p1 BIO 260, Sum 2019, Exam 2 Name:_________KEY________________

Please place your name legibly at the top and the first letter of your last name in the box.
Written answers should be concise and final answers should be copied into blanks
provided where designated.
MULTIPLE CHOICE (3 pts each) Exam is worth 100 points overall

(1) Which of the following is TRUE?

(A) The normal and X2 distributions are symmetric whereas the t distribution is skewed.
(B) The normal and t distributions are symmetric whereas the F distribution is skewed.
(C) The normal and F distributions are symmetric whereas the X2 distribution is skewed.
(D) The F and X2 distributions are symmetric whereas the t distribution is skewed.
(E) The F and X2 distributions are symmetric whereas the normal distribution is skewed.

(2) Which of the following is TRUE

(A) When comparing two population variances we can always perform a heteroscedastic t test.
(B) When comparing two population variances we can always perform a homoscedastic t test.
(C) When comparing two population means we can always perform a paired t test.
(D) When comparing two population means we can always perform a heteroscedastic t test.
(E) When comparing two population means we can always perform a homoscedastic t test.

(3) Global warming is happening, but so is death. Each year many older people pass away and
with them the memory of how cold typical winders used to be. The younger individuals that
remain do not have this experience. This process can lead to a society (which is just living
people after all) not realizing that temperatures have increased as much as they have since
things are not that different from what everyone personally recalls. This general phenomenon
was described in class and termed which of the following?
(A) Bevis effect (C) Cherry-picking (E) Shifting baselines
(B) Bradley effect (D) File-drawer problem

(4) The best description of what a p value represents is:

(A) The probability that H0 is true.
(B) The probability of obtaining the test statistic if HA is false.
(C) The probability of obtaining the test statistic if HA is true.
(D) The probability of obtaining the test statistic if H0 is false.
(E) The probability of obtaining the test statistic if H0 is true.

(5) The technical definition of a p value is:

(A) The probability of making a type II error.
(B) The probability of seeing the sample data if H0 is false.
(C) The probability of seeing the sample data if HA is true.
(D) The smallest  value we could choose and still reject H0.
(E) The largest  value we could choose and still reject H0.

(6) For a given difference between two sample means, the p value associated with that
difference:
(A) Decreases as the sample sizes increase and decreases as the sample variances decrease.
(B) Decreases as the sample sizes increase and increases as the sample variances decrease.
(C) Increases as the sample sizes increase and decreases as the sample variances decrease.
(D) Depends on the sample sizes, not the sample variances.
(E) Depends on the sample variances, not the sample sizes.
p2 BIO 260, Sum 2019, Exam 2 Name:_________KEY________________

(7) Doris thinks that she may be pregnant, but being a good statistician, decides her null
hypothesis will be that she is not pregnant when she takes an EPT pregnancy test. The test
returns a “false positive”; it tells her she is pregnant when in fact she is not. When Doris then
decides that she is pregnant what type of mistake has been made?
(A) Heteroscedastic error (C) p value error (E) Type II error
(B) Median error (D) Type I error

(8) A researcher is interested in whether a drug alters the pH of blood in users. She takes
blood samples from a set of individuals before and after taking the experimental medication.
Unfortunately, a small number of the sample jar labels within each set got switched and she
cannot guarantee which samples are from the same individuals in a few cases. What option
below best explains her next step.
(A) Because only a few labels are incorrect she can still do a paired t test, she should just use a
smaller p value in her analysis.
(B) She cannot do a paired t test, but since the same people are in both samples she can analyze the
data with a homoscedastic t test.
(C) She cannot do a paired t test, but she can analyze the data with a heteroscedastic t test.
(D) She cannot do a t test, but she can analyze the data with an F ratio test to answer her overall
question.
(E) Since the labels are not correct she cannot do a paired t test and she needs to redo the whole
experiment.

(9) What is the best description of the logic of statistical testing?

(A) We calculate data with summary statistics and plot the data to make sure they are valid.
(B) We calculate population parameters from sample statistics and use these parameters to test
our models.
(C) We calculate statistics based on samples and try to infer patterns in the data that are stronger
than can easily be accounted for by sampling error.
(D) When data is not normally distributed we need to transform the values.
(E) The standard deviation is the square root of the variance.

(10) The t distribution is wider than the Z distribution because:

(A) It includes the uncertainty in our estimate of the sample mean.
(B) It includes the uncertainty in our estimate of the sample variance.
(C) It includes the uncertainty in our estimate of the population mean.
(D) It includes the uncertainty in our estimate of the population variance.
(E) Larger sample sizes cause it to be wider than the Z distribution.

