Deck 18: The Binomial Test

Question 1

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

A)​100
B)​80
C)​40
D)​20

Answer 1

​80

Question 2

A binomial 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

Answer 2

​n = 72

Question 3

​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

Answer 3

​2/3

Question 4

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

A)​p = 0.20
B)​p = 0.10
C)​p = 0.40
D)​p = 0.50

Question 5

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 6

​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 7

​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 8

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 9

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 10

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

A)​.30
B)​.50
C)​.70
D)​1.30

Question 11

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)​p = 4.0

Question 12

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

A)pn or qn ≥ 10
B)​pn and qn ≥ 10
C)​pn = qn
D)​p + q = n

Question 13

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

Question 14

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)​10
D)​50

Question 15

What is the standard deviation for the normal approximation to the binomial distribution with p = 1/2 and n = 400?​

A)​200
B)​100
C)​25
D)​10

Question 16

The probability of correctly predicting the outcome of a coin toss is p = 1/2.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)​25
C)​10
D)​5

Question 17

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 18

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)​p = 0.05

Question 19

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

A)​9 Heads in 12 tosses (75% Heads)
B)​12 Heads in 16 tosses (75% Heads)
C)​30 Heads in 40 tosses (75% Heads)
D)​75 Heads in 100 tosses (75% Heads)

Question 20

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

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

Question 21

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

A)​npq
B)​pn
C)​pq
D)​pnq

Question 22

Which test 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 23

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)​3
B)​6
C)​9
D)​1/3

Question 24

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 25

A multiple choice exam has 50 questions with five 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??

A)?µ = 10 and ? = $\sqrt { 8 }$
B)?µ = 25 and ? = $\sqrt { 8 }$
C)?µ = 10 and ? = 16
D)?µ = 25 and ? = 8

Question 26

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

A)​0.50
B)​1.00
C)​2.00
D)​0.00

Question 27

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)​p = 0

Question 28

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 29

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 30

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

A)??² = $\sqrt { z }$
B)??² = z
C)?? ² = z²
D)?? ² = z?

Question 31

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 = 0.8
B)​z = 1.8
C)​z = 2.25
D)​z = 0.5625

Question 32

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 33

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?​

A)​Reject the null hypothesis with α = .05 but not with α = .01.
B)​Reject the null hypothesis with either α = .05 or α = .01.
C)​Fail to reject the null hypothesis with either α = .05 or α = .01.
D)​No decision is possible without additional information.

Question 34

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 35

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

A)​12
B)​9
C)​3
D)​1

Question 36

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 37

What is indicated by zero differences in a sign test?​

A)​They provide support for the null hypothesis.
B)​They provide 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 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?Hint: Use interval-based calculations because no critical region is involved.​

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

Question 39

For the normal approximation to the binomial distribution with p = 1/2 and n = 100,what is the z-score corresponding to X = 60?​

A)​z = 0.4
B)​z = 2.0
C)​z = 0.2
D)​z = 1.0

Question 40

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?Hint: Use interval-based calculations because no critical region is involved.​

A)​p(z > 0.17)
B)​p(z > 0)
C)​p(z > 0.27)
D)​p(z > 0.33)

Question 41

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

Question 42

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

Question 43

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

Question 44

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

Question 45

For any binomial distribution,p + q = 1.00.​

Question 46

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

Question 47

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

Question 48

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

Question 49

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

Question 50

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 51

For a binomial distribution with p = 1/2 and σ = 3,the mean is µ = 18.​

Question 52

The binomial distribution with p = 1/4 has a standard deviation of 3.For this distribution,there are n = 36 scores in the sample.​

Question 53

Binomial data exist whenever a measurement procedure classifies individuals into exactly two distinct categories.​

Question 54

For a binomial distribution with p = 1/4 and a mean of m = 12,the standard deviation is s = 9.​

Question 55

The binomial distribution with p = .10 has a mean of m = 10.For this distribution,there are n = 100 scores in the sample.​

Question 56

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

Question 57

Assume there are two categories,A and B,and the symbol X stands for the number of individuals classified as belonging to category A in a sample of size n.X can have any value from 0 to n and each value of X has a specific probability.The distribution of probabilities for each value of X is called the binomial distribution.​

Question 58

For a binomial test with p = 1/2 and n = 36,the z-score for X = 21 is z = +1.00.​

Question 59

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 60

For a binomial distribution with p = 1/2 and n = 30,the value of X ranges from 1 to 30.​

Question 61

In an ESP experiment,the participants are required to predict the suit of a card drawn randomly from a complete deck.If a participant correctly identifies the suit for 18 out of 48 trials,is the participant performing significantly better than chance? Test at the .05 level of significance.​

Question 62

For the binomial test,p = q.​

Question 63

State the four-step procedure used in a binomial hypothesis test.​

Question 64

Explain the four specific cases in which a t test is inappropriate or inconvenient.​

Question 65

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

Question 66

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

Question 67

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

Question 68

A local traffic light is set so that it cycles between 30 seconds of red and 30 seconds of green.What is the probability of randomly hitting a red light more than 25 times in n = 40 trips through the intersection?​

Question 69

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 70

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

Question 71

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

Question 72

A new face cream advertises that 9 out of 10 people will see a noticeable improvement in their skin after only 30 days of using the product.To test this claim,a researcher selects a sample of n = 100 women between the ages of 40 and 50.Each woman uses the product for 30 days and reports the result.If there are 85 women who report improved skin and 15 who report no improvement,are the data sufficient to refute the manufacturer's claim? Use a two-tailed test with a = .05.​

Question 73

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 74

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

Question 75

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