Download 1. (TCO 9) The hours of study and the final exam grades have this

1. (TCO 9) The hours of study and the final exam grades have this type of relationship: ŷ = 7.35(hours) + 34.62. Based on
this linear regression equation, estimate the expected grade for a student spending 8 hours studying. Round your
answer to two decimal places. (Points : 6)
58.80
82.25
91.97
93.42
2. (TCO 5) Historical sales records show that 40% of all customers who enter a discount department store make a
purchase. We are interested in calculating the probability that 3 of 5 customers make purchase. Choose the best answer
of the following: (Points : 6)
This is an example of a Poisson probability experiment
This is an example of a Binomial probability experiment
This is neither a Poisson nor a Binomial probability experiment
Not enough information to determine the type of experiment
3. (TCO 5) Microfracture knee surgery has a 75% chance of success on patients with degenerative knees. The surgery is
performed on 5 patients. Find the probability of the surgery being successful on more than 3 patients? (Points : 6)
0.487304
0.367188
0.632813
0.762695
4. (TCO 5) It has been recorded that 10 people get killed by shark attack every year. What is the probability of having 7
or 8 people get killed by shark attack this year? (Points : 6)
0.130141
0.202678
0.220221
0.797321
5. (TCO 2) The mean teaching hours for a full time faculty at a state university is eight hours per week. What does this
tell you about the typical teaching hours for full time faculty at that university? (Points : 6)
Half the full time faculties teach less than eight hours per week while half teaches more than eight hours per week.
The average teaching hours for full time faculty is eight hours per week.
More full time faculty teaches eight hours per week than any other number of teaching hours.
The number of teaching hours for full time faculty in not very consistent because eight is such a low number.
6. (TCO 6) Assuming that the data are normally distributed with a mean of 45 and a standard deviation of 3.25, what is
the z-score for a value of 40? (Points : 6)
1.54
2.38
-1.36
-1.54
7. (TCO 8) The mean hours of Internet usage by adults in the US in claimed to be 25 hours per week. A hypothesis test is
performed at a level of significance of 0.05 with a P-value of 0.08. Choose the best interpretation of the hypothesis test.
(Points : 6)
Reject the null hypothesis; there is enough evidence to reject the claim that the mean of hours Internet usage by adults
in the US is 25 hours per week.
Reject the null hypothesis; there is enough evidence to support the claim that the mean hours Internet usage by adults
in the US is 25 hours per week.
Fail to reject the null hypothesis; there is not enough evidence to reject the claim that the mean hours of Internet usage
by adults in the US is 25 hours per week.
Fail to reject the null hypothesis; there is not enough evidence to support the claim that the mean hours of Internet
usage by adults in the US is 25 hours per week.
8. (TCO 8) A result of an entry level exam reveals that more than 22% of students fail that exam. In a hypothesis test
conducted at a level of significance of 2%, a P-value of 0.035 was obtained. Choose the best interpretation of the
hypothesis test. (Points : 6)
Fail to reject the null hypothesis; there is not enough evidence to reject the claim that 22% of students fail the entry
level exam.
Fail to reject the null hypothesis; there is not enough evidence to support the claim that 22% of students fail the entry
level exam.
Reject the null hypothesis; there is enough evidence to reject the claim that 22% of students fail the entry level exam.
Reject the null hypothesis; there is enough evidence to support the claim that 22% of students fail the entry level exam.
9. (TCO 2) You want to buy light bulbs and you want to choose between two vendors. Vendor A’s light bulbs have a
mean life time of 800 hours and a standard deviation of 175 hours. Vendor B’s light bulbs also have a mean life time of
800 hours, but a standard deviation of 225 hours. You want light bulbs that have more life time consistency, which
vendor will you purchase from? (Points : 6)
Vendor A because you will be more likely get light bulbs with the same life time
Vendor B because you will be more likely get light bulbs with the same life time
Either one because both produce light bulbs with the same mean life time.
Neither one because a mean height of 800 inches is too short for a light bulb.
10. (TCO 4) A jar contains balls of four different colors; red, blue, yellow and green. The total balls are divides as 45%
red, 35% blue, 15% yellow, and 5% green. If you are to select one ball at random. Find the expected value of your
winning amount if the payments are set to be $5, $15, $25, $60 for red, blue, yellow and green ball respectively.
