Deck 18: The Binomial Test

Question 1

If a coin is balanced so that p(Heads) = p(Tails) = 1/2, then which of the following outcomes is more unlikely to occur?

A)12 Heads in 16 tosses (75% Heads)
B)30 Heads in 40 tosses (75% Heads)
C)75 Heads in 100 tosses (75% Heads)
C)The other 3 outcomes are all equally likely to occur.

Answer 1

A

Question 2

The probability of correctly predicting the outcome of a coin toss is p = ½.What is the standard deviation of the normal approximation to the binomial distribution for the number of correct predictions in a series of 100 tosses?

A)50
B) $\surd$ 50
C)25
D)5

Answer 2

5

Question 3

What is the standard deviation for the normal approximation to the binomial distribution with n = 72 and p = 1/3?

A)4
B)6
C)16
D)24

Answer 3

A

Question 4

Which of the following is true for any binomial test?

A)p = q
B)p > q
C)(p)(q) = 1.00
D)p + q = 1.00

Question 5

What is the value of μ for the normal approximation to the binomial distribution with n = 72 and p = 1/3?

A)12
B)24
C)36
D)48

Question 6

What is the standard deviation for the normal approximation to the binomial distribution with p = ½ and n = 400?

A)200
B)100
C)25
D)10

Question 7

A binomal distribution with p = 1/3 has a standard deviation of 4.What is the sample size?

A)n = 16
B)n = 24
C)n = 36
D)n = 72

Question 8

For a binomial distribution with n = 100, which of the following has the largest standard deviation?

A)p = 0.50
B)p = 0.20
C)p = 0.10
D)All of the other options have exactly the same standard deviation.

Question 9

If a binomial distribution satisfies the criterion for using the normal approximation with p = 0.1, then what can be concluded about the value of n?

A)n = 50
B)n = 100
C)n > 50
D)n > 100

Question 10

If pn = 15 and qn = 45, what is the value for p?

A)p = 1/3
B)p = 0.30
C)p = 1/4
D)cannot be determined

Question 11

If pn = 20 and qn = 60, then what is the value of n?

A)100
B)80
C)40
D)none of the above

Question 12

On a multiple-choice exam for which each question has four possible answers, the probability of guessing the correct answer is p = 1/4.What is the mean of the binomial distribution for the number of correct guesses for a series of 100 questions?

A)5
B)25
C) $\surd$ 50
D)50

Question 13

A binomial distribution has p = 1/3 and q = 2/3.How large a sample (n) is necessary to satisfy the criterion for using the normal approximation?

A)10
B)15
C)27
D)30

Question 14

For a binomial distribution with p = 0.10 and n = 100, what is the range of possible values for X?

A)0 to 1
B)0 to 100
C)1 to 100
D)0.01 to 0.09

Question 15

For a sample of n = 20, which of the following p values satisfies the criterion for using the normal approximation?

A)p = 0.70
B)p = 0.60
C)p = 0.50
D)All of the other options satisfy the criterion for the normal approximation.

Question 16

Under what circumstances is the normal approximation to the binomial distribution justified?

A)pn or qn $\geq$ 10
B)pn and qn $\geq$ 10
C)pn = qn
D)p + q = n

Question 17

A binomial distribution has a mean of µ = 40 for a sample of n = 60.What is the value of p?

A)1/3
B)2/3
C)1.50
D)0.5

Question 18

If a binomial distribution has p = .30, then what is the value for q?

A).30
B).50
C).70
D)1.30

Question 19

What value(s) are specified by the null hypothesis in a binomial test?

A)the value for X
B)the value for X/n
C)the value for p
D)the value for pn

Question 20

What are the mean and standard deviation for the normal approximation to the binomial distribution with n = 100 and p = .20?

A) = 50 and
= 5
B) = 50 and
= 4
C) = 20 and
= 16
D) = 20 and
= 4

Question 21

What is indicated by zero differences in a sign test?

A)They provide support for the null hypothesis.
B)They provided evidence that the null hypothesis should be rejected.
C)They are not relevant to the null hypothesis and should be discarded.
D)They indicate that assumptions have been violated and the test should not be done.

Question 22

A researcher is testing a null hypothesis stating that for the general population there is no preference between the two leading brands of cola.In a sample of n = 100 people, 35 preferred brand A and 65 preferred brand B.Assuming that the researcher uses a two-tailed test, what is the appropriate statistical decision?

Question 23

For binomial data, what is the value of p + q?

A).5
B)1.00
C)2.00
D)None of the other 3 choices is correct.

Question 24

A researcher obtains z = 3.00 for a binomial test.If a chi-square test for goodness of fit had been used instead of the binomial test, what value would be obtained for chi-square?

A) $\surd$ 3
B)3
C)9
D)Cannot be determined with the information given.

Question 25

For a binomial distribution with p = 0.10 and n = 100, what is the z-score for X = 16?

A)1/3 = 0.33
B)2/3 = 0.66
C)1.00
D)2.00

Question 26

How are the difference scores coded in a sign test?

A)by their ranked size, with increases and decreases ranked separately
B)by their ranked size, independent of sign (increase or decrease)
C)as increases (+) or decreases (-)
D)as probabilities, p and q

Question 27

Which of the following is the mean for a binomial distribution?

A)npq
B)pn
C) $\surd$ pn
D) $\surd$ pq

Question 28

For the binomial test, what is the relationship between chi-square and z?

A)?² = $\surd$ z
B)? ² = z
C)? ² = z²
D) ? ² = z?

Question 29

A report noted that for the population of 9th graders, one?third of the students are unable to pass a quiz in basic geography.One teacher, having spent a great deal of time on geography instruction, gave the same quiz to a group of n = 72.Only X = 18 students in the group did not pass the test.The teacher would like to know if the number of students in this class who failed the quiz is significantly different from the general population.For this test, what is the z-score corresponding to X = 18?

