A cell phone company offers two plans to its subscribers. At the time new subscribers sign up, they are asked to provide some demographic information. The mean yearly income for a sample of 40 subscribers to Plan A is $50,500 with a standard deviation of $6,700. For a sample of 25 subscribers to Plan B, the mean income is $53,300 with a standard deviation of $6,300.
At the 0.02 significance level, is it reasonable to conclude the mean income of those selecting Plan B is larger? Hint: For the calculations, assume the Plan A as the first sample.
The test statistic is ____. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)
In: Statistics and Probability
HW8#11
A genetic experiment involving peas yielded one sample of offspring consisting of 430 green peas and 168 yellow peas. Use a 0.01 significance level to test the claim that under the same circumstances, 27% of offspring peas will be yellow. Identify the null hypothesis, alternative hypothesis, test statistic, Pvalue, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the Pvalue method and the normal distribution as an approximation to the binomial distribution.
A. Identify the null and alternative hypotheses.
B. What is the test statistic?
z=
Round two decimal places as needed.
C. What is the Pvalue?
D. Fail to reject OR Reject the null hypothesis?
E. There is or is not sufficient evidence?
In: Statistics and Probability
The file medinc.mtw contains data on the median incomes (medinc) of census dissemination areas in Toronto. (a) Treating this set of data as the population, use Minitab to calculate the population mean and the population standard deviation for the medinc variable. Set aside all population information until parts (d) and (e). (b) Use Minitab (Calc Menu – Random Data – Sample from Columns) to draw twenty samples of size n = 40 from the Toronto medinc population. This procedure must be replicated twenty times (note that if you open up the same sampling dialog box each time from the menu, then you only have to replace the last destination column with the next one. In Minitab Express, you must specify the sample size each time but you do not need to specify the destination column). For each sample, use Minitab to calculate the sample mean. Note that when you can use the Descriptive Statistics function, you can specify the calculation of only the sample means of all your samples at once. (c) Copy the sample means into a new column and calculate the mean and standard deviation of your sample means. (d) The sampling distribution of the sample mean has an average equal to the population mean. Explain why the mean in part (c) may be different from the population mean in part (a). (e) How would you use the sample standard deviation in part (c) to estimate the population standard deviation in part (a)? How close is your estimate to the true value? I am only looking for how we calculate e) I have all the others done and my sample standard deviation is 1593.5 with a mean of 25251.7. I'm using n=40 and perhaps that is where I am going wrong
In: Statistics and Probability
3.2 Our overworked student trudges to his 3rd exam of the day, a true/false exam with 100 questions. Again,he just guesses the answers. Notice that this time he has a 50% chance of getting each particular question correct. (10 Marks: 2 Marks for each of parts a), b), c), d) and e).
a. What is the probability that the student gets at least one question correct?
b. What is the probability that the student gets between 15 and 35 questions (inclusive) correct?
c. What is the probability that the student gets between 40 and 60 questions (inclusive) correct?
d. What is the probability that the student passes the exam (gets 60 or more questions correct)?
e. Why does the student have a better chance of passing the exam in question 3.2 than the one in question 3.1?
In: Statistics and Probability
Read the “Evaluating the Quality of Open Source Software” article (Spinellis, et al., 2009). What are the strengths and weaknesses of this particular study? (For example, does the study do an adequate job of collecting and analyzing representative samples?) What would you suggest that the authors do to remedy those weaknesses and why? Use both your text and the article An Introduction to Research Design (Ganster, 2003). You may also draw on any book, article, website, or other reliable resource in answering this question.
In: Statistics and Probability
Choose one of the tools listed here that was not utilized in the course (SAS, R, or JMP,). Provide a brief description of this tool including its strengths and weaknesses. Describe a scenario where you would make use of this tool and explain why this tool would be preferred in that case.
In: Statistics and Probability
HW8#10
A certain drug is used to treat asthma. In a clinical trial of the drug,17 of 288 treated subjects experienced headaches (based on data from the manufacturer). The accompanying calculator display shows results from a test of the claim that less than 10% of treated subjects experienced headaches. Use the normal distribution as an approximation to the binomial distribution and assume a 0.05 significance level to complete parts (a) through (e) below.