(11) FDA approval requires that to be an approved "drug" a substance must:

(A) Be safe and 100% harmless. (D) Be safe and relatively harmless.
(B) Be effective and 100% harmless. (E) Be effective and relatively harmless.
(C) Be artificial and 100% effective.

(12) Imagine you take a sample of 21 values from a population and the sample mean and
standard deviation are 36 and 25 respectively. Which of the following pairs of values are the
closest to the 95% confidence interval for the population mean?
(A) { 24.3 , 47.7 } (C) { 33.4 , 38.6 } (E) { 34.1 , 37.9 }
(B) { 26.4 , 45.6 } (D) { 33.7 , 38.3 }
p3 BIO 260, Sum 2019, Exam 2 Name:_________KEY________________
The next 3 questions are based on the list of "misuses of statistics" that you were instructed to read
for this exam.
(13) Polls of people's opinions about abortion can differ widely when done by organizations
favoring or not favoring legal abortion. Polls that ask whether people "favor laws that allow the
destruction of unborn babies" will yield very different results from those that ask whether
people "favor laws that allow a woman to decide to undergo a medical procedure that
terminates pregnancy." This exemplifies which of the following misuses of statistics?
(A) Data manipulation (D) Misreporting of standard error
(B) Discarding unfavorable data (E) Proof of the null hypothesis
(C) Loaded questions
(14) Similarly, if a pair of polls were created that avoided the issue above, but one was
conducted on a people exiting a church while the other was performed on college students
leaving a Women's Studies final exam this is also poor practice. This exemplifies which of the
following misuses of statistics?
(A) Biased samples (D) False causality
(B) Cherry-picking (E) Loaded questions
(C) Data manipulation
(15) Many psychological studies are conducted using large numbers of WEIRD (Western,
Educated, and from Industrialized, Rich, and Democratic countries) students. This population
has been used for almost all studies of modern psychology and has been used to help us
understand how the human mind works. There is a fundamental problem with this approach
however; the problem of:
(A) Data dredging. (D) Overgeneralization.
(B) False causality (E) Proof of the null hypothesis.
(C) Loaded questions.

(16) Which of the following was NOT discussed as a bias in the samples we have historically
used for drug testing?
(A) Participants are often personally connected by friendship to the researchers.
(B) Participants are often the same individuals in multiple studies.
(C) Participants are overwhelmingly Caucasian.
(D) Participants are overwhelmingly male.
(E) Participants are overwhelmingly younger than 30.

(17) A 90% confidence interval calculated from a set of sample data is the region in which:
(A) there is only a 10% probability the sample mean is outside this region.
(B) there is only a 10% probability the population mean is outside this region.
(C) there is a 90% probability that the sample median lies
(D) 90% of the sample data lies.
(E) 90% of the population data lies.

(18) Which of the following is the best description of the way the technical term "statistically
significant" is most commonly used?
(A) When the null hypothesis of a statistical test can be rejected at the  =1% level.
(B) When the null hypothesis of a statistical test can be rejected at the  =5% level.
(C) When the alternative hypothesis of a statistical test can be rejected at the =1% level.
(D) When the alternative hypothesis of a statistical test can be rejected at the =5% level.
(E) When the values of the two populations are meaningfully different.
p4 BIO 260, Sum 2019, Exam 2 Name:_________KEY________________

(19) One of the topics I study in my research lab is how the attractiveness of a person may be
influenced by their eye color. A few years ago, I conducted a study in which people were asked to rate
the attractiveness of faces that had been altered to have blue or brown eyes (higher number is better).
Some subjects received the blue-eyed version while others received the brown-eyed one. Imagine
that we collected data from 15 subjects rating a particular face and the scores were as below:
Blue Brown
5 5
8 2
6 2
5 8
5 3
8 5
4 3
7
(a, 3 pts each) Conduct an F variance ratio test on these two data sets. Provide your calculated Fcalc
value and the Fcrit value you will use to interpret your results. Report all calculated values to the
nearest 0.001. Tables of F critical values are on the last page.

Fcalc = 2.042 Fcrit (=0.05) = 5.12

(b, 3 pts) In the box below, state the technical conclusion of your F test in the box below. Use the
grammar presented in lecture and be sure to include a statement about your degree of confidence
with a range of p values (using the tables on the last page), whether the conclusions are "significant"
or not, and a statement about any directionality seen. Note: no credit will be given for ANY text
outside the box or hard to read answers and a lack of precision or unnecessary information and filler
text will result in a loss of points.

