Statistics 100 Final Review

We record the zip codes of newly admitted students. How should we treat this data?

As categorical data

A sample of size 50 is obtained, with replacement, from a binary population. Which parameter value would give you the most accurate estimate of the population proportion? p = 0.25 p = 0.75 The other answers all give the same accuracy

The other answers all give the same accuracy

The standard deviation measures spread. T or F

True

Knowing that a distribution is bell-shaped allows us to approximate specific frequencies with which any given standardized values occur. T or F

True

The farther apart the 25th percentile and the 75th percentile of a dataset are, the more spread out the data. T or F

True

The probability of a type II error in a binomial test decreases as the sample size increases (all other things equal). T or F

True

The probability of a type II error in a binomial test is smallest for true values of the unknown proportion p that are farthest from the value specified by the Null hypothesis. T or F

True

If P(+|D) = 0.1 for some test, what is its sensitivity? 0.1 0.9 Not enough info.

0.1

The false positive rate, P(+|N), for a test is given as 0.04. What is the specificity for this test? 0.04 0.96 Not enough info.

0.96

What is the IQR for data that has a standard normal distribution?

1.35

Suppose that P(A) = 0.6, P(B) = 0.2, and that whenever B happens, A must happen as well. What is the probability that B happens, given that A happens? 1/5 1/3 3/5

1/3

Which best describes the Null distribution for a Chi-squared test of independence? A Fisher's distribution A Binomial distribution A Hypergeometric distribution A Chi-squared distribution

A Chi-squared distribution

Which best describes the Null distribution for a Fisher's exact test? A Fisher's distribution A Binomial distribution A Hypergeometric distribution A Chi-squared distribution Smelly

A Hypergeometric distribution

If A and B are two independent events with positive probabilities, then P(A or B) = P(A) + P(B). T or F

False

The y-intercept of the least squares regression line usually is the key parameter describing the relationship between predictor x and response y. T or F

False

Suppose that events A and B in a probability model have P(A) = 0.7 and P(B) = 0.8 . Are A and B mutually exclusive?

No

Which distribution is used to compute the p-value, if the alternative hypothesis of the test is true? The null distribution The probability distribution of the test statistic under the true alternative hypothesis

The null distribution

The simple linear regression model assumes equal variances for the response y given different predictors x. T or F

True

The slope of the least squares regression line always has the same sign (+ or -) as the pearson correlation between the predictor x and response y. T or F

True

The slope of the least squares regression line is always less than or equal to the ratio of the SD of the response y to the SD of the predictor x (hint: what are the possible values of the pearson correlation?) T or F

True

When a left-skewed data set is standardized, the standardized values will have a median that is greater than 0. T or F

True

When the sample size is small relative to the size of the population, the standard error for the sample proportion when sampling with replacement will be similar to that obtained when sampling without replacement. T or F

True

Roll two six-sided dice; let X1 represent the result from the first roll, and X2 the second. Which of the following random variables has the largest expected value? X1 + X2 X1 - X2 The other answers have the same expected value

X1 + X2

Suppose that we use a hypothesis test to evaluate a claim about the proportion of Narwhals with tusks longer than 3 meters. If we use a a Chi-squared test, would the value of our test statistic be the square of the standardized value of the statistic that we would have used if we had chosen a binomial test instead? Yes No

Yes

We record the genus of every tree identified along a transect. How should we treat this data?

as categorical data

We record the wavelengths of light reflecting off of several bird-of-paradise feathers. How should we treat this data?

as numeric data

If a cylindrically shaped flagellar base extends to a depth of 18.1 nm (standardized value -0.31) into the cytoplasm below a plasma membrane, then this depth is, relative to the average (mean):

below average

Typically, when we increase the probability of a type I error for a hypothesis test, we: decrease the power of the test increase the power of the test

increase the power of the test

Typically, when we decrease the probability of a type I error for a hypothesis test, we: decrease the probability of a type II error increase the probability of a type II error

increase the probability of a type II error

The t-test can be used to evaluate a claim about an unknown population mean standard deviation fourth central moment kurtosis

mean

What does the line bisecting the box in a boxplot represent for a given set of data?

median

Which sample size would yield the largest confidence interval for an unknown proportion, all other things being equal? n = 500 n = 188 n = 50 n = 17

n = 17

If a cylindrically shaped flagellar base extends to a depth of 18.1 nm (standardized value -0.31) into the cytoplasm below a plasma membrane, then the standard deviation of the depths is:

not enough information given

A sample of size 63 is obtained, with replacement, from a binary population. Which parameter value would give you the most accurate estimate of the population proportion? p = 0.1 p = 0.3 p = 0.6 The other answers all give the same accuracy

p=0.1

Armed with the results of the seedling study above, which tool would you use to evaluate the claim that the treated plants have an average weight of 4 grams? Chi squared test for goodness of fit Chi squared test for independence Fisher's exact test t-test for an unknown mean t-test for a difference in means

t-test for an unknown mean

Which of the following pairs of events is mutually exclusive? {⚀, ⚁} and {⚂, ⚃} {⚀, ⚁, ⚃} and {⚂, ⚃, ⚄, ⚅} "the result is even" and "the result is a multiple of two"

{⚀, ⚁} and {⚂, ⚃}

For Fisher's exact test, if the resulting p-value is less than your significance level, you: Conclude that the factors in question are independent Conclude that the factors in question are not independent Fail to find evidence that the factors in question are not independent Fail to find evidence that the factors in question are independent

Conclude that the factors in question are not independent

If two samples are drawn independently from the same population, then the sample means will be the same. T or F

False

20% of a population of tree frogs are brightly-colored. One hundred of the frogs are sampled randomly; let X represent the number of them that are brightly colored. In which of the following cases would the standard deviation of X be smaller? The sampling is without replacement The sampling is with replacement Not enough information given

The sampling is without replacement.

