I have an exam today and would like someone to complete the Practice Exam to see what I got right and wrong, and what I need to focus on. I merely want the correct answers circled, our professor never gave us an answer key as this is also graded as HW.

mth_245_practice_exam_2020.docx

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MATH-2600

Spring/2020

Name: __________________________________________

Circle the correct answer.

1) (2 pts) Which of the following statements about hypothesis tests is INCORRECT?

H 0 must always include equality.

i.

ii.

A one-sided test means the alternative hypothesis is either of these symbols: < >

iii.

A large p-value indicates that the claim in the H 0 is true.

iv.

The smaller a p-value, the stronger the evidence is against H 0

—————————————————————————————————————————————–2) (10 pts) We asked 144 students if they are fluent in one, two, three, or more languages.

Here are the results;

One

Two

Three or More Total

Male

38

20

12

70

Female 44

21

9

74

Total

82

41

21

144

a. What is the probability that a person randomly selected is fluent in 2 languages?

i.

20

40

ii.

41

144

iii.

21

41

iv.

70

144

v.

74

144

vi. None of the above

b. Are selecting a female and a person fluent in 2 languages disjoint events?

i. Yes, because there are no common outcomes.

ii. No, because there are outcomes in common.

iii. No, because the outcome of one influences the probability of the other.

iv. Yes, because the outcome of one does not influence the probability of the other.

c. What is the probability of randomly selecting a woman or a person fluent in 3 languages?

i.

115

144

ii.

86

144

iii.

74

144

70

iv. 144

v.

41

144

vi. None of the above

d. What is the probability of selecting two people fluent in three languages?

i. 0.5694

ii. 0.3242

iii. 0.0204

iv. 0.0066

e. What is the correct interpretation of the calculation

20

41

v. 0.1817

vi. None of the above

= 48.8%?

i.

48.8% of men are fluent in two languages.

ii.

48.8% of women are fluent in two languages.

iii.

48.8% of those fluent in two languages are men.

iv.

48.8% of those fluent in two languages are women.

—————————————————————————————————————————————–3) (2 pts) The null and alternative hypotheses are statements about;

i.

A population parameter

ii.

A sample statistic

iii.

It depends – sometimes a population parameter and sometimes a sample statistic

iv.

A p-value

1

4) (6 pts) The histogram shows the neck sizes (in inches) of 250 men from a health study.

a. Using the histogram, find the approximate percentage of men with neck sizes between 14 and 15

inches.

i. 75%

ii. 60%

iii. 50%

iv. 40%

v. 30%

b. Which statement best describes the spread of neck sizes based on the IQR.

i.

The middle 50% of neck sizes for these men ranges from 12 to 17.5 inches.

ii.

The middle 50% of neck sizes for these men ranges from 14.33 to 15.51 inches.

iii.

On average, men’s neck sizes differ from 14.94 inches by 0.902 inches.

iv.

On average, men’s neck sizes differ from 14.96 inches by 1.18 inches

c. Which statement best describes the spread of neck sizes based on standard deviation.

i.

The middle 50% of neck sizes for these men from Utah ranges from 12 to 17.5 inches.

ii.

The middle 50% of neck sizes for these men from Utah ranges from 14.33 to 15.51 inches.

iii.

On average, men’s neck sizes differ from 14.94 inches by 0.902 inches.

iv.

On average, men’s neck sizes differ from 14.96 inches by 0.902 inches

—————————————————————————————————————————————–5) (6 pts) To determine the mean cost of groceries in a certain city, an identical grocery basket of food

is purchased at each store in a random sample of 33 stores. Suppose that a 95% confidence interval

for the mean cost was computed to be (46.30, 48.74).

a. The sample mean price in our survey is:

i.

46.3

ii. 48.74

iii. 95.04

iv. 47.52

v. 1.22

iv. 47.52

v. 1.22

b. The margin of error (E) in our survey is:

i.