Winning amount 5 15 25 60
Probability 45% 35% 15% 5%
(Points : 6)
The expected winning amount is $28.50
The expected winning amount is $14.25
The expected winning amount is $25.50
The expected winning amount is $11.25
11. (TCO 3) The grades of 20 students are listed in the stem and leaf diagram below. What is the probability of randomly
selected student to have a grade more than or equal to 60 and less than or equal to 80.
4|4
5|68
6|579
7|157889
8|0257889
9|7
(Points : 6)
0.65
0.50
0.45
-0.55
12. (TCO 1) A researcher is considering using 90% confidence interval for his research project instead of 95%. What
happens to the required sample size if the confidence level is decreased from 95% to 90% and the same error margin is
allowed in each case? (Points : 6)
The sample size remains unchanged
The sample size needs to increase
The sample size needs to decrease
Not enough information is provided to draw a conclusion regarding the sample size in this case.
13. (TCO 6) Horse race time is found to be normally distributed with a mean value of 18 minutes and a standard
deviation of 4 minutes. Horses whose race time is in the top 6% will not be eligible to participate in a second round.
What is the lowers race time that makes a horse losses his eligibility to participate in a second round? (Points : 6)
26.6
11.8
24.2
20.3
14. (TCO 5) A class containing 15 students 5 of them are females. In how many ways can we select a group of 4 male
students? (Points : 6)
260
120
5040
210
15. (TCO 6) Research shows that the life time of Everlast automobile tires is normally distributed with a mean value of
65,000 miles and a standard deviation of 6,500 miles. What is the probability of having a tire that lasts more than 75,000
miles? (Points : 6)
0.0618
1.54
0.9382
0.0606
16. (TCO 10) A research shows that employee salaries at company XYX, in thousands of dollars, are given by the equation
y-hat= 48.5 + 2.2 a + 1.5 b where ‘a’ is the years of experience, and ‘b’ is the education level in years. In thousands of
dollars, predict the salary for an employee with 7 years experience and 12 years education level. (Points : 6)
52.2
81.9
67.5
63.9
17. (TCO 9) Describe the correlation in this graph.
Graph is missing?
(Points : 6)
moderate positive
strong negative
moderate negative
strong positive
1. (TCO 8) For the following statement, write the null hypothesis and the alternative hypothesis. Also label which one is
the claim.
A car manufacturer claims that their cars makes at least 35 miles per gallon of fuel. (Points : 8)
Ho: μ ≥ 35
Ha: μ < 35
Ho is the claim
2. (TCO 11) A pizza restaurant manager claims that the average home delivery time for their pizza is no more than 18
minutes. A random sample of 36 home delivery pizzas was collected. The sample mean was found to be 19.25 minutes
and the standard deviation was found to be 3.3 minutes. Is there evidence to reject the manager’s claim at alpha =.02?
Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to
obtain the results. (Points : 20)
x-bar = 19.25, s = 3.3, n = 36, α = 0.02
Ho: μ ≤ 18
Ha: μ > 18
z = (x-bar - μ)/(s/√n) = (19.25 - 18)/(3.3/√36) = 2.2727
P- value = P(z > 2.2727) = 0.0115
Since 0.0115 < 0.02, we reject Ho and accept Ha
There is sufficient evidence to reject the manager’s claim. It is not valid.
3. (TCO 5) A multiple choice exam contains 50 questions. Each question has 5 choices, one of which is correct. We are
interested in knowing the probability guessing exactly 18 questions correctly.
(a) Is this a binomial experiment? Explain how you know.
(b) Use the correct formula to find the probability of guessing exactly 18 questions correctly out of the 50 questions.
Show your calculations or explain how you found the probability. (Points : 20)
(a) Yes, this is a binomial experiment because the number of trials is finite (50) and the probability of success in every
trial is constant (= 1/5 = 0.2)
(b) n = 50, x = 18, p = 0.2, q = 1 - p = 0.8
P(x) = nCx p^x q^(n - x)
P(18) = 50C18 0.2^18 0.8^(50 - 18) = 0.0037
4. (TCO 6) The monthly utility bills are normally distributed with a mean value of $160 and a standard deviation of $25.
(a) Find the probability of having a utility bill between 120 and 180.
(b) Find the probability of having a utility bill less than $120.