The variance of attractiveness scores for the face when it had blue eyes is
NOT SIGNIFICANTLY DIFFERENT from the variance of the scores when it had
brown eyes ( 0.1 < p )

(c, 3 pts each) Regardless of the results of your F test, conduct a heteroscedastic t test on this data.
Provide your calculated tcalc value, your degrees of freedom and the tcrit value you will use to interpret
your results. Report all calculated values to the nearest 0.001 (except for df, provide that as the
appropriate integer). Tables of t critical values are on the last page.

tcalc = 2.049 t test df = 10 tcrit (=0.05) = 2.228

(d, 3 pts) State the technical conclusion of your t test in the box below. Use the grammar presented in
lecture (i.e., you should NOT have extraneous wording or terms). You must use either the phrase
“significantly larger” or “not significantly different”, and provide the most precise range of p values that
your test results allow (using the tables on the last page). Note: no credit will be given for ANY text
outside the box or hard to read answers and a lack of precision or unnecessary information and filler
text will result in a loss of points.

The mean attractiveness scores for the face when it had blue eyes was
NOT SIGNIFICANTLY DIFFERENT from the scores when it had brown
eyes ( 0.05 < p < 0.1 )
p5 BIO 260, Sum 2019, Exam 2 Name:_________KEY________________

(20) One of my former graduate students studied the asymmetry of specific traits in individuals from
wild populations. Not asymmetry in terms of consistent differences, just how different the two sides
are from each other in each individual. For theoretical reasons beyond the scope of this course, these
values allowed her to make estimates of the relative ability of these populations to evolve. There is a
potential problem though, if the sides are consistently different (i.e., the overall mean of the left sides
is different from the overall mean of the right sides) then she must perform an extra step in her data
processing to answer this question. One of the traits she studied was the number of femoral pores on
lizards; consider the example data below to be such data from the left and right sides of 9 individuals.

Liz # Left Right

1 12 16
2 19 18
3 14 16
4 10 12
5 11 17
6 15 19
7 11 12
8 18 19
9 7 15

(a, 3 pts each) Conduct a paired t test on the values above and fill in the blanks below with the values
indicated. Report all calculated values to the nearest 0.001 (except for df, provide that as the
appropriate integer). Tables of t critical values are on the last page.

tcalc = -3.233 t test df = 8 tcrit (=0.05) = 2.306

(b, 3 pts) In the box below, state the technical conclusion of your t test in the box below. Use the
grammar presented in lecture (i.e., you should NOT have extraneous wording or terms). You must
use either the phrase “significantly larger” or “not significantly different”, and provide the most precise
range of p values that your test results allow. Note: no credit will be given for ANY text outside the box
or hard to read answers and a lack of precision or unnecessary information and filler text will result in
a loss of points.

The mean number of pores on the left side is SIGNIFICANTLY SMALLER than the
mean for the right side ( 0.01 < p < 0.02 )

(c, 3 pts) In the box below, state the plain language version of your conclusion in the box below. Does
my student have to do the extra step in her data processing or not?

YES, the lizards ARE asymmetric so the student has to do the extra step.
p6 BIO 260, Sum 2019, Exam 2 Name:_________KEY________________

(21) One of my other former students just finished her PhD at UC Santa
Cruz in a lab that studies side-blotched lizards. These lizards are interesting
because there are three color morphs that seem to exhibit a rock-papers-
scissors ecological dynamic. Orange males maintain territories and mate
with females inside, blue males pair-bond with individual females, and
yellow males sneak around and quickly mate with females. Orange males
can displace blue males, but are vulnerable to yellows sneaking into their
territories; blues can recognize and prevent yellows from sneaking, but
cannot fight against oranges; Yellows can steal matings from oranges, but
not from blue. Mathematical theory predicts that the frequencies of the color morphs should therefore
change over time as the rarest morph has an advantage each year. Imagine that we collect the data
shown below for adult individuals in three successive years. We can then use the 𝜒 2 test to determine
whether the frequencies are independent of the year or whether they show evidence of cycling (i.e.,
they change over the years).
Year 1 Year 2 Year 3
Red 6 11 23
Orange 10 8 14
Blue 14 6 8

Conduct a 𝜒 2 test of independence using the values above.

Report your value to the nearest 0.001
2
(a, 4 pts) What is the 𝜒 2 value you obtain? 𝑋𝑐𝑎𝑙𝑐 = __10.072__

(b, 3 pts) In the box below, state the technical conclusion of your 𝜒 2 test. Use the grammar presented
in lecture (i.e., you should NOT have extraneous wording or terms). Be sure to include a statement
about your degree of confidence with a range of p values (using the tables on the last page) and
whether the conclusions are "significant" or not. Remember that you are talking about "frequencies of
color morphs". Note: no credit will be given for ANY text outside the box or hard to read answers and
a lack of precision or unnecessary information and filler text will result in a loss of points.