A)z = -0.375
B)z = -1.00
C)z = -1.50
D)z = -2.00

Question 30

For the normal approximation to the binomial distribution with p = ½ and n = 100, what is the z-score corresponding to X = 60?

A)z = 10/25
B)z = 10/5
C)z = 5/25
D)z = 5/5

Question 31

Which of the following tests is often used for the same kind of research study for which the sign test is appropriate?

A)an independent-measures t test
B)a repeated-measures t test
C)a Pearson correlation
D)a chi-square test for goodness of fit

Question 32

The state lottery claims that the probability of winning is p = 1/10 for one of its scratch-off games.If this is true, then what is the probability of getting at least 10 winning tickets in a sample of n = 100?

A)p(z > -0.17)
B)p(z > 0)
C)p(z > +0.17)
D)p(z > 0.33)

Question 33

If sample data are suitable for evaluation with a binomial test, what other test could also be used for the same data?

A)an analysis of variance.
B)a test comparing two population means.
C)the chi square test for goodness of fit.
D)the Pearson correlation

Question 34

The null hypothesis for a binomial test states that p = 1/5.What is the z-score for X = 29 in a sample of n = 100?

A)z = 4/5
B)z = 9/5
C)z = 9/4
D)z = 9/16

Question 35

For binomial data with p = .50 and n = 36, what is the value of $\sigma$ for the normal approximation?

A)12
B)9
C)3
D)1

Question 36

A binomial distribution has p = 4/5.How large a sample would be necessary to justify using the normal approximation to the binomial distribution?

A)at least 10
B)at least 13
C)at least 40
D)at least 50

Question 37

A multiple choice exam has 50 questions with 5 choices for each question.If an individual is simply guessing at each answer, what are the values for the mean and the standard deviation of the normal approximation to the binomial distribution for the number of correct answers?

Question 38

For a binomial distribution with p = 0.20 and n = 100, what is the probability of obtaining a score less than or equal to X = 12?

A)p = 0.3085
B)p = 0.0301
C)p = 0.0228
D)p = 0.0170

Question 39

The null hypothesis specifies a value of p for the population.What is the corresponding statistic for the sample?

A)X
B)X/n
C)z
D)pn

Question 40

Which of the following is the correct null hypothesis for a sign test?

A)p = q
B)p ≠ q
C)p + q = 1.00
D)None of the other options is correct.

Question 41

For binomial data, if n = 40 and q = 0.60, then pn = 16.

Question 42

The binomial test can be used as an alternative to the chi?square test for goodness of fit provided the observed frequencies fit in exactly two categories.

Question 43

The binomial distribution with p = ¼ has a standard deviation of 3.For this distribution there are n = 36 scores in the sample.

Question 44

The sign test can be used as an alternative to the independent-measures t test.

Question 45

For a binomial test with p = ½ and n = 36, the z-score for X = 21 is z = +1.00.

Question 46

In a binomial hypothesis test, the value for μ must always be a whole number (not a fraction or decimal value).

Question 47

For a binomial distribution with p = ½ and n = 30, the value of X ranges from 1 to 30.

Question 48

For the binomial test, p = q.

Question 49

In a binomial hypothesis test, the value for X must always be a whole number (not a fraction or decimal value).

Question 50

For any binomial distribution, p + q = 1.00.

Question 51

For binomial data that satisfy the criterion for using the normal approximation, you can either compute a z-score or a value for chi-square.The relationship between the two statistics is z = χ².

Question 52

If p = 1/5, the binomial distribution for samples of n = 100 will have a standard deviation of σ = 4.

Question 53

The mean for the normal approximation to the binomial distribution is μ = pn.

Question 54

For a binomial test, if pn = 10 and qn = 90, then n = 100.

Question 55

It would not be appropriate to use a binomial test with p = 0.80 and n = 50.

Question 56

The binomial test is only used when the data consist of classifying each individual into one of two categories.

Question 57

For a binomial test, if pn = 12 and qn = 36, then p = 0.25.

Question 58

The binomial distribution with p = .10 has a mean of $\mu$ = 10.For this distribution there are n = 100 scores in the sample.

Question 59

For a binomial distribution with p = ½ and $\sigma$ = 3, the mean is $\mu$ = 18.

Question 60

For a binomial distribution with p = ¼ and a mean of $\mu$ = 12, the standard deviation is $\sigma$ = 9.

Question 61

For a binomial distribution based on n = 100, the standard deviation would be larger for p = 0.90 than for p = 0.80.

Question 62

If other factors are held constant, both the mean and standard deviation for the binomial distribution will both increase as the sample size increases.

Question 63

For a binomial test with p = ½, p (X > 60) for n = 100 is equal to p(X > 240) for n = 400.

Question 64

For a binomial test with p = 0.20 and n = 100, the z-score for X = 24 is z = 0.25.

Question 65

If either pn or qn is greater than 10, the test statistic for the binomial test is a z-score and the critical values are obtained from the unit normal table.

Question 66

The null hypothesis for the sign test always states that p = q.

Question 67

Discarding the zero differences for a sign test increase the likelihood of rejecting the null hypothesis.

Question 68

In a sign test, dividing the zero differences evenly between the two groups will increase the likelihood of rejecting the null hypothesis.

Question 69

For a two-tailed binomial test with n = 100, $\alpha$ = .05, and a null hypothesis stating that p = 0.10, a score of X = 13 would be sufficient to reject the null hypothesis.

Question 70

The normal approximation is appropriate for binomial data with n = 36 and p = 0.80.