‚ #* *

‚ "' '

If you were to do a chi-square analysis on the above data, what would be the value in cell (1,2) of the expected table?

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17. Consider the data in the following contingency table

Biological Offspring Parental Handedness Right-Handed Left-Handed

(father mother) Right Right

Right Left Left Right

‚

‚ $!$ $(

‚ #* *

‚ "' '

If you were to do a chi-square analysis on the above data, what would be the degrees of freedom for the chi-square test statistic?

(a) 2 (b) 3 (c) 4 (d) 5 (e) 6

18. A researcher wants to test whether there is a relationship between education level and smoking status. So the researcher collects some data and produces the following Minitab output. Using αœ Þ!&, what is the null hypothesis that is being tested in the output, and what is the conclusion?

---Tabulated statistics: smokingstatus2, edlevel2

Rows: smokingstatus2 Columns: edlevel2

H N All

D 39 8 47 40.89 6.11 47.00

S 48 5 53 46.11 6.89 53.00

All 87 13 100 87.00 13.00 100.00

Cell Contents: Count

Expected count

Pearson Chi-Square = 1.268, DF = 1, P-Value = 0.260

Likelihood Ratio Chi-Square = 1.271, DF = 1, P-Value = 0.260

---(a) L!: smoking status and education level are independent; reject L!

(b) L!: smoking status and education level are dependent; reject L!

(c) L!: smoking status and education level are dependent; do not reject L!

(d) L!: the population variances are equal; do not reject L!

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19. A researcher wishes to test the hypothesis that the rate of nausea for pregnant women taking the drug Erythromycin is less than 30%. The researcher takes a sample 200 women who are taking erythromycin and does not reject the null hypothesis. Suppose that the rate of nausea for all pregnant women in the population taking erythromycin is actually 40%. Which of the following is true?

(a) The null hypothesis is L À : Þ$!!

(b) The probability of Type II error is Þ!&

(c) A Type I error has occurred

(d) The population must follow a normal distribution (e) A Type II error has occurred

20. Correctly fill out the bubbles corresponding to your student number and the version number of your test in the correct places on the computer card.

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Minitab Output #1

---Source DF SS MS F P

EXERCISE 3 2001 667 4.55 0.005 Error 96 14084 147

Total 99 16085

S = 12.11 R-Sq = 12.44% R-Sq(adj) = 9.71%

Individual 95% CIs For Mean Based on Pooled StDev

Level N Mean StDev ---+---+---+---+---0 38 ? 13.---+---+---+---+---04 (----*---) 1 38 ? 12.12 (---*----)

2 13 ? 9.71 (---*---) 3 11 ? 11.09 (---*---)

119.0 126.0 133.0 140.0

Pooled StDev = 12.11

Tukey 95% Simultaneous Confidence Intervals

All Pairwise Comparisons among Levels of EXERCISE

Individual confidence level = 98.97%

EXERCISE = 0 subtracted from:

EXERCISE Lower Center Upper +---+---+---+---1 -+---+---+---+---13.0+---+---+---+---1 -5.74 +---+---+---+---1.53 (---*---)

2 -20.11 -9.93 0.25 (---*---) 3 -23.92 -13.07 -2.22 (---*---)

-24 -12 0 12

EXERCISE Lower Center Upper +---+---+---+---2 -14.37 -4.19 5.99 (---*---)

3 -18.18 -7.33 3.52 (---*---)

-24 -12 0 12

EXERCISE Lower Center Upper +---+---+---+---3 -16.17 -+---+---+---+---3.14 9.89 (---*---)

-24 -12 0 12

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---Some Partial Tables

Percentiles of the Distribution Percentiles of the Chi-Square Distribution df.

>

>Þ*& >Þ*(& >Þ** >Þ**& 6 1.9432 2.4469 3.143 3.7074 7 1.8946 2.3646 2.998 3.4995 8 1.8595 2.3060 2.896 3.3554 12 1.7823 2.1788 2.681 3.0545 13 1.7709 2.1604 2.650 3.0123

ã

" #Þ(!' $Þ)%" &

d.f. ;# ;# ;# ;#

Þ*! Þ*& Þ*(& Þ**

Þ!#% 'Þ'$&

# %Þ'!& &Þ**" (Þ$() *Þ#"!

$ 'Þ#&" (Þ)"& *Þ$%) ""Þ$%&

Percentiles of the J Distribution Denominator

Degrees of Numerator Degrees of Freedom

Freedom 8 9 10 12 15 20

JÞ*5

11 2.95 2.90 2.85 2.79 2.72 2.65

12 2.85 2.80 2.75 2.69 2.62 2.54

13 2.77 2.71 2.67 2.60 2.53 2.46

14 2.70 2.65 2.60 2.53 2.46 2.39

15 2.64 2.59 2.54 2.48 2.40 2.33

More Percentiles of the J Distribution Denominator

Degrees of Numerator Degrees of Freedom

Freedom 8 9 10 12 15 20

JÞ*75

11 3.66 3.59 3.53 3.43 3.33 3.23

12 3.51 3.44 3.37 3.28 3.18 3.07

13 3.39 3.31 3.25 3.15 3.05 2.95

14 3.29 3.21 3.15 3.05 2.95 2.84

15 3.20 3.12 3.06 2.96 2.86 2.76

Percentage Points of the Studentized Range for 2 Through 10 Treatments Upper 5% Points

Error

d.f. 2 3 4 5 6 7 8 9 10

1 2 3

17.97 26.98 32.82 37.08 40.41 43.12 45.40 47.36 49.07 6.08 8.33 9.80 10.88 11.74 12.44 13.03 13.54 13.99

4.50 5.91 6.82 7.50 8.04 8.48 8.85 9.18 9.46

3.34 4.16 4.68 5.06 5.36 5.61 5.82 6.00 6.16

3.26 4.04 4.53 4.89 5.17 5.40 5.60 5.77 5.92

3.20 3.95 4.41 4.76 5.02 5.24 5.43 5.59 5.7

ã

7 8

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Answers :(Version 1)