Calculus and Above

Calculus Questions? Ask a Mathematician for Answers ASAP

Connect one-on-one with {0} who will answer your question

REMEMBER, these are assessed preparatory...

REMEMBER, these are assessed preparatory problems related to the content of Unit 3. The Unit 3 Exam will consist of similar types of problems, but not exactly the same. Thus, make sure you are thinking about the concepts and procedures you studied in this unit versus simply “copying” the process of an example problem. Also, take time to examine the complete objective list in the Unit 3 Review document. All answers should be calculated, as needed, within this Excel sheet, and final concluding answers given directly below or to the right of the problem. Please make your answers are easily found--for example use a different color (not red) of font. No numerical answer resulting from a calculation will be accepted unless the process is performed in Excel and formulas/calculations used are evident when the cell is selected.

Also, note that the templates for hypothesis testing provided in the Excel Guides for this unit are also given in the next worksheet in this document--see folder tabs at the bottom of the sheet. You may use these templates by copying from the second worksheet, pasting the copy to the right of the associated problem, then changing values as needed. This set of problems is due on 11/25/14.

1. Determine the two chi-squared (χ2) critical values for the following confidence levels and sample sizes.

a. 95% and n=36

b. 99% and n=18

2. We are also interested in estimating the population standard deviation (σ) for all FHSU students' IQ score. We will assume that IQ scores are at least approximately normally distributed. Below are the IQ scores of 30 randomly chosen students from FHSU campus.

135 127 104 139 133 114 110 137 141 118

115 118 121 141 112 134 115 132 132 118

127 116 136 132 117 129 116 109 115 129

Construct a 95% confidence interval estimate of sigma (σ), the population standard deviation.

3. Assume you need to build a confidence interval for a population mean within some given situation. Naturally, you must determine whether you should use either the t-distribution or the z-distribution or possibly even neither based upon the information known/collected in the situation. Thus, based upon the information provided for each situation below, determine which (t-, z- or neither) distribution is appropriate. Then if you can use either a t- or z- distribution, give the associated critical value (critical t- or z- score) from that distribution to reach the given confidence level.

a. 95% confidence n=40 σ known population data believed to be normally distributed

Appropriate distribution:

Associated critical value:

b. 90% confidence n=31 σ unknown population data believed to be normally distributed

Appropriate distribution:

Associated critical value:

c. 99% confidence n=29 σ unknown population data believed to be skewed right

Appropriate distribution:

Associated critical value:

d. 98% confidence n=100 σ known population data believed to be very skewed

Appropriate distribution:

Associated critical value:

4. (Multiple Choice) A hypothesis test is used to test a claim. Suppose the test is left-tailed and the critical value is -2.75. If the collected sample's test statistic is -2.15, which of the following is the correct decision statement for the test?

A. Fail to reject the null hypothesis

B. Fail to reject the alternative hypothesis

C. Reject the null hypothesis

D. Reject the alternative hypothesis

5. (Multiple Choice) A hypothesis test is used to test a claim. Suppose the P value for a hypothesis test is .008, and the significance level is 0.01. Then which of the following is the correct decision statement for the test?

A. Fail to reject the null hypothesis

B. Fail to reject the alternative hypothesis

C. Reject the null hypothesis

D. Reject the alternative hypothesis

6. (Multiple Choice) Type II error is:

A. Rejecting a true null hypothesis

B. Rejecting a false null hypothesis

C. Failing to reject a false null hypothesis

D. Failing to reject a true null hypothesis

7. It is claimed that more than 75% of college students in Kansas take education loans. Last year 97 out of 120 randomly selected college students from Kansas reported that they had student loans. Conduct a hypothesis test to determine if the proportion of students who have student loan is more than 75% as claimed. Use a 10% significance level.

a. Is the above information sufficient for you to be absolutely certain that more than 75% of all students of Kansas have education loans? Why or why not?

b. In establishing a statistical hypothesis testing of this situation, give the required null and alternative hypotheses for such a test, if the claim is that more than 75% of the Kansas college students have education loans.

H0:

H1:

c. Based on your answer in part b, should you use a right-tailed, a left-tailed, or a two-tailed test? Briefly explain how one determines which of the three possibilities is to be used.

d. Describe the possible Type I error for this situation--make sure to state the error in terms of the percent of Kansas college students with education loans.

e. Describe the possible Type II error for this situation--make sure to state the error in terms of the percent of Kansas college students with education loans.

f. Determine the appropriate critical value(s) for this situation.

g. Determine/calculate the value of the sample test statistic.

h. Detemine the P-value.

i. Based upon your work above, is there statistically sufficient evidence in this sample to support that more than 75% of Kansas college students have education loans? Briefly explain your reasoning.

8. It is claimed that the national average for the price of gasoline is $3.42 per gallon. Listed below are gas prices from a sample of 32 gas stations from Kansas. At the 5% significance level, follow the steps below to conduct a hypothesis test determine if the average price of gasoline in Kansas is significantly different than the national average of $3.42.

3.15 3.27 3.14 3.38 3.49 3.12 3.22 3.31

3.58 3.76 3.26 3.59 3.73 3.12 3.62 3.52

3.08 3.28 2.98 3.33 3.48 3.18 3.28 3.28

3.48 3.46 3.48 3.11 3.48 2.88 3.23 3.48

a. Give the null and alternative hypotheses for this test in symbolic form.

H0:

H1:

b. Determine the value of the test statistic.

c. Determine the appropriate critical value(s).

d Detemine the P-value.

e. Is there sufficient evidence to support the claim that average price of gasoline in Kansas is significantly different than the national average of $3.42.