(c) Find the probability of having a utility bill more than $210. (Points : 20)
μ = 160, σ = 25
z = (x - μ)/σ
(a) z = (120 - 160)/25 = -1.6 and z = (180 - 160)/25 = 0.8
P($120 < x < $180) = P(-1.6 < z < 0.8) = 0.7333
(b) P(x < $120) = P(z < -1.6) = 0.0548
(c) z = (210 - 160)/25 = 2
P(x > $210) = P(z > 2) = 0.0228
5. (TCO 8) A Mall manager claims that in average every customer spends $37 per a single visit to the mall. To test this
claim, you took a sample of 64 customers and found the sample mean to be $34 and the sample standard deviation to
be $5. At alpha = 0.05, test the Mall’s manager claim. Perform an appropriate hypothesis test, showing the necessary
calculations and/or explaining the process used to obtain the results. (Points : 20)
x-bar = 34, s = 5, n = 64, α = 0.05
Ho: μ = 37
Ha: μ ≠ 37
z = (x-bar - μ)/(s/√n) = (34 - 37)/(5/√64) = -4.8
P- value = P(z < -4.8 or z > 4.8) = 0
Since 0 < 0.05, we reject Ho and accept Ha
There is sufficient evidence to reject the manager’s claim
6. (TCO 7) A bank manager wanted to estimate the mean number of transactions businesses make per month. For a
sample of 50 businesses, he found the mean number of transaction per month to be 35 and the standard deviation to be
9.5 transactions.
(a) Find a 99% confidence interval for the mean number of business transactions per month. Show your calculations
and/or explain the process used to obtain the interval.
(b) Interpret this confidence interval and write a sentence that explains it. (Points : 20)
(a) n = 50, x-bar = 35, s = 9.5
z- score for 99% confidence is z = 2.576
SE of the mean, SE = s/√n = 9.5/√50 = 1.3435
Margin of error, E = z * SE = 2.576 * 1.3435 = 3.4609
The 99% confidence interval is [x-bar - E, x-bar + E] = [35 - 3.4609, 35 + 3.4609] = [31.5391, 38.4609]
(b) Interpretation: If samples of size 50 are repeatedly drawn from the population and confidence intervals for mean
number of transactions are constructed, such intervals will include the true mean number of transactions 99% of the
time.
7. (TCO 7) A company’s CEO wanted to estimate the percentage of defective product per shipment. In a sample
containing 600 products, he found 45 defective products.
(a) Find a 99% confidence interval for the true proportion of defective product. Show your calculations and/or explain
the process used to obtain the interval.
(b) Interpret this confidence interval and write a sentence that explains it. (Points : 20)
(a) p = 45/600 = 0.075
q = 1 - p = 0.925
n = 600
Standard error of proportion, SE = √(pq/n) = √(0.075 * 0.925/600) = 0.0108
z- score for 99% confidence is z = 2.5758
Margin of error, E = z * SE = 2.5758 * 0.0108 = 0.0278
The 99% confidence interval is [p - E, p + E] = [0.075 - 0.0278, 0.075 + 0.0278] = [0.0472, 0.1028]
(b) Interpretation: If samples of size 600 are repeatedly drawn from the lot and confidence intervals for proportion of
defectives are constructed, such intervals will include the true proportion of defectives 99% of the time.
8. (TCO 2) The ages of 10 students are listed in years:{ 17,20,18,24,21,26,29,18,22,28}
(a) Find the mean, median, mode, sample variance, and range.
(b) Do you think that this sample might have come from a normal population? Why or why not? (Points : 20)
(a)
Raw Scores:
x
17
20
18
24
21
26
29
18
22
28
Count =
10
Range = Max value - Min value =
12
Median = Middle value =
21.5
d = x - x-bar
-5.3
-2.3
-4.3
1.7
-1.3
3.7
6.7
-4.3
-0.3
5.7
d^2
28.09
5.29
18.49
2.89
1.69
13.69
44.89
18.49
0.09
32.49
Mode = Most frequent value =
18
Sums =
223
Mean, x-bar = Sum(x)/Count =
22.3
Variance, s^2 (Sample) = Sum(d^2)/(Count - 1) =
18.46
166.1
(b) Since mean, median and mode are all different, it appears that this sample has not come from a normal population