The observed and predicted values are SIGNIFICANTLY DIFFERENT from one
another ( 0.01 < p < 0.05 ), the frequencies of the color morphs and the year in
which the measurement was taken are not independent of one another

(c, 3 pts) State the plain language version of your conclusion in the box below. Do the frequencies of
the color morphs seem to change over time or not?

The color morph frequencies seem to change from year to year.

 p7 BIO 260, Sum 2019, Exam 2 Name:_________KEY________________

able of t values
TABLES OF t and F VALUES
is table shows the t value corresponding to the  value as shown. 
Table
e  value is the area shows
under theto tthevalues
the curve corresponding
right of the t value.
hen doing two-tailedto the indicated critical  value.
tests the a value should be double for overall . t
df  =0.1  =0.05  =0.025  =0.02  =0.01  =0.005  =0.0025  =0.001
df t0.1 t0.05 t0.025 t0.02 t0.01 t0.005 t0.0025 t0.001
1 3.078 6.314 12.710 15.890 31.820 63.660 127.300 318.300
2 1.886 2.920 4.303 4.849 6.965 9.925 14.090 22.330
1 3.078 6.314 12.710 15.890 31.820 63.60 127.30 318.30
3 1.638 2.353 3.182 3.482 4.541 5.841 7.453 10.210
4 2
1.533 1.886
2.132 2.920
2.776 4.3032.9994.849 3.747
6.965 9.925
4.604 14.090
5.598 22.330
7.173
5 3
1.476 1.638
2.015 2.353
2.571 3.1822.7573.482 3.365
4.541 5.841
4.032 7.453
4.773 10.210
5.893
6 1.440
4 1.943
1.533 2.447
2.132 2.7762.6122.999 3.143 3.707
3.747 4.604 4.317
5.598 7.1735.208
7 1.415 1.895 2.365
5 1.476 2.015 2.5712.5172.757 2.998 3.499
3.365 4.032 4.029
4.773 5.8934.785
8 1.397 1.860 2.306 2.449 2.896 3.355 3.833 4.501
9 1.383 1.833 2.262 2.398 2.821 3.250 3.690 4.297
10 6
1.372 1.440
1.812 1.943
2.228 2.4472.3592.612 2.764
3.143 3.707
3.169 4.317
3.581 5.2084.144
11 1.363
7 1.796
1.415 2.201
1.895 2.3652.3282.517 2.718 3.106
2.998 3.499 3.497
4.029 4.7854.025
12 1.356 1.782 2.179
8 1.397 1.860 2.3062.3032.449 2.681 3.055
2.896 3.355 3.428
3.833 4.5013.930
13 1.350 1.771 2.160 2.282 2.650 3.012 3.372 3.852
14 9
1.345 1.383
1.761 1.833
2.145 2.2622.2642.398 2.624
2.821 3.250
2.977 3.690
3.326 4.2973.787
15 10
1.341 1.372
1.753 1.812
2.131 2.2282.2492.359 2.602
2.764 3.169
2.947 3.581
3.286 4.1443.733
16 1.337 1.746 2.120 2.235 2.583 2.921 3.252 3.686
17 1.333 1.740 2.110 2.224 2.567 2.898 3.222
11 1.363 1.796 2.201 2.328 2.718 3.106 3.497 4.0253.646
18 1.330 1.734 2.101 2.214 2.552 2.878 3.197 3.611
19 12
1.328 1.356
1.729 1.782
2.093 2.1792.2052.303 2.539
2.681 3.055
2.861 3.428
3.174 3.9303.579
20 13
1.325 1.350
1.725 1.771
2.086 2.1602.1972.282 2.528
2.650 3.012
2.845 3.372
3.153 3.8523.552
21 1.323
14 1.721
1.345 2.080
1.761 2.1452.1892.264 2.518 2.831
2.624 2.977 3.135
3.326 3.7873.527
22 1.321 1.717 2.074 2.183 2.508 2.819 3.119
15 1.341 1.753 2.131 2.249 2.602 2.947 3.286 3.7333.505
23 1.319 1.714 2.069 2.177 2.500 2.807 3.104 3.485
24 1.318 1.711 2.064 2.172 2.492 2.797 3.091 3.467
25 16
1.316 1.337