A. Is the test twotailed, Lefttailed, or right tailed?
B. What is the test statistic?
z=
Round two decimal places as needed.
C. What is the Pvalue?
Round four decimal places as needed.
D. What is the null hypothesis, and what do you conclude about it?
E. What is the final conclusion?
There is or is not sufficient evidence?
In: Statistics and Probability
Question 1:In the layout of a printed circuit board for an electronic product, there are 12 different locations that can accomodate chips. (a) If Five different types of chips are to be placed on the board, how many different layouts are possible? (b) What is the probability that five chips that are placed on the board are of the same type? Question 2: A Web ad can be designed from 4 different colors, 3 font types, 5 font sizes, 3 images, and 5 text phrases. A specific design is randomly generated by the Web server when you visit the site. Let A denote the event that the design color is red and let B denote the event that the font size is not the smallest one. Find P(A ∪ B0 ) and P(BA). Question 3: A batch of 500 containers for frozen orange juice contains 10 defective containers. Three are selected randomly without replacement from the batch. (a) What is the probability that the second one is defective given that the third one is defective? (b) What is the probability that the third one is defective? (c) What is the probability that the first one is defective given that the other ones are not defective? Question 4: A player of a video game is confronted with a series of 4 opponents and an 80% probability of defeating each opponent. Assume that the results are independent (and that when the player is defeated by an opponent the game ends). (a) What is the probability that a player defeats all 4 opponents in a game? (b) If the game is played 4 times, what is the probability that the player defeats all 4 opponents at most twice. Question 5: A credit card contains 16 digits. It also contains a month and year of expiration. Suppose there are one million credit card holders with unique numbers. A hacker randomly selects a 16digit credit card number. (a) What is the probability that it doesn’t belong to a real user? (b) Suppose a hacker has a 10% chance of correctly guessing the month 2 of the expiry and randomly selects a year from 2018 to 2025. What is the probability that the hacker correctly selects the month and year of expiration (all the years are equally likely)? Question 6: An optical inspection system is to distinguish among different parts. The probability of a correct classification of any part is 98%. Suppose that 3 parts are inspected and that the classifications are independent. Let the random variable X denote the number of parts that are correctly classified. (a) Determine the probability mass function X. (b) Find P(X ≤ 2)
In: Statistics and Probability
A loan officer compares the interest rates for 48month fixedrate auto loans and 48month variablerate auto loans. Two independent, random samples of auto loan rates are selected. A sample of eight 48month fixedrate auto loans and a sample of five variablerate auto loans had the following loan rates:
Fixed(%)  Variable(%) 
4.29 
3.59 
3.75 
2.75 
3.5 
2.99 
3.99 
2.5 
3.75 
3 
3.99 

5.4 

4 
Answer the following questions:
Let's define μFμF as the population mean loan rate for fixedrate auto loans and
μVμV as the population mean loan rate for variablerate auto loans.
a. The loan officer thinks the mean loan rates for fixedrate auto loans is at least 1% greater than the mean loan rates for the variablerate auto loans. Set up the null and alternative hypotheses needed to determine whether this claim is correct.
H0: μFμFμVμV (Click to select)≠0<1≠1≤ 1=0≥1>1>0≥0≤ 0=1<0
Ha: μFμFμVμV (Click to select)≤1>1≠0=0≤0>0 ≠1<0<1≥1=1
b. What is the critical value rejection rule. (Assume unequal variances and a significance level of 0.05.Answers should be in 4 decimals.)
Critical value rule: Reject H0 if (Click to select)t<t alphat > t alphat > t alpha/2 or t <t alpha/2 where the critical value is .
c. What is the t test statistic and pvalue? (4 decimals)
t=
pvalue=
What is the value in the numerator of the test statistic?
What is the value in the denominator of the test statistic?
