# mathematics

Question 18.

18. Find the confidence interval for a population mean of 615 acres at a 90% level of confidence with a sample size of 52 and standard deviation of 27 acres. (Points : 2)

189 to 1190 acres
608.84 to 621.16 acres
452 to 4252 acres
172 to 2008 acres

Question 19.

19. Given that a sample of size 12 was taken from a finite population of 60 with a population standard deviation of 1.8, what would be the margin of error at a 95% level of confidence? (Points : 2)

±1.018
±0.9186
±12.22
±0.4452

Question 20.

20. The two most commonly used types of estimates in statistics are ________. (Points : 2)

cluster intervals and standard estimates
unbiased estimator and standard distribution
point estimates and confidence intervals
sampling estimates and central limit interval

Question 21.

21. Regarding the standard error of the mean, ________. (Points : 2)

as the sample size increases, the standard error increases
as the sample size decreases, the standard error decreases
as the sample size increases, the standard error decreases
it is defined as one-half of the population standard deviation

Question 22.

22. Find the standard error of the mean when the population standard deviation is 2.4 and a sample of size 36 is taken. (Points : 2)

4.03
0.6
14.4
0.4

Question 23.

23. The standard error of the mean is ________. (Points : 2)

the variance of the sampling distribution of the mean
the standard deviation of the sampling distribution of the mean
the range of the sampling distribution of the mean
the mean of the sampling distribution of the standard deviations

Question 24.

24. What is the value of the finite population correction factor when a sample size of 250 is taken from a finite population of 1001? (Points : 2)

0.7510
0.8667
1.9960
0.2498

Question 25.

25. Use the information below to answer the question.

The following table provides data on a sample of customers who visited a local restaurant. The restaurant owner believes that the average profit per customer exceeds \$25.

36.73

35.50

25.92

38.36

41.65

25.50

18.78

19.78

33.14

22.22

20.85

26.23

22.13

32.33

28.46

34.15

34.72

24.21

24.20

28.95

21.84

19.74

20.75

Formulate the null and the alternative hypotheses to determine if the data supports the restaurant owner’s claim. (Points : 2)

H0: The average profit per customer = \$25
H1: The average profit per customer ? \$25
H0: The average profit per customer = \$25
H1: The average profit per customer > \$25
H0: The average profit per customer = \$25
H1: The average profit per customer < \$25
H0: The average profit per customer > \$25
H1: The average profit per customer = \$25

Question 26.

26. A one-tailed test is employed when the null hypothesis ________. (Points : 2)

is structured as “?”
specifies a direction of relationship
is structured as “=”
falls in the upper tail of the distribution

Question 27.

27. The confidence coefficient is ________. (Points : 2)

the probability of correctly failing to reject the null hypothesis
the probability of making a Type II error
the probability of making a Type I error
the probability of correctly rejecting the null hypothesis

Question 28.

28. If the confidence coefficient is 0.9, ________. (Points : 2)

we expect that 9 samples out of 100 will support the null hypothesis
we expect that 90 out of 100 samples will support the null hypothesis
we expect that 10 samples out of 100 will support the null hypothesis
we expect that all 100 samples will support the null hypothesis

Question 29.

29. Hypothesis testing always assumes that ________. (Points : 2)

the alternative hypothesis is true
the null hypothesis is true
the probability of the null hypothesis being true is less than 50%
the probability of the alternative hypothesis being true is less than 50%

Question 30.

30. The null hypothesis ________. (Points : 2)

describes an existing theory or belief that is accepted as correct in the presence of contradictory data
describes an existing theory or belief that is accepted as correct in the absence of contradictory data
is based on new information provided by sample data
is based on new information provided by population data

Question 31.

31. Use the information below to answer the question.

The following table provides data on a sample of customers who visited a local restaurant. The restaurant owner believes that the average profit per customer exceeds \$25.

36.73

35.50

25.92

38.36

41.65

25.50

18.78

19.78

33.14

22.22

20.85

26.23

22.13

32.33

28.46

34.15

34.72

24.21

24.20

28.95

21.84

19.74

20.75

Which of the following is the critical value using a level of significance of 0.05? (Points : 2)

1.717
-1.717
1.7139
-2.0739

Question 32.

32. The power of the test has a value of ________. (Points : 2)

1 – a
1 + ß
1 – ß
a – ß

Question 33.

33. In the construction of decision trees, which of the following shapes represents a state of nature node? (Points : 2)

square
circle
diamond
triangle

Question 34.

34. In the construction of decision trees, which of the following shapes represents a decision node? (Points : 2)

square
circle
diamond
triangle

Question 35.

35. A market research study is being conducted to determine if a product modification will be well received by the public. A total of 1,000 consumers are questioned regarding this product.
The table below provides information regarding this sample.

Positive

Reaction

Neutral

Reaction

Negative

Reaction

Male

240

60

100

Female

260

220

120

What is the probability that a randomly selected person would be a female who had a positive reaction? (Points : 2)

0.250
0.260
0.455
0.84

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