1.708 1.746
2.060 2.1202.1672.235 2.485
2.583 2.921
2.787 3.252
3.078 3.6863.450
26 1.315
17 1.706
1.333 2.056
1.740 2.1102.1622.224 2.479 2.779
2.567 2.898 3.067
3.222 3.6463.435
27 1.314 1.703 2.052 2.150 2.473 2.771 3.057
18 1.330 1.734 2.101 2.214 2.552 2.878 3.197 3.6113.421
28 1.313 1.701 2.048 2.154 2.467 2.763 3.047 3.408
29 19
1.311 1.328
1.699 1.729
2.045 2.0932.1502.205 2.462
2.539 2.861
2.756 3.174
3.038 3.5793.396
30 20
1.310 1.325
1.697 1.725
2.042 2.0862.1472.197 2.457
2.528 2.845
2.750 3.153
3.030 3.5523.385
31 1.309 1.696 2.040 2.144 2.453 2.744 3.022 3.375
32 1.309 1.694 2.037
21 1.323 1.721 2.0802.1412.189 2.449 2.738
2.518 2.831 3.015
3.135 3.5273.365
33 1.308 1.692 2.035 2.138 2.445 2.733 3.008 3.356
34 22
1.307 1.321
1.691 1.717
2.032 2.0742.1362.183 2.441
2.508 2.819
2.728 3.119
3.002 3.5053.348
35 23
1.306 1.319
1.690 1.714
2.030 2.0692.1332.177 2.438
2.500 2.807
2.724 3.104
2.996 3.4853.340
40 1.303
24 1.684
1.318 2.021
1.711 2.0642.1232.172 2.423 2.704
2.492 2.797 2.971
3.091 3.4673.307
50 1.295 1.676 2.009
25 1.316 1.708 2.0602.1092.167 2.403 2.678
2.485 2.787 2.937
3.078 3.4503.261
60 1.296 1.671 2.000 2.099 2.390 2.660 2.915 3.232
70 1.294 1.667 1.994 2.093 2.381 2.648 2.899 3.211
80 26
1.292 1.315
1.664 1.706
1.990 2.0562.0882.162 2.374
2.479 2.779
2.639 3.067
2.887 3.4353.195
90 1.291
27 1.662
1.314 1.987
1.703 2.0522.0842.150 2.368 2.632
2.473 2.771 2.878
3.057 3.4213.183
100 1.290 1.660 1.984 2.081 2.364 2.626 2.871
28 1.313 1.701 2.048 2.154 2.467 2.763 3.047 3.4083.174
150 1.287 1.655 1.976 2.072 2.351 2.609 2.849 3.145
200 29
1.286 1.311
1.653 1.699
1.972 2.0452.0672.150 2.345
2.462 2.756
2.601 3.038
2.839 3.3963.131
250 30
1.285 1.310
1.651 1.697
1.969 2.0422.0652.147 2.341
2.457 2.750
2.596 3.030
2.832 3.3853.123
300 1.284 1.650 1.968 2.063 2.339 2.592 2.828 3.118
500 1.283 1.648 1.965 2.059 2.334 2.586 2.820 3.107
40 1.303 1.684 2.021 2.123 2.423 2.704 2.971 3.307
1000 1.282 1.646 1.962 2.056 2.330 2.581 2.813 3.098
Infinity 50
1.282 1.295
1.645 1.676
1.960 2.0092.0542.109 2.326
2.403 2.678
2.576 2.937
2.807 3.2613.090
60 1.296 1.671 2.000 2.099 2.390 2.660 2.915 3.232
80 1.292 1.664 1.990 2.088 2.374 2.639 2.887 3.195

100 1.290 1.660 1.984 2.081 2.364 2.626 2.871 3.174

1000 1.282 1.646 1.962 2.056 2.330 2.581 2.813 3.098
inf. 1.282 1.640 1.960 2.054 2.326 2.576 2.807 3.091
p8 BIO 260, Sum 2019, Exam 2 Name:_________KEY________________

Table of critical 𝜒 2 values

 value

df 0.05 0.01 0.001

1 3.84 6.64 10.83
2 5.99 9.21 13.82
3 7.82 11.35 16.27
4 9.49 13.28 18.47
5 11.07 15.09 20.52

6 12.59 16.81 22.46

7 14.07 18.48 24.32
8 15.51 20.09 26.13
9 16.92 21.67 27.88
10 18.31 23.21 29.59

11 19.68 24.73 31.26

12 21.03 26.22 32.91
13 22.36 27.69 34.53
14 23.69 29.14 36.12
15 25.00 30.58 37.70
p9 BIO 260, Sum 2019, Exam 2 Name:_________KEY________________
p10 BIO 260, Sum 2019, Exam 2 Name:_________KEY________________