Which one of the following is the correct pvalue calculation?(Click to select)2 x (1t.inv(0.95,10))1t.dist(0.430,10,true)t.dist(0.430,10,true)2 x (1t.dist(0.430,10,true))t.inv(0.95,10)1t.inv(0.95,10)
d. With 95% confidence we (Click to select)cancannot conclude that the mean loan rate for fixedrate autoloans is at least 1% greater than the loan rate for variablerate autoloans.
e. We have (Click to select)extremely strongsomenovery strongstrong evidence that the mean loan rates for fixedrate auto loans is at least 1% greater than the mean loan rates for the variable rate auto loans.
f. Calculate a 95 percent confidence interval for the difference between the mean rates for fixedrate and variablerate 48month auto loans.
_____ ≤ μFμFμVμV ≤ _____ (4 decimals).
In: Statistics and Probability
In the book Essentials of Marketing Research, William R. Dillon, Thomas J. Madden, and Neil H. Firtle discuss a research proposal in which a telephone company wants to determine whether the appeal of a new security system varies between homeowners and renters. Independent samples of 140 homeowners and 60 renters are randomly selected. Each respondent views a TV pilot in which a test ad for the new security system is embedded twice. Afterward, each respondent is interviewed to find out whether he or she would purchase the security system.
Results show that 25 out of the 140 homeowners definitely would buy the security system, while 9 out of the 60 renters definitely would buy the system.
a. Letting p_{1} be the population proportion of homeowners who would buy the security system, and letting p_{2} be the population proportion of renters who would buy the security system, set up the null and alternative hypotheses needed to determine whether the proportion of homeowners who would buy the security system differs from the proportion of renters who would buy the security system.
H0: p1−p2p1−p2(Click to select)><=≠≤≥ 0
Ha: p1−p2p1−p2(Click to select)=≠≤<>≥ 0
b. Find the test statistic z and the pvalue for testing the hypotheses of part a. (α=0.05)
z= , pvalue=
c. Determine the rejection rule:
Critical Value Rule:
Reject H_{0} if (Click to select)t> t alpha/2 or t < t alpha/2t > t alphat < t alpha/2z> z alpha/2 or z < z alpha/2z > z alphaz < z alpha
d. What is the meaning of pvalue for the hypothesis test in part a if pˆ1−pˆ2p^1−p^2 = 0.17860.15= 0.0286? (Hint: pvalue is the probability that we will get the sample values (or more extreme) from a population where the null hypothesis holds. THIS IS A TWOSIDED TEST.)
(Click to select)The probability that the difference in sample proportions is greater than 0.0286.The probability that the difference in sample proportions is less than 0.0286The probability that the difference in sample proportions is more extreme than 0.0286 if the difference in population proportions is equal to 0.
e. We have (Click to select)someextremely strongvery strongnostrong evidence that the proportions of homeowners and renters differ.
f. Calculate a 90 percent confidence interval for the difference between the proportions of homeowners and renters who would buy the security system.
≤ p1−p2p1−p2 ≤
g. Can we conclude at the 90% confidence that the difference between the proportions of homeowners and renters who would buy the security system is greater than 0?
(Click to select)Yes, because the whole interval is above 0. No, because 0 is within the confidence interval. Yes, because the whole interval is below 0.
h. Can we conclude at the 90% confidence that the difference between the proportions of homeowners and renters who would buy the security system is less than 0.1?
(Click to select)Yes, because the whole interval is above 0.1. Yes, because the whole interval is below 0.1.No, because 0.1 is within the confidence interval.
In: Statistics and Probability
1. From a box containing 10 red, 30 white, 20 blue and 15 orange
balls, 5 are drawn at random. Find the probability that:
a) All are white  0.008256723
b) Be red, white or blue  0.009169617
c) They are neither red nor blue  0.070788
2. A company will launch three new shampoos. It is believed that
the probability that the first one is successful is 0.45, that the
second one has it is 0.55 and that the third one has it is 0.75.
What is the probability that
a) The three succeed?  0.185625
b) At least two succeed? 
c) None succeed?
