STATOISTIC PAPER AND SOLUTION

Question 1

Fifty-three percent of the population possesses a certain characteristic N. If 15 people are randomly selected from the population, what is the probability that exactly 9 possess characteristic N?

.1653

.1780

.1102

.2009

Question 2

Click here to access demo problem

Solve the following problems by using the binomial tables.

a. If n = 20 and p = 0.4, find   = .

b. If n = 20 and p = 0.4, find   = .

c. If n = 20 and p = 0.6, find   = .

d. If n = 20 and p = 0.8, find   = .

e. If n = 15 and p = 0.4, find   = .

f. If n = 10 and p = 0.7, find   = .

Round your answer to 3 decimal places.

The tolerance is +/- 0.005

Question 3

In a binomial experiment, p is .29 and n = 18. What is the standard deviation of this binomial distribution?

3.425

1.046

1.925

2.129

Question 4

Suppose a researcher wants to work a binomial problem by using a normal curve approximation. The researcher should use the:

binomial correction factor

adjustment for discrete distributions

correction for continuity

finite correction factor

Question 5

A researcher is working a binomial problem using a normal curve approximation. In the binomial problem, the researcher is trying to determine the probability of 51 < X < 56. In working the problem by the normal curve, the solution will be found at:

50.5 < X < 55.5

50.5 < X < 56.5

50.5 ≤ X ≤ 56.5

51.5 < X < 55.5

Question 6

Suppose 57% of all shoppers use credit cards for their purchase in department stores. If 80 such shoppers are randomly selected, what is the probability that more than 49 use a credit card?

.2578

.2946

.1894

.3106

Question 7

Suppose 29% of all commuter cars leaving the city at 5 P.M. are going somewhere other than home. If 45 commuter cars leaving downtown at 5 P.M. are tracked, what is the probability that more than 11 are going somewhere other than home?

.1950

.6950

.7486

.2486

Question 8

A company believes that it controls more than 40% of the total market share for one of its products. To prove this belief, a random sample of 165 purchases of this product are contacted. It is found that 70 of the 165 purchased this company's brand of the product. If a researcher wants to conduct a statistical test for this problem, the alternative hypothesis would be:

the population proportion is greater than 0.40.

the population proportion is not equal to 0.40.

the population mean is equal to 0.40.

the population proportion is less than 0.40.

Question 9

A bank inspector monitors the default rate on personal loans at Victorian banks. One standard that she examines is that no more than 5% of personal loans should be in default. On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. The bank inspector's alternate hypothesis is:

p ≠ .05

p = .05

p < 0.05

p > 0.05

Question 10

A business researcher is testing the following hypotheses using a 10% level of significance.
H0: p = .70
Ha: p < .70
A sample of 415 is taken and the sample proportion is .66. The business researcher's decision from this test is:

not enough information to conduct the hypothesis test.

reject the null hypothesis.

take a larger sample.

fail to reject the null hypothesis.

Question 11

A study by Hewitt Associates showed that 79% of companies offer employees flexible scheduling. Suppose a researcher believes that in accounting firms this figure is lower. The researcher randomly selects 415 accounting firms and through interviews determines that 303 of these firms have flexible scheduling. With a 1% level of significance, does the test show enough evidence to conclude that a significantly lower proportion of accounting firms offer employees flexible scheduling?

The value of the test statistic rounded to 2 decimal places is z =  and we fail to reject the null hypothesisreject the null hypothesis.

The tolerance is +/- 0.05.

Question 12

A business researcher wants to compare her observed distribution of frequency data to an expected distribution of data using the chi-square goodness-of-fit test. The data are given below. The degrees of freedom for this test are:

observed

  expected

12

     9

20

     7

38

     32

24

     38

18

     20

11

      7

5

4

10

6

Question 13

A business researcher wants to compare her observed distribution of frequency data to an expected distribution of data using the chi-square goodness-of-fit test. The data are given below. The observed chi-square value for this test is:

observed

expected

15

9

20

7

38

32

24

38

18

20

11

10

34.73

33.9

47.63

41.46

Question 14

A researcher wants to test the following observed distribution of values to determine if the values are uniformly distributed. The researcher is using the chi-square goodness-of-fit test for this analysis.