46.3

ii. 48.74

iii. 95.04

c. The correct interpretation of a 95% confidence interval of $46.30 to $48.74 is.

i. The mean cost of groceries in a certain city falls in the interval $46.30 and $48.74.

ii. 95% of grocery basket cost is in the interval $46.30 and $48.74

iii. There is a 95% probability the mean cost of groceries in a certain city is in the interval

$46.30 and $48.74

iv. We are 95% confident that the mean cost of groceries in a certain city is in the interval

$46.30 and $48.74.

2

6)

(10 pts) A company that develops credit score would like to examine the relationship between the

age and credit score of an individual. They used the credit scores and ages of 10 randomly selected

people ranging in age between 25 and 60 years to come up with the model below.

Credit Score = 533.9616 + 4.0942 (Age), = 0.5686

a) The response variable is;

i.

Age

ii. The credit score

iii.

Number of individuals

b) The correlation Coefficient is;

i. 0.3233

ii. 0.7541

c) The correlation is:

i.

Weak

ii. Strong

iv. The company

iii. -0.3233

iii. Moderate

iv. – 0.7541

v. No correlation

v. 1.1372

v. cannot be determined.

d) The slope means;

i.

For every additional credit score, the predicted age increases by 4.09 years.

ii.

For every additional year in age, the predicted credit score increases by 4.09 points.

iii.

For every additional credit score, the predicted age decreases by 4.09 years.

iv.

For every additional year in age, the predicted credit score increases by 533.9616 points.

v.

None of the Above.

e) The predicted credit score for 30 years old college student is;

i.

712

ii.

452

iii.

Not meaningful

iv.

657

v.

534

—————————————————————————————————————————————–7) (4 pts) The USDA limit for salmonella contamination for chicken is 20%. A meat inspector reports

that the chicken produced by a company exceeds the USDA limit. You perform a hypothesis test to

determine whether the meat inspector’s claim is true.

a) The correct null and alternative hypotheses are:

i.

ii.

iii.

iv.

v.

0 : = 0.20 1 : > 0.20

0 : > 0.20 1 : ≤ 0.20

0 : = 0.20 1 : ≥ 0.20

0 : = 0.20 1 : > 0.20

0 : = 0.20 1 : ≥ 0.20

b) Type I error could result in

i.

Sickness or even death.

ii.

A health scare and hurt the sales for no good reason.

iii.

Increasing the sales of chicken.

iv.

Get the inspector a promotion.

3

8) (2 pts) The median selling price of homes in metro Toledo is $129,000 as of last May (Toledo Blade).

Which of the following is the most plausible value for the standard deviation?

i.

−$19,000

ii. $2000

iii. $55,000

iv. $200,000

v. $10,000

—————————————————————————————————————————————–9) (2 pts) What would you do if the − = 0.042, = 0.05?

i.

Reject the claim

ii.

Fail to reject the claim

iii.

Reject the null hypothesis,

iv.

Accept the null hypothesis,

v.

Fail to reject

—————————————————————————————————————————————–10) (2 pts) A busiess bought three new computers from a manufacturer who just announced a recall

because 12% of those computers are defective. What is the probability that at least one of the

computers is defective? Circle correct answer.

i.

0.0017

ii. 0.9983

iii. 0.6815

iv. 0.3185

v. 0.8800

—————————————————————————————————————————————–11) (2 pts) At a local college, 32% of the students live on campus. If 11% of the students live on campus

and have jobs. What is the probability that the student has a job given the student lives on campus?

i. 2.909

ii. 0.344

iii. 0.035

iv. 0.430

v. none of the listed options

—————————————————————————————————————————————–12) (2 pts) For a given random survey,

i.

As we increase the sample size, we increase the margin of error.

ii.

As we increase the confidence level, we decrease the margin of error.

iii.

As we increase the sample size, we decrease the margin of error.

iv.

As we increase the sample size, we decrease the confidence level.

v.

None of the above.