3. You have three boxes. In the first there are 6 rabbits and 2
pigeons; in the second, 8 rabbits and 5 pigeons, and in the third 4
rabbits and 6 pigeons. What is the probability of
a) take out a rabbit?
b) that the rabbit comes from the third box?
4. An exam has 10 multiplechoice questions. There are four
possible answers for each question. Luis has not studied for the
exam and has decided to do it at random. Assuming that you need 70%
of the correct questions to pass, calculate the probability that
Luis will pass the exam.
5. On average, four imperfections are observed in each 50m
stretch of network cable. Calculate the probability that, in a 25 m
section of this type of network cable:
a) More than three imperfections are observed b) At least one
imperfection
6. According to one study, 30% of adults suffer from insomnia.
If you find a group of randomly selected adults, what is the
probability that:
a) the sixth revised is the first to suffer insomnia?
b) the fifth review is the third to suffer insomnia?
7. The weight of a newborn baby in a certain country is a random
variable that follows a normal distribution with an average of 3.2
kg. And standard deviation of 0.4 kg.
a) Determine the percentage of newborn babies weighing 3.5 kg or
more  0.2266
b) Calculate the conditional probability that a newborn baby weighs
more than 3.5 kg, if it is known to weigh at least 3 kg 
0.3277
c) From what weight is 10% of babies born weighing more?  3.7126
Kg
8. In a hospital, 22% of transplants are cornea. Use the
approximation to the binomial distribution by normal to calculate
the probability that, in the following 120 transplants:
a) 30 are cornea  0.0641
b) at least 30 are from the cornea  0.1831
9. In a company of 5000 workers, it is desirable to know if the positive assessment of management management has varied greatly, which last year was conclusively concluded that it was 80% of the workers. For this, a sample of size 200 is carried out, resulting in the positive assessment being considered by 55% of the workers surveyed. Can we affirm that the valuation has varied with the probability of being 1% wrong?  Yes it has varied
10. A company producing pasteurized milk has as a rule not to
accept raw milk with a fat content exceeding 34 g / 100g. A sample
of 36 liters of milk obtained from as many cows belonging to the
same farm gave an average value of fat content in milk of 35.2 g /
100g with a deviation of 4.1 g / 100g. Can milk be accepted by the
pasteurizer? The company admits an error level of 1%.  Yes milk is
accepted.
11. Calculate Zα / 2 in the following sections
a) With a confidence level of 96%  2.05
b) With a confidence level of 99.5% and 92%  2.81 and 1.75
c) with a level of significance of 2% and 7%  2.32 and 1.81
d) With α = 0.03 and α = 0.11  2.17 and 1.6
12. A factory produces steel cables, whose resilience follows a normal distribution of unknown mean and standard deviation σ = 10 KJ / m3. A sample of 100 pieces was taken and through a statistical study a confidence interval (898.04  901.96) was obtained for the average resilience of the steel cables produced in the factory.
a) Calculate the value of the average resilience of the 100
pieces of the sample.  900
b) Calculate the level of confidence with which this interval has
been obtained.  95% confidence
c) If you would like to have an error of 3 KJ / m3 in the
confidence interval, what size should the sample be? A sample
of
13. It is known that the average electric power consumption in a certain province is 721 Kwh.
A technology company in the region believes that its employees consume more than the provincial average. Collect information on the consumption of 15 randomly chosen employees, and obtain the following data:
710 774 814 768 823
732 675 755 770 660
654 757 736 677 797
If the distribution of monthly electricity consumption is normal:
a) Is there evidence to state that the average household
electric power consumption of the company's employees is higher
than the average consumption at the provincial level? Use a
significance level of 10%.  Yes there is evidence.
b) What is the pvalue of the decision?  0.0878
14. An electric company manufactures cell phone batteries that have a duration that is distributed approximately normally with an average of 800 hours and a standard deviation of 40 hours. A random sample of 30 batteries has an average duration of 785 hours.
a) Do the data show sufficient evidence to say that the average
duration is less than 800? Use a significance level of 5%.  Yes
there is evidence to say that it is minor.
