BIOL 570

You walk into a classroom and find that of 30 men, 20 are wearing jeans. Of the 25 women in the class, 10 are wearing jeans. Create a two x two contingency table with these data. What is the expected number of men wearing jeans IF the probability of wearing jeans is independent of the probability that a randomly chosen student is male? A. (30*30)/55 B. (30*30) C. 20/55 D. (30*10)/30

A. (30*30)/55

(choose the answer to fill in the blank). If we want to be precise, we could say that 95% of the values from a normal distribution are within ______________ standard deviations of the mean. A. 1.96 B. 2.00 C. 1.52 D. 1.00

A. 1.96

The normal distribution is a ________________ probability distribution (choose the answer that correctly fills in the blank) A. Continuous B.Discrete C. Mutually exclusive D. Categorical

A. Continuous

When you look up a test statistic in the standard normal table (which is shown in your book and a table that we will provide on your exam), the number that you look up represents the probability that a number drawn from the standard normal distribution will be: A. Larger than the test statistic. B. Smaller than the test statistic C. Larger or smaller than the test statistic D. Larger in magnitude (or "absolute value") than the test statistic.

A. Larger than the test statistic.

The standard normal distribution is characterized by: A. Mean=0, standard deviation=1 B. Mean=0, standard deviation=0 C. Mean=1, standard deviation=1 D. Mean=1, standard deviation=0

A. Mean=0, standard deviation=1

In addition to the binomial test, Chapter 7 also introduces a confidence interval. All are true statements about this confidence interval EXCEPT: A. The authors of the book recommend using the Wald method for confidence intervals. B. The authors of the book recommend using the Agresti-Coull method for confidence intervals. C. In the example on pp. 189-190, a confidence interval was calculated. This confidence interval suggests that radiologists tend to have fewer sons than typically seen in human populations. D. Chapter 7 focuses on confidence intervals for population proportions.

A. The authors of the book recommend using the Wald method for confidence intervals.

If your decision is that the null hypothesis is not rejected, which is the best interpretation? A. The data are more consistent with the null hypothesis than the alternative hypothesis B. The null hypothesis must be true

A. The data are more consistent with the null hypothesis than the alternative hypothesis

Look at Figure 7.1-2 on page 184. What is the main concept being emphasized by this picture? A. The larger the sample size, the less the variation in proportion of successes (i.e. with larger sample sizes, the proportion of successes in one sample is more similar to the proportion of successes in another sample than would be expected with small sample sizes) B. Sample size affects the "location" of the curve on the x axis - i.e. with large sample sizes, the estimates (i.e., p-hat) are on average smaller than with small sample sizes. C. The larger the sample size, the more the variation in proportion of successes (i.e. with larger sample sizes, the proportion of successes in one sample differs more from the proportion of successes in another sample than would be expected with small sample sizes) D. Sample size affects the "location" of the curve on the x axis - i.e. with large sample sizes, the estimates (i.e., p-hat) are on average larger than with small sample sizes.

A. The larger the sample size, the less the variation in proportion of successes (i.e. with larger sample sizes, the proportion of successes in one sample is more similar to the proportion of successes in another sample than would be expected with small sample sizes)

As an aspiring doctor, you hear at a medical conference that a new drug may offer advantages for treating a condition. You later read a scientific study about the drug and find that the CI for an odds ratio was from .95 to 1.05 (where the ratio is odds of successful treatment with the drug over odds of successful treatment without the drug). You conclude: A. There isn't evidence that the drug is successful for treating the condition. B. There is cause for great concern: the use of the drug leads to a lower success rate than not using any drug at all. C. There is evidence that the drug is successful for treating the condition.

A. There isn't evidence that the drug is successful for treating the condition.

Reducing Type I error can increase the chance of Type II error. Is this statement: A. True B. False

A. True

Which of the following aspects of the normal distribution is not necessarily equal to the others? A. Variance B. Mode C. Median D. Mean

A. Variance

Look at the ice cream sales and violent crime example on p. 201-2. Think about the concepts being presented in this "interleaf." All of the following statements are true EXCEPT: A. We should never ask research questions that may be complicated by confounding variables. B. In the data set used for the ice cream study, both ice cream sales and violent crime likely increase in warm weather. C. The ice cream study is an observational study. D. The heat in summer (i.e. the variable of "temperature") is a confounding variable in the ice cream study, and likely the cause of the apparent association.