Your colleague makes a claim about the mean of the viral loads among patients in a particular demographic. Which of the following hypothesis tests could be used to evaluate this claim? Binomial exact test Fisher's exact test Chi squared test for independence t-test

t-test

Armed with the results of the seedling study above, which tool would you use to evaluate the claim that a special treatment has no effect on the average weight of the resulting plants? Chi squared test for goodness of fit Chi squared test for independence Fisher's exact test t-test for an unknown mean t-test for a difference in means F-test for equality of group means

t-test for a difference in means

A Chi-square goodness of fit test results in a test statistic value of 8. If the test is evaluating a claim about a population with 7 categories, which of the following represents the correct degrees of freedom for the test statistic? 6 7 8

6

The probability of a Type II error depends on which alternative hypothesis is true. T or F

True

Which best describes the proportion of standardized measurements that are between -2 and 2, if the data has a bell shaped distribution? Approx 95% At least 88% Atleast 75% Approx. 68%

Approx. 95%

Which of the following describes the Null distribution for the test statistic in a Chi-squared test for goodness-of-fit? Approximately Chi-squared with degree of freedom one less than the number of categories Exactly Chi-squared with degree of freedom one less than the number of categories Exactly Binomial

Approximately Chi-squared with degree of freedom one less than the number of categories

Which best describes the proportion of standardized measurements that are between -3 and 3? Approx. 5% At least 88% Approx. 68% Approx 95%

At least 88%

A study will evaluate whether the type of animal in a picture (Puppy, Bear cub, Owlet, or Kitten) will have an effect on its level of engagement on instagram (Low, Medium, or High). Which hypothesis test could you use to evaluate the result of this study? Binomial Test Chi-squared test for goodness of fit Fisher's Exact Test Chi-squared test for independence

Chi-squared test for independence

One of a treatment (a nutritionally enriched environment) or a control group (no nutritional enrichment) are randomly selected to be applied to each of a number of otherwise similar seeds. After a fixed time, the resulting seedling plants are dried and then weighed. Armed with the results of this study, which tool would you use to evaluate the claim that 25% of the treatment plants will have a weight greater than 5 grams? Binomial exact test Chi squared test for goodness of fit Chi squared test for independence Fisher's exact test

Binomial exact test

Your colleague makes a claim about the proportion of the viral loads among patients in a particular demographic that are above a certain level. Which of the following hypothesis tests could be used to evaluate this claim? Binomial exact test Fisher's exact test Chi squared test for independence t-test

Binomial exact test

For Fisher's exact test, if the resulting p-value is greater than your significance level, you: Conclude that the factors in question are independent Conclude that the factors in question are not independent Fail to find evidence that the factors in question are not independent Fail to find evidence that the factors in question are independent

Fail to find evidence that the factors in question are not independent

A random variable with binomial distribution is binary (i.e. it only has two possible values). T or F

False

For a Chi-squared test of goodness-of-fit, a large p-value would reflect strong evidence against the Null hypothesis. T or F

False

If two populations have the same variances, then the pooled estimate of the SE for the estimated difference between them will lead to larger confidence intervals. T or F

False

If two samples are drawn independently from the same population, then their sample standard deviations will be the same. T or F

False

In simple linear regression, a fraction of variance explained close to zero suggests that there is insufficient evidence to conclude that there is an association between x and y. T or F

False

Roll two six-sided dice; let X1 represent the result from the first roll, and X2 the second. Then X1 is independent of X1+X2. T or F

False

The height of bars in a histogram represent frequencies T or F

False

Whenever one data set has a mean that is larger than another data set, it also has a standard deviation that is larger. T or F

False

A study will evaluate whether the type of animal in a picture (Puppy or Kitten) will have an effect on its level of engagement on instagram (Low or High). Which hypothesis test could you use to evaluate the result of this study? Binomial Test Chi-squared test for goodness of fit Fisher's exact test Chi-squared test for independence

Fisher's exact test

Suppose that we use a hypothesis test to evaluate a claim about the proportion of Narwhals with tusks longer than 3 meters. If we use a binomial test, would the Null distribution be the same as the Null distribution we would use if we had chosen a Chi-squared test instead? Yes No

No

Roll two six-sided dice. Let A be the event that the total number of dots is twelve, and B be the event that the first roll is six. Which of the following is true? A and B are mutually exclusive A and B are independent Neither of the other answers is true