b) What is the probability of deciding that the average is 800
hours when in reality it is 780 hours?  0.1357 (they don't come
like this on the exam, it's difficult and they have to deduce
several things)
15. A cake factory manufactures, in its usual production, 3% of
defective cakes. A customer receives an order of 500 cakes from the
factory. Calculate the probability that ...
a) Find more than 5% of defective cakes.  0.004375
b) Find between 1% and 3% of defective cakes.  0.4956
c) Calculate a 95% confidence interval for the percentage of
defective cakes. (0.0150.4495)
16. It is assumed that the distribution of the temperature of
the human body in the population has an average of 37ºC and a
standard deviation of 0.85ºC. A sample of 105 people is chosen,
calculate the following probabilities:
a) That the average is less than or equal to 36.9 ºC  0.114
b) That the average is greater than 38.5 ºC  0
c) Find from what temperature 10% of the hottest bodies are found.
 38.09
d) Find from what temperature 5% of the coldest bodies are found. 
35.6
In: Statistics and Probability
Consider the following hypothesis tests. (Give your answer bounds exactly.)
(a) Calculate the pvalue for
H_{a}: σ^{2} ≠ 22, n =
16, χ^{2} = 28.2.
_______< p <_______
(b) Calculate the pvalue for
H_{a}: σ^{2} > 28, n
= 26, χ^{2} = 32.6.
_______< p <________
(c) Calculate the pvalue for
H_{a}: σ^{2} ≠ 44, df = 30,
χ^{2} = 39.
_______< p < _______
(d) Calculate the pvalue for
H_{a}: σ^{2} < 13, df = 40,
χ^{2} = 26.5.
_______< p < ________
In: Statistics and Probability
A headline read, “More than half of Americans Say Federal Taxes Too High.” The headline was based on a random sample of 1026 adult Americans in which 534 stated the amount of federal tax they have to pay is too high.
a. State the null and alternative hypotheses.
b. Check whether np0(1p0) is greater or equal to 10.
c. Manually calculate the test statistic.
d. Find pvalue.
In: Statistics and Probability
(Question: Is the combined scores data approximately normal? Yes or no?)
Data:
Race  Position  Oral exam results  Written exam results  Combined results 
B  Lieutenant  45.83  46  45.932 
B  Lieutenant  52.92  49  50.568 
B  Captain  54.76  49  51.304 
H  Lieutenant  48.33  58  54.132 
B  Lieutenant  52.08  56  54.432 
H  Lieutenant  40.83  64  54.732 
B  Captain  60  53  55.8 
W  Captain  53.81  58  56.324 
B  Lieutenant  58.75  55  56.5 
W  Lieutenant  54.58  58  56.632 
B  Lieutenant  55.83  58  57.132 
W  Lieutenant  45.42  65  57.168 
H  Lieutenant  44.17  66  57.268 
H  Captain  42.86  67  57.344 
W  Lieutenant  44.58  66  57.432 
W  Lieutenant  51.25  62  57.7 
W  Lieutenant  57.92  58  57.968 
B  Captain  70.48  50  58.192 
B  Lieutenant  60.83  58  59.132 
H  Lieutenant  46.25  68  59.3 
H  Captain  57.14  61  59.456 
W  Lieutenant  60  60  60 
W  Lieutenant  49.58  67  60.032 
B  Lieutenant  51.25  66  60.1 
B  Lieutenant  55  64  60.4 
B  Captain  67.62  56  60.648 
H  Lieutenant  51.25  67  60.7 
H  Lieutenant  42.5  73  60.8 
W  Captain  48.57  69  60.828 
B  Lieutenant  56.25  64  60.9 
B  Lieutenant  56.67  64  61.068 
W  Lieutenant  56.25  66  62.1 
H  Captain  58.57  65  62.428 