A. We should never ask research questions that may be complicated by confounding variables.

Type II error occurs: A. When the null hypothesis is false but one does not reject the null hypothesis B. When the null hypothesis is true but one does not reject the null hypothesis C. When the null hypothesis is false but one does reject the null hypothesis D. When the null hypothesis is true but one does reject the null hypothesis

A. When the null hypothesis is false but one does not reject the null hypothesis

You are testing whether the mass of an individual is consistent with it being drawn from a specific normal distribution. You get a test statistic of Z=0.82. When you look this up in the Z table, you find that it corresponds to the entry of 0.20611. What is the P-value for your test? A. 0.82 B. .41222 C. .20611 D. 1.64

B. .41222

You are interested in testing whether the sex ratio of frogs in a pond is even (50:50). You catch 8 frogs and determine the gender of each. What type of test would you use to conduct the hypothesis test? A. Z test B. Binomial test C. Chi-squared goodness of fit D. Chi-squared contingency test

B. Binomial test

A population of birds is polymorphic in terms of plumage. Some individuals are brown, others are blue. Both sexes are polymorphic, but you are not sure of the frequency of each coloration. You would like to know whether the plumage differences affect the breeding/parenting behavior. In particular you want to know if the plumage color of a female bird is independent of the plumage color of her mate. You observe the male and female plumage colorations at 50 randomly chosen nests. What type of hypothesis test would you use to test the null that male coloration is independent of female coloration in nesting pairs? A. Chi-squared goodness-of-fit test B. Chi-squared contingency test C. Z test D. Binomial test

B. Chi-squared contingency test

Which is a TRUE statement about a "critical value?" A. It refers to a probability (typically 0.05). B. It refers to a value of a test statistic that is associated with a defined area/probability (such as 0.05). C. It is another name for the P-value.

B. It refers to a value of a test statistic that is associated with a defined area/probability (such as 0.05).

Increasing "power": A. Likely will decrease Type I error B. Likely means increasing sample size C. Is something to avoid in statistics

B. Likely means increasing sample size

In most cases, if you do NOT reject a null hypothesis about a particular parameter A. That value of the parameter would not be included in a 95% confidence interval (assuming the same alpha level) B. That value of the parameter would be included in a 95% confidence interval (assuming the same alpha level)

B. That value of the parameter would be included in a 95% confidence interval (assuming the same alpha level)

Standard error is an important concept that we will return to often in this course. All of the following are true EXCEPT: A. A standard error is actually a standard deviation; for example, for SE of the mean, it is the standard deviation of sample means (after many, many samples are taken from a population). B. The "Law of Large Numbers" means that in a study with large numbers one has large standard errors. C. For standard errors, it is helpful to imagine a case where a very large number of samples are taken from a population, and a statistic is calculated (i.e. sample mean or sample proportion). However, in practice, we don't literally take all these samples from one population. That is, this is a useful conceptual idea but not something we literally do with our studies. D. Both SE of the mean and SE of the proportion refer to the spread of their respective sampling distributions.

B. The "Law of Large Numbers" means that in a study with large numbers one has large standard errors.

Consider a hypothesis test similar to those discussed in Chapter 6 (i.e. null hypothesis: p = .5) Which is a true statement? A. The "p" in this hypothesis refers to the p-value. B. The "p" in this hypothesis refers to a population proportion. C. The "p" in this hypothesis refers to the sample proportion.

B. The "p" in this hypothesis refers to a population proportion.

When you conduct a chi-square test, you look up a number in the statistical table. If you are conducting a test at the 0.05 significance level, you would look up the number in the 0.05 column of the appropriate row in the table. You will reject the null if your test statistic is greater than this number. In statistical jargon, what is the name for the number that you look up in the table? A. The degrees of freedom B. The critical value C. The expectation D. The P-value

B. The critical value

You read two studies about sex ratio in a species. In study 1, the proportion of males was .54 with a 95% CI between .49 and .59. In study 2, the proportion of males was .56 with a 95% CI between .42 and .70. All of the following are true EXCEPT: A. In both cases, we are 95% confident that the true proportion of males is in the defined intervals. B. These results don't make sense. Two studies of the same species should have yielded identical confidence intervals. C. It is reasonable to guess that Study 2 may have had a smaller sample size. D. Both studies are consistent with a 50/50 sex ratio.

B. These results don't make sense. Two studies of the same species should have yielded identical confidence intervals.

What assumption is common to all of the hypothesis tests that we have covered? A. The data are normally distributed B. We have a random sample C. The test statistic is a discrete variable D. We expect more that 5 "successes"

B. We have a random sample

To calculate a binomial formula, one needs to understand factorials. For example, to calculate 5!, one multiplies 5 x 4 x3 __________. Fill in the blank. A. x 3 x 4 x 5 B. x 2 x 1 C. x 1 D. x 5

B. x 2 x 1

In a binomial test, the number of successes that would be most consistent with the expectations according to the null hypothesis is ____________ where p is the probablity of success for each trial if the null is true and n is the sample size. In both the chi-sqare test and a Z-test, if the data corresponds exactly to what is predicted by the null hypothesis then the test statistic would have a value of __________. (choose the answer that correctly fills in both blanks). A. "np(1-p)" for the first blank. "n*n" for the second blank. B. "np" for the first blank. "0" for the second blank. C. "0" for both blanks. "np(1-p)" for the first blank. D. "n" for the second blank.