213

219

209

210

216

199

217

213

For α = .10, the researcher's decision is to:

fail to reject the null hypothesis that the observed distribution is not uniform.

reject the null hypothesis that the observed distribution is uniform.

reject the null hypothesis that the observed distribution is not uniform.

fail to reject the null hypothesis that the observed distribution is uniform.

Question 15

The following percentages come from a national survey of the ages of prerecorded-music shoppers. A local survey produced the observed values. Does the evidence in the observed data indicate that we should reject the national survey distribution for local prerecorded-music shoppers? Use α = 0.01 (Alpha = 0.01)

Find the observed value of chi-square. Round the answer to 2 decimal places.

Age

Precent from Survey

10-14

9

22

15-19

23

50

20-24

22

43

25-29

14

29

30-34

10

19

  35

22

49

The observed  x2 =  .

There is not enoughenough evidence to declare that the distribution of observed frequencies is different from the distribution of expected frequencies.

The tolerance is +/- 0.05.

Question 16

Click here to access demo problem

A group of 30-year-olds is interviewed to determine whether the type of music most listened to by people in their age category is independent of the geographic location of their residence. Use the chi-square test of independence,  α = 0.01 (Alpha = 0.01) , and the following contingency table to determine whether music preference is independent of geographic location.

Find the observed value of chi-square. Round the answer to 2 decimal places.

Type of Music Preferred

Geographic 
Region

Rock

R & B

Country

Classical

Victoria

137

28

6

18

Western Australia

130

36

47

6

Tasmania

154

25

10

12

The observed  x2 = .

Type of music preferred is independentnot independent of region of the country.

The tolerance is +/- 0.05.

Question 17

A researcher interviewed 2,067 people and asked whether they were the primary decision makers in the household when buying a new car last year. Two hundred seven were men and had bought a new car last year. Sixty-five were women and had bought a new car last year. Eight hundred eleven of the responses were from men who did not buy a car last year. Nine hundred eighty-four were from women who did not buy a car last year. Use these data to determine whether gender is independent of being a major decision maker in purchasing a car last year. Let  α = 0.05 (Alpha = 0.05)

Find the observed value of chi-square. Round the answer to 2 decimal places.

The observed  x2 = .

Purchasing a car or not is independentnot independent of gender.

The tolerance is +/- 0.05.

Question 18

Is a manufacturer’s geographic location independent of type of customer? Use the following data for companies with primarily industrial customers and companies with primarily retail customers to test this question. Let  α= 0.10 (Alpha = 0.10)

Find the observed value of chi-square. Round the answer to 2 decimal places.

        Geographic Location

Customer 
Type

Northern Territory

Western Australia

South Australia

Industrial 
Customer

230

115

68

Retail 
Customer

185

143

89

The observed  x2 = .

Type of customer is not independentindependent of geographic region.

The tolerance is +/- 0.05.

Question 19

The game show Deal or No Deal involves a series of opportunities for the contestant to either accept an amount of money from the show's banker or to decline it and open a specific number of briefcases in the hope of exposing and, thereby eliminating, low amounts of money from the game, which would lead the banker to increase the amount of the next offer. Suppose that 700 people aged 21 years and older were selected at random. Each of them watched an episode of the show until exactly four briefcases were left unopened. The money amounts in these four briefcases were $750, $5000, $50000, and $400000, respectively. The banker's offer to the contestant was $81600 if the contestant would stop the game and accept the offer. If the contestant were to decline the offer, he or she would choose one briefcase out of these four to open, and then there would be a new offer. All 700 persons were asked whether they would accept the offer (Deal) for $81600 or turn it down (No Deal), as well as their ages. The responses of these 700 persons are listed in the following table.

Age Group (years)

21-29

30-39

40-49

50-59

60 and over

Deal

76

84

89

92

63

No Deal

56

70

60

63

47

Test at the 5% significance level whether the decision to accept or not to accept the offer (Deal or No Deal) and age group are dependent.

The decision to accept/not accept the offer and age group are not dependentdependent