Statistics Assignment | Online Homework Help

Doing with the process and answer, prefer the process with calculatorMath 117 Final Exam Name___________________________________
(15 pts) 1. The amount of protein (in grams) for a variety of fast food sandwiches is reported here.
12 12 14 15 15 18 19 20 20 21 22 22 23 24 24 25 25 26 26 26
27 27 27 27 29 30 31 33 34 35 35 35 38 40 42 43 44 45 57 58
Source: The Doctor’s Pocket Calorie, Fat, and Carbohydrate Counter.
(a) Construct a frequency distribution using 6 classes.
Class width: ___________
Class Class Boundaries Frequency Relative Frequency Cumulative Frequency
(b) Draw a histogram using frequencies.
(15 pts) 2. The volume of a stock is the number of shares traded on a given day. The following data, given in
millions so that 3.78 represents 3,780,000 shares traded, represent the volume of Altria Group Stock
traded for a random sample of 35 trading days in 2004. For convenience the data has been placed in
numerical order.
3.01 4.35 5.32 6.07 7.57
3.04 4.43 5.34 6.23 7.97
3.25 4.50 5.53 6.52 8.40 (a) Determine the median of the data set.
3.38 4.74 5.58 6.57 8.74
3.38 4.88 5.64 6.92 9.70
3.56 5.00 5.75 7.16 10.32 (b) Determine Quartile 1 and Quartile 3 of the data set.
3.78 5.02 6.06 7.25 10.96
Source: yahoo.finance.com
(c) Construct a boxplot using the above data showing: the minimum, quartile 1, the median, quartile 3,
and the maximum. The boxplot needs to be drawn to scale, indicating the scale clearly.
(15 pts) 3. A random variable X is normally distributed. Its mean is μ = 500 and its standard deviation
is s =100 . Determine the required probabilities. Draw a representative sketch in each case.
(a) The probability that one random observation of the variable X is larger than 550.
(b) The probability that one random observation of the variable X is less than 450.
(c) The probability that a random sample of size n = 25 has a sample mean x larger than 550.
(Remember that, according to the Central Limit Theorem, the distribution of the sample
means x is normal, with mean x μ = μ and standard deviation x
n
s
s = )
(15 pts) 4. The world’s smallest mammal is the Kitti’s hog-nosed bat, with a mean weight of 1.5 grams
and a standard deviation of 0.25 grams. Assume that the weights are normally distributed.
Find the probability of randomly selecting a bat that weighs between 1.40 grams and 1.65 grams.
Show a sketch of the normal curve, labeled, with the correct area shaded.
(15 pts) 5. A researcher for the FAA wants to estimate the average flight time (in minutes) from
Albuquerque, New Mexico, to Dallas, Texas, for flights with American Airlines. He
randomly selects nine flights between the two cities and obtains the data shown.
Assume that the duration of all flights with American Airlines between Albuquerque and
Dallas follows a normal distribution, with population standard deviation s = 8 minutes).
120 95 109 103 110 95 100 99 106
(a) Use the data to compute a point estimate (the sample mean) for the population mean
flight time between Albuquerque and Dallas on American Airlines flights.
(b) Construct a 95% confidence interval for the mean flight time. Using complete sentences,
explain what this confidence interval means.
(15 pts) 6. The USGA requires that golf balls have a weight that is less than 1.62 ounces. An engineer
for the USGA wants to test the claim that Maxfli XS golf balls have a mean weight less than
1.62 ounces. He obtains a random sample of 12 Maxfli XS golf balls. Their weights are:
1.614 1.619 1.614 1.614 1.610 1.610 1.621 1.612 1.615 1.621 1.602 1.617
Source: Michael McCraith, Joliet Junior College
You may assume that the weight is normally distributed. Using a test of hypothesis, determine
whether the golf balls meet Maxfli’s standard at the a = 0.01 level of significance. This is a
left-tailed test, since we are testing if the mean weight of this kind of golf balls is less than 1.62.
State the appropriate hypotheses, the test statistic 0 x
t
s
n
−μ
=
 
 
 