C. "np" for the first blank. "0" for the second blank.

Look at p. 183. The probabilities in table 7.1-1 are plotted in figure 7.1-1. Based on what we know about sampling distributions, what value would you get if you summed all the "Pr(X)" values (both columns) in the table? A. .05 B. 2 C. 1 D. .5

C. 1

Asssume that a null hypothesis is really false. Which one of the following statements is therefore correct? A. A study with a larger sample is less likely than a smaller study to get the results that P < 0.05. B. A study with a larger sample is equally likely compared to a smaller study to get the result that P < 0.05. C. A study with a larger sample is more likely compared to a smaller study to get the result that P < 0.05.

C. A study with a larger sample is more likely compared to a smaller study to get the result that P < 0.05.

The following are true statements about the null distribution for the Chi square test statistic EXCEPT: A. It lacks negative numbers. B. The particular shape of the distribution depends on the degrees of freedom. C. It is a bell shaped curve. D. It is skewed with a "tail" to the right hand side.

C. It is a bell shaped curve.

In courses that have math, there is a tendency to just memorize formulas without thinking them through. We want to discourage that approach in this course. In particular, the binomial forumula actually "makes sense" if you think it through. Look carefully at the binomial formula and think about the binomial coefficient. All the statements below are true EXCEPT: A. By calculating this number, you learn the number of different ways you could have X successes in a sample of size n. B. It is calculated as n! divided by X! (n-X)! C. It is a term that calculates p, the hypothesized population proportion.

C. It is a term that calculates p, the hypothesized population proportion.

Consider a problem with two categories (such as people with or without a "free" ear lobe). All of the statements below are true EXCEPT: A. If you have access to computing power, the binomial test has advantages because it provides an exact P-value. B. One must keep track of the assumptions of the chi-square goodness of fit test - if they are violated, go with the binomial test. C. It is always recommended that you use the chi-square goodness-of-fit test

C. It is always recommended that you use the chi-square goodness-of-fit test

To reduce Type I error A. Alpha has no effect on this issue B. One could increase alpha C. One could reduce alpha

C. One could reduce alpha

A study was done to see if there was a 50:50 sex ratio in a population of insects A sample of 15 insects was taken, and of these 5 were female. Hypothesis testing was done with a two-tailed alternative hypothesis. The P-value for this problem would be: A. Pr (5) + (Pr (4) + Pr (3) + Pr (2) + Pr (1) + Pr (0) B. Pr (5) C. Pr (5) + (Pr (4) + Pr (3) + Pr (2) + Pr (1) + Pr (0) + Pr (10) + Pr (11) + Pr (12) + Pr (13) + Pr (14) + Pr (15) D. Pr (5) + Pr (6) + Pr (7) + Pr (8) + Pr (9) + Pr (10) + Pr (11) + Pr (12) + Pr (13) + Pr (14) + Pr (15)

C. Pr (5) + (Pr (4) + Pr (3) + Pr (2) + Pr (1) + Pr (0) + Pr (10) + Pr (11) + Pr (12) + Pr (13) + Pr (14) + Pr (15)

Section 8.5 is often challenging for students. All of the statements are true EXCEPT: A. Once one has the observed and expected numbers, calculations are done just like any other chi-square goodness of fit test. B. Section 8.5 refers to a chi-square goodness of fit test, but the expected numbers are calculated using the binomial formula. C. Section 8.5 refers to a more complex type of binomial test.

C. Section 8.5 refers to a more complex type of binomial test.

One-sided tests: A. Are commonly used and recommended by the book's authors B. Involve a situation where the null hypothesis and the alternative hypothesis are identical to each other C. Should be avoided in most situations

C. Should be avoided in most situations

The binomial test we cover in Chapter 7 is conceptually identical to the hypothesis tests we've already covered in lecture (i.e. red/blue shirts; dogs matching/not matching owners). However, taking the Chapter 7 approach of the binomial test has several advantages. All of the items below are true statements about the binomial test EXCEPT: A. The null hypothesis for the binomial test can use any value of p (i.e., p = .3, p = .9, etc.). Thus it is not restricted to p = .5, like in the early examples of hypothesis testing that we used in lecture. B. The binomial test allows you to calculate an exact P value using the binomial distribution. C. The binomial test can be used with continuous numerical variables.

C. The binomial test can be used with continuous numerical variables.

All of the following are true statements about "one-sided" tests EXCEPT: A. All else being equal, one is more likely to reject a null hypothesis with a one-sided test than with a two-sided test. B. The alternative hypothesis has a > or < sign in it. C. The null hypothesis is only rejected if the data depart from it in the direction stated by the null hypothesis. D. One-sided tests are not commonly used, and are not recommended for use by authors of the textbook.