Neither of the other answers is true

Suppose that P(A) = 0.5, P(B) = 0.4, and P(A and B) = 0.1. Which of the following is true? A and B are mutually exclusive A and B are independent Neither of the other answers is true

Neither of the other answers is true

A set of biomechanical measurements have as their unit of measurement Newtons. Which of the following gives the unit of measurement of the 15th percentile of this data? Newtons Percent None

Newtons

Your colleague makes a claim about the standard deviation of the viral loads among patients in a particular demographic. Which of the following hypothesis tests could be used to evaluate this claim? Binomial exact test Fisher's exact test Chi-squared test for independence t-test None of the other answers

None of the other answers

A test for malignalitaloptereosis has a sensitivity 0.92 and specificity 0.77. When a patient tests positive, what is the probability that they have this disease? 0.23 0.77 0.92 Not enough info.

Not enough info.

Roll two six-sided dice. Let A be the event that the total number of dots is five, and B be the event that the first roll is four. Which of the following is true? P(A|B) > P(A) P(A|B) = P(A) P(A|B) < P(A)

P(A|B) > P(A)

Suppose that A and B are mutually exclusive, that P(A) = 0.7, and that P(B) = 0.2. Which of the following is true? P(B|A) > P(B) P(B|A) = P(B) P(B|A) < P(B)

P(B|A) < P(B)

Which of the following can not be part of a reasonable assignment of probabilities for the probability experiment of rolling a six-sided die? P({⚀}) = 1/6, and P({⚀, ⚁, ⚂}) = 1/2 P({⚀}) = 0, P({⚂}) = 0, and P({⚃}) = 0 P({⚀}) = 1/3, P({⚁, ⚂}) = 1/2, and P({⚃, ⚄}) = 1/2

P({⚀}) = 1/3, P({⚁, ⚂}) = 1/2, and P({⚃, ⚄}) = 1/2

Which distribution is used to compute the p-value, if the Null hypothesis of the test is true? The null distribution The probability distribution of the test statistic under one of the alternative hypothesis

The null distribution

Roll two six-sided dice; let X1 represent the result from the first roll, and X2 the second. Which of the following random variables has the largest standard deviation? X1+X2 X1-X2 The other answers have the same SD

The other answers have the same SD

If a hypothesis test is carried out at significance level 0.05, which of the following is true? The probability of a type I error is at most 0.05 The probability of a type I error is at most 0.095 The probability of a type II error is at most 0.95 The p-value is greater than 0.05.

The probability of a type I error is at most 0.05

If a hypothesis test is carried out at significance level 0.1, which of the following is true? The probability of a type I error is at most 0.1 The probability of a type I error is at most 0.9 The probability of a type II error is at most 0.9 The p-value is greater than 0.05

The probability of a type I error is at most 0.1

In which circumstance would a t-test not be valid? The sample size is small and the population is right-skewed The sample size is small and the population is bell-shaped The sample size is large and the population is right-skewed The sample size is large and the population is bell-shaped

The sample size is small and the population is right-skewed

Which of the following would be the best estimate of the population standard deviation? The sample proportion The sample mean The sample standard deviation The sample correlation

The sample standard deviation

A Chi-square goodness of fit test results in a test statistic value of 8. If the test is evaluating a claim about a population with 7 categories, and the test is carried out at significance level 0.1, which of the following best describes the conclusion of the test? The null hypothesis is confirmed There is not sufficient evidence to reject the null hypothesis The null hypothesis is rejected

There is not sufficient evidence to reject the null hypothesis

For a Chi-squared test of goodness-of-fit, the p-value is computed using the Null distribution. T or F

True

Homogeneous populations tend to have smaller SE's for estimating population proportions than heterogeneous ones T or F

True

If two populations have the same variances, then the pooled estimate of the SE for the estimated difference between them will lead to more power in hypothesis tests. T or F

True

In simple linear regression, a fraction of variance explained close to one suggests that the between-fitted-value variation is large relative to the residual variation. T or F

True

In simple linear regression, the fraction of variability in y that is explained by a linear relationship in x can be determined from the pearson correlation between x and y. T or F

True

More than one histogram may be drawn for a given set of numerical data. T or F

True

Mosaic plots use areas to represent frequencies, while histograms use heights. T or F

True

Relative frequencies are equal to absolute frequencies divided by the number of measurements. T or F

True

Roll two six-sided dice. Let A be the event that the total number of dots (sum of the two results) is even, and B be the event that the total is odd. Then A and B are mutually exclusive. T or F

True

Roll two six-sided dice. Let A be the event that the total number of dots is even, and B be the event that the total is odd. Then P(A or B) = P(A) + P(B). T or F

True

Roll two six-sided dice. Let X2 be the result from the second roll. Then X2 is a random number with a uniform distribution. T or F

True

Sampling without replacement from a binary population always results in a smaller standard error for the sample proportion than sampling with replacement. T or F

True

The IQR is not attracted to extreme values. T or F

True

The Null hypothesis assigns a specific probability distribution to a test statistic. T or F

True

The probability of a Type I error is determined by the Null distribution. T or F

True