—————————————————————————————————————————————–13) (2 pts) The two types of hypotheses used in a hypothesis test are?

i.

Left-tailed and right-tailed

ii.

Null and alternative

iii.

Population and sample

iv.

Type I and type II

—————————————————————————————————————————————–14) (2 pts) The probability that a test correctly rejects a false null hypothesis is called?

i.

P-value

ii.

Significance level

iii.

Type II error

iv.

Power of the test

v.

Type I error

4

15) (8 pts) A credit card company claims that the mean credit card debt for individuals is greater than $

4,801. You want to test this claim. You find that a random sample of 27 cardholders has a mean

credit card balance of $ 4, 700 and a standard deviation of $ 675. At = 0.05, = 1.706.

a. The 95% confidence interval for the population mean is.

675

i. 4700 ± 1.706√ 27

iv. 1.706 ± 4801

675

√27

ii. 4801 ± 1.706

675

√27

iii. 4700 ± 1.706

675

√27

675

v. 4801 ± 1.706√ 27

b. Choose the correct null and alternative hypothesis.

i.

0 : = 4801 1 : > 4801

ii.

0 : = 4801 1 : > 4801

iii.

0 : = 4801 1 : > 4700

iv.

0 : ≥ 4801 1 : < 4801
v.
0 : = 4700 1 : > 4700

c. Choose the test statistic. Circle One.

i. =

4700−4801

675/√27

iv. =

4801−4700

675/√27

ii. =

4700−4801

675/√27

iii. =

4801−4700

675/√27

v. None of the Above

d. At the significance level of 0.05 and using the − = 0.2219, state the conclusion of the

test in the context of the problem.

i.

There is sufficient evidence to support the claim that the mean credit card debt is less

than $4801.

ii.

There is sufficient evidence to support the claim that the mean credit card debt is

greater than $4801.

iii.

There is sufficient evidence to reject the claim that the mean credit card debt is greater

than $4700.

iv.

There is sufficient evidence to reject the claim that the mean credit card debt is greater

than $4801.

—————————————————————————————————————————————-16) (2 pts) If the distribution of scores on a test are normally distributed, then a score is considered

unusual if;

i.

The score is below the first quartile.

ii.

The score in within 2-stanndard deviations of the mean.

iii.

The score is beyond 2-standard deviations from the mean.

iv.

The score is beyond 3-standard deviations from the mean.

v.

The score is below the average.

5

17) (3 pts) Name each sampling method (Systematic, Stratified, cluster, simple SRS, convenience)

a) Three out of ten sections of MATH 2600 are selected at random and all students in the three

sections were surveyed. __________________

b) A tire company selects 40 tires in a warehouse and test them for quality and performance.

____________________

c) The university generates a random sample of 100 students at UT and they ask you to survey them

about their political party. _____________________

—————————————————————————————————————————————–18) (4 pts) The probability of selecting a female student from the class is 64%. The probability of

selecting a student who is from Ohio is 85%. The probability of selecting a female student who is

also from Ohio is 53%.

a) What is the probability of selecting a female student or a student from Ohio?

i. 4%

ii. 96%

iii. 53%

iv. 45%

b)

What is the probability of selecting a female student who is not from Ohio?

i.

45%

ii.

96%

iii.

53%

iv.

11%

—————————————————————————————————————————————–19) (2 pts) To graph quantitative data, we may use

i.

Histograms, Pie charts, or dot plots

ii.

Histograms, bar charts, or dot plots

iii.

Bar charts, Pie charts, or dot plots

iv.

Histograms, stem-and leaf plots, or dot plots

v.

All options listed above

—————————————————————————————————————————————–20) (2 pts) Assume that your z-scored on a test is 1.25, the class mean score is 82, and the standard

deviation is 8. The professor decided to give an extra credit of 2 points to all. What is your score

after the extra credit was applied?

i.

91.25

ii.

92

iii. 68

iv.

94

6

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