C. The null hypothesis is only rejected if the data depart from it in the direction stated by the null hypothesis.

The binomial formula is used in the binomial test, a kind of hypothesis test. To think about this, imagine a series of "trials" where each trial could be the flip of a coin. All of the following are true EXCEPT: A. The probability of success (in this case p = .5) is the same for every flip of the coin B. A coin flip is a good example to use to illustrate the binomial distribution since there are only two outcomes - heads and tails - for each flip C. The number of trials (n) does not have to be known to use the formula D. One must assume that each trial is independent - for example, the result from the first flip of the coin must not alter the result from the second flip of the coin

C. The number of trials (n) does not have to be known to use the formula

The P-value is defined as ... A. The same as alpha, the type I error rate. B. The type II error rate. C. The probability of obtaining a value of the test statistic as extreme or more extreme than what was observed if the null hypothesis were true D. The probability that the null hypothesis is true.

C. The probability of obtaining a value of the test statistic as extreme or more extreme than what was observed if the null hypthesis were true

Imagine that you knew that the time between cell divisions for a particular cell type in culture was normally distributed with mean of 3785 seconds and a standard deviation of 231 seconds. You measure the division time for a singe cell, and you would like to test the null hypothesis that this cell division time is a random draw from the population of times known for this cell type. What test would you use? A. Chi-squared goodness-of-fit test B. Chi-squared contingency test C. Z test D. Binomial test

C. Z test

In all of the tests that we perform in this class, we calculate a P-value by using the value of our ________________ to delimit the extreme tails of the ___________________. The probability of getting a result in these tails is our P-value. (Choose the correct answer that gives the phrases that fill in the two blanks). A. "significance level" and "sampling distribution of the mean" B. "type I error rate" and "normal distribution" C. "type II error rate" and "chi-squared distribution" D. "test statistic" and "null distribution"

D. "test statistic" and "null distribution"

(choose the pair of words that correctly fill in the first and then second blank). The probability distribution that characterizes the probability of a number of successes out of a fixed number of independent trials (in which the probability of success is the same for each trial) is the ____________ distribution; however when we have a large number of trials, we can approximate the tails of this distribution by using the ______________ distribution. A. Chi-squared, normal B. Normal, poisson C. Binomial, chi-squared D. Binomial, normal

D. Binomial, normal

A game theorist predicts that a certain population of sunfish will be made up of 40% territorial males, 35% courting non-territorial males, and 25% "sneaker" males. You observe males in the population and record that 23 are territorial, 64 are courting, non-territorial and 20 are sneakers. What type of hypothesis test would you use to test the hypothesis that the theorist is correct about the population proportions? A. Z test B. Chi-squared contingency test C. Binomial test D. Chi-squared goodness-of-fit test

D. Chi-squared goodness-of-fit test

A standard normal deviate (also known as a Z statistic) for a variable is simply... (choose the answer the completes the sentence). A.The sum of the variable and the mean. B. The difference between the mean and the variable. C. The value of the variable divided by the standard deviation. D. How many standard deviations higher or lower than the mean the variable is.

D. How many standard deviations higher or lower than the mean the variable is.

All the following are true statements about goodness-of-fit tests EXCEPT: A. The chi-square statistic is the "test statistic" used in chi-square goodness-of-fit hypothesis testing. B. Chi square goodness-of-fit tests can be used with both categorical variables (e.g., days of the week) and discrete numerical variables (e.g., number of boys in families with two children). C. The binomial test (Chapter 6) is a goodness-of-fit test. D. In the formula for the chi-square statistic, one uses the observed proportions (for example, proportion of births on different days, not numbers of births on different days).

D. In the formula for the chi-square statistic, one uses the observed proportions (for example, proportion of births on different days, not numbers of births on different days).

The Central Limit Theorem states that the sum of many random variables (regardless of what distribution describes these variables) will be always be distributed as a.... A. Binomial distribution B. Poisson distribution C. Chi-squared distribution D. Normal distribution

D. Normal distribution

Type I error occurs: A. When the null hypothesis is true but one does not reject the null hypothesis B. When the null hypothesis is false but one does not reject the null hypothesis C. When the null hypothesis is false but one rejects the null hypothesis D. When the null hypothesis is true but one rejects the null hypothesis

D. When the null hypothesis is true but one rejects the null hypothesis

Look at the alternative hypothesis on p. 205. Another way to state this alternative hypothesis would be: "The probability of a birth on Monday does not equal the probability of a birth on Tuesday does not equal the probability of a birth on Wednesday.................(and so on)........ Is this statement true or false?

False

The P-value for a chi-square hypothesis test involves focusing on both tails of the distribution. True or False?

False

An extremely small P value could be the result of having a very large sample size, and not reflect anything that is biologically interesting. True or False?

True