, the P-value and a conclusion using
the context of this problem. Do not simply answer “Fail to reject 0 H ” or “Reject 0 H ”.
(15 pts) 7. A psychological test measures study habits and attitude toward school, with scores ranging
from 0 to 200 points. The mean score for all college students who have taken the test is
μ =115 and the population standard deviation is s = 30 . A teacher suspects that the mean score
on this test is higher for older students (28 years old or older) than the overall mean of 115.
The teacher gives the test to a random sample of 45 older students. The sample mean is
x =125.8.
(a) Write down the Null and the Alternative hypothesis to test if the mean score on the psychological test
for older students is higher than 115.
(b) Conduct the test at the 5% level of significance. Answer using full sentences, in the context of this
problem. Do not just say: “reject 0 H ”, “do not reject 0 H ”, or “we have enough evidence”, or
“we don’t have enough evidence”. Your answer needs to be a statement about the mean score
for older students.
(c) Construct a 95% confidence interval for the mean score on the test for older students.
Explain what this interval means.
(15 pts) 8. A state labor department is comparing the annual salaries of cooks and truck drivers,
to determine if there is a difference between the mean salaries. Assume that the standard
deviations of both populations are known: s1 = 4250 for the cooks’ salaries, and 2 s = 3800
for the truck drivers’salaries. Random samples of 42 cooks and 65 truck drivers were taken,
and the sample means were: 1 x = 57320 for the sample of cooks, and 2 x = 54000 for the sample
of truck drivers.
(a) Conduct a 5% level of significance test. State the Null and Alternative hypotheses and
explain your decision. Do not just say: “reject 0 H ”, “do not reject 0 H ”, or “we have
enough evidence”, or “we don’t have enough evidence”. Your answer needs to be a
statement about the difference between the mean salary for cooks and the mean salary for
truck drivers.
(b) Construct a 95% confidence interval for the difference between the two means 1 2 μ −μ .
Explain what this confidence interval means
(15 points) 9. A candy manufacturer produces “Fun Size” candy bars that are advertised to weigh 20 grams.
The engineers calibrate the equipment so that the mean weight of the candy bars is 20.1 grams,
to be on the safe side. As a matter of routine, a simple random sample of 15 candy bars is taken,
to test if the mean is different from 20.1, and if this is the case, to stop production and recalibrate
the equipment.
Suppose that a random sample of size 15 gave the following weights for the candy bars:
19.78 20.66 20.55 21.57 20.63 20.36 19.98
19.74 19.61 21.02 20.68 20.39 19.75 19.89 21.02
(a) Write down the Null and the Alternative hypotheses for a test to decide if the mean
weight of all candy bars being produced is different from 20.1
(b) Conduct the test (t-test) at the 5% level of significance. What is your conclusion regarding
the need or no need to recalibrate the equipment?
(c) Determine a 95% confidence interval (t-interval) for the mean weight of all candy bars being
produced by this equipment.
(15 pts) 10. A report summarizes the findings of a researcher in a city. She worked with a simple random
sample of 45 renters. Her summary indicates that the mean rent in the city is between $1350 and
$1800 per month. Suppose that this range corresponds to a 95% confidence interval.
(a) What was the sample mean rent?
(b) What is the margin of error?
(15 pts) 11. A summer institute is designed to improve the skills of high school teachers of foreign languages.
Following are the scores on a Pretest before taking a summer institute to improve listening of
French and a Posttest, for 20 participating teachers. The differences between the PostTest score
and the PreTest score are listed in the “gain” column.
Teacher Pretest PostTest Gain Teacher Pretest PostTest Gain
1 32 34 2 11 30 36 6
2 31 31 0 12 20 26 6
3 29 35 6 13 24 27 3
4 10 16 6 14 24 24 0
5 30 33 3 15 31 32 1
6 33 36 3 16 30 31 1
7 22 24 2 17 15 15 0
8 25 28 3 18 32 34 2
9 32 26 −6 19 23 26 3
10 20 26 6 20 23 26 3
(a) State appropriate null and alternative hypotheses for examining the question of whether or not the course
improves French spoken-language skills (the course improves skills if the mean gain for all participants
is greater than 0).
(b) Conduct the test at the 5% level of significance. Explain your conclusion in the context of this problem
(is there enough evidence to conclude that the course works?)
(c) Construct a 95% confidence interval (t-interval) for the mean gain (that is, the mean difference between
the PostTest score and the PreTest score for all participants in the course). Explain what this interval
means.
(15 pts) 12. Are men and women college students equally likely to be frequent binge drinkers?
(a) If 1 p is the proportion of men college students who are frequent binge drinkers and 2 p is
the proportion of women college students who are frequent binge drinkers, state appropriate
null and alternative hypotheses to test if these proportions are different.
(b) The following data correspond to a survey of 530 men college students and 847 women college
students regarding their binge drinking. X is the number of students in each sample who
reported that they are frequent binge drinkers. Compute the sample proportions
p1, p2
Population
n
X
X
p
n
=
Men 530 139
Women 847 192
(c) Conduct the test at the 5% level of significance. Explain what your conclusion means
regarding the difference between the proportion of men college students who are frequent
binge drinkers and the proportion of women college students who are.
(d) Construct a 95% confidence interval for 1 2 p − p , the difference between the proportion of
men college students who are frequent binge drinkers and the proportion of women college
students who are. Explain what this interval means.
(10 pts) 13. A retail trade association’s records show that last year, the tax preparation methods of adults
were distributed as follows:
Accountant: 30%, Computer Software: 45%, Tax Preparation Service: 25%
A random sample of 300 adults had the following results for their tax preparation method this year:
Accountant: 96 Computer Software: 117 Tax Preparation Service: 87
(a) State the Null and Alternative Hypotheses for a Goodness of Fit test regarding the distribution
of tax preparation methods of adults.
(b) The following table gives the observed values:
Accountant Computer Software Tax Prep Service
96 117 87
Complete the table of expected values according to the Null Hypothesis:
Accountant Computer Software Tax Prep Service
(c) What are the degrees of freedom for the 2 c distribution that is needed?
(d) Conduct a 5% level of significance test. Write down the critical value 2 c that has area on
its right tail = 0.05.
(e) Write down the value of the test statistic 2 c =sum of
( )2
observed expected
expected
−
(f) What do you conclude? Explain what your conclusion means regarding the distribution of tax
preparation methods of adults this year compared to the distribution last year.
(10 pts) 14. Following are the ages (x) and the systolic blood pressure (y) of 10 men:
Age (x)
16
25
39
45
49
64
70
29
57
22
Systolic
Pressure( y)
109
122
143
132
169
185
172
130
165
118
(a) Determine the correlation coefficient r and explain what it means regarding the linear
association between x and y.
(b) Find the line of regression or line of least squares: y = mx + b
(c) What is the predicted systolic pressure of a 72 year old man?