H  Lieutenant  50.42  71  62.768 
W  Lieutenant  71.67  57  62.868 
W  Captain  55.24  68  62.896 
H  Lieutenant  51.67  71  63.268 
B  Lieutenant  69.17  60  63.668 
H  Lieutenant  57.5  70  65 
W  Lieutenant  50.42  75  65.168 
B  Lieutenant  66.25  65  65.5 
W  Lieutenant  55  73  65.8 
H  Captain  67.14  65  65.856 
H  Lieutenant  56.25  73  66.3 
W  Lieutenant  79.17  59  67.068 
B  Captain  52.38  77  67.152 
W  Lieutenant  64.58  69  67.232 
B  Lieutenant  70.83  65  67.332 
W  Captain  57.14  75  67.856 
W  Lieutenant  51.67  79  68.068 
H  Lieutenant  62.5  72  68.2 
W  Lieutenant  51.25  80  68.5 
W  Lieutenant  73.75  66  69.1 
W  Lieutenant  58.75  76  69.1 
H  Lieutenant  70.83  68  69.132 
H  Captain  60.48  75  69.192 
W  Captain  59.05  76  69.22 
W  Captain  71.43  68  69.372 
W  Captain  71.43  68  69.372 
W  Lieutenant  64.58  73  69.632 
W  Captain  78.57  64  69.828 
W  Captain  62.38  75  69.952 
W  Lieutenant  71.67  69  70.068 
W  Lieutenant  73.75  68  70.3 
B  Captain  70.95  70  70.38 
W  Lieutenant  77.5  66  70.6 
H  Lieutenant  53.75  82  70.7 
W  Lieutenant  65.83  74  70.732 
W  Lieutenant  58.33  79  70.732 
H  Lieutenant  69.17  72  70.868 
H  Lieutenant  55  82  71.2 
W  Captain  56.67  81  71.268 
W  Captain  82.38  64  71.352 
B  Captain  68.57  74  71.828 
W  Lieutenant  73.33  71  71.932 
W  Lieutenant  72.5  72  72.2 
B  Lieutenant  92.08  59  72.232 
W  Lieutenant  66.67  76  72.268 
B  Lieutenant  70.83  74  72.732 
W  Lieutenant  78.33  70  73.332 
W  Captain  70  76  73.6 
W  Captain  73.33  74  73.732 
B  Lieutenant  65.83  80  74.332 
W  Lieutenant  87.5  66  74.6 
B  Captain  82.38  70  74.952 
W  Captain  76.67  74  75.068 
W  Lieutenant  63.33  83  75.132 
W  Captain  73.81  77  75.724 
W  Lieutenant  74.17  77  75.868 
B  Lieutenant  80.42  73  75.968 
H  Captain  79.05  74  76.02 
B  Lieutenant  61.25  86  76.1 
W  Captain  80  74  76.4 
W  Captain  87.62  69  76.448 
B  Lieutenant  77.5  76  76.6 
W  Lieutenant  58.75  89  76.9 
W  Captain  84.29  72  76.916 
W  Lieutenant  73.75  81  78.1 
W  Captain  73.81  81  78.124 
H  Captain  70  84  78.4 
W  Lieutenant  69.58  86  79.432 
W  Captain  76.19  82  79.676 
H  Captain  76.19  82  79.676 
W  Captain  76.19  84  80.876 
W  Captain  88.57  76  81.028 
W  Lieutenant  68.33  91  81.932 
W  Lieutenant  63.75  95  82.5 
W  Lieutenant  80.83  84  82.732 
W  Lieutenant  73.33  89  82.732 
W  Lieutenant  73.75  91  84.1 
W  Lieutenant  80  87  84.2 
W  Lieutenant  85  84  84.4 
W  Captain  82.38  87  85.152 
W  Lieutenant  77.5  91  85.6 
W  Lieutenant  87.5  87  87.2 
W  Captain  80  95  89 
W  Lieutenant  88.75  91  90.1 
W  Captain  89.52  95  92.808 
In: Statistics and Probability
A statistician would like to construct a hypothesis test of the mean using the Pvalue approach. Rank the steps that the statistician can follow to carry out this hypothesis test at a level of significance of α. Note that there may be more than one correct answer. Step Rank Collect sample data Define the null and alternative hypotheses Draw a conclusion Calculate the Pvalue Define the distribution of the test statistic Calculate the test statistic
In: Statistics and Probability