9. Captoril is a drug to lower systolic blood pressure. When seven randomly selected subjects were treated with this drug, their systolic pressure reading (in MM Hg) were measured before and after the drug was taken. Using a 1% significance level, is there sufficient evidence to support the claim that Captoril is effective in lowering the systolic blood pressure? Perform an appropriate hypothesis test showing necessary statistical evidence to support your final given conclusion.

PreTest PostTest

200 160

175 171

198 177

170 167

193 176

209 183

155 145

10. Multiple Choice:

For each of the following data sets, choose the most appropriate response from the choices below the table.

Data Set #1 Data Set #2

x y x y

7.4 23.9 -1 -4

23.9 75.1 -2 -10

16.6 55.7 2 5

21.8 68.5 3 4

7 22 -3 -19

13.5 48.3 6 -10

20.9 67.7 7 -20

9.7 30.5 -1 -4

10.4 36 0 1

A. A strong positive linear relation exists A. A strong positive linear relation exists

B. A strong negative linear relation exists B. A strong negative linear relation exists

C. A curvilinear relation exists C. A nonlinear relation exists

D. No relation exists D. No relation exists

11. Create a paired data set with five data points (i.e., five x-values and five corresponding y-values) with a strong (but not perfect) positive linear correlation. Determine the correlation coefficient value for your data.

x y

12. To answer the following, use the list below that contains information on the age of 12 female staffs in FHSU and their corresponding pulse rate.

Ages Pulse rates

42 98

34 80

49 98

27 63

42 84

18 49

41 80

21 55

21 56

19 53

19 61

30 74

a. Construct a scatterplot for this data set in the region to the right (ages as the independent variable, and pulse rate as the dependent.)

b. Based on the scatterplot, does it look like a linear regression model is appropriate for this data? Why or why not?

c. Add the line-of-best fit (trend line/linear regression line) to your scatterplot. Give the equation of the trend line below.

d. Determine the value of the correlation coefficient. Explain what the value tells you about the data pairs?

e. Does the value of the correlation coefficient tell you there is or is not statistically significant evidence that a linear correlation exists between the variables? Explain your position. (HINT: application of table A-6 is needed!)

f. What is the predicted pulse rate of a female staff who is 50 years old.

g. What is the predicted age of a female staff whose pulse rate is 64?

Also, note that the templates for hypothesis testing provided in the Excel Guides for this unit are also given in the next worksheet in this document--see folder tabs at the bottom of the sheet. You may use these templates by copying from the second worksheet, pasting the copy to the right of the associated problem, then changing values as needed. This set of problems is due on 11/25/14.

1. Determine the two chi-squared (χ2) critical values for the following confidence levels and sample sizes.

a. 95% and n=36

b. 99% and n=18

2. We are also interested in estimating the population standard deviation (σ) for all FHSU students' IQ score. We will assume that IQ scores are at least approximately normally distributed. Below are the IQ scores of 30 randomly chosen students from FHSU campus.

135 127 104 139 133 114 110 137 141 118

115 118 121 141 112 134 115 132 132 118

127 116 136 132 117 129 116 109 115 129

Construct a 95% confidence interval estimate of sigma (σ), the population standard deviation.

3. Assume you need to build a confidence interval for a population mean within some given situation. Naturally, you must determine whether you should use either the t-distribution or the z-distribution or possibly even neither based upon the information known/collected in the situation. Thus, based upon the information provided for each situation below, determine which (t-, z- or neither) distribution is appropriate. Then if you can use either a t- or z- distribution, give the associated critical value (critical t- or z- score) from that distribution to reach the given confidence level.

a. 95% confidence n=40 σ known population data believed to be normally distributed

Appropriate distribution:

Associated critical value:

b. 90% confidence n=31 σ unknown population data believed to be normally distributed

Appropriate distribution:

Associated critical value:

c. 99% confidence n=29 σ unknown population data believed to be skewed right

Appropriate distribution:

Associated critical value:

d. 98% confidence n=100 σ known population data believed to be very skewed

Appropriate distribution:

Associated critical value:

4. (Multiple Choice) A hypothesis test is used to test a claim. Suppose the test is left-tailed and the critical value is -2.75. If the collected sample's test statistic is -2.15, which of the following is the correct decision statement for the test?

A. Fail to reject the null hypothesis

B. Fail to reject the alternative hypothesis

C. Reject the null hypothesis

D. Reject the alternative hypothesis

5. (Multiple Choice) A hypothesis test is used to test a claim. Suppose the P value for a hypothesis test is .008, and the significance level is 0.01. Then which of the following is the correct decision statement for the test?

A. Fail to reject the null hypothesis

B. Fail to reject the alternative hypothesis

C. Reject the null hypothesis

D. Reject the alternative hypothesis

6. (Multiple Choice) Type II error is:

A. Rejecting a true null hypothesis

B. Rejecting a false null hypothesis

C. Failing to reject a false null hypothesis

D. Failing to reject a true null hypothesis

7. It is claimed that more than 75% of college students in Kansas take education loans. Last year 97 out of 120 randomly selected college students from Kansas reported that they had student loans. Conduct a hypothesis test to determine if the proportion of students who have student loan is more than 75% as claimed. Use a 10% significance level.

a. Is the above information sufficient for you to be absolutely certain that more than 75% of all students of Kansas have education loans? Why or why not?

b. In establishing a statistical hypothesis testing of this situation, give the required null and alternative hypotheses for such a test, if the claim is that more than 75% of the Kansas college students have education loans.

H0:

H1:

c. Based on your answer in part b, should you use a right-tailed, a left-tailed, or a two-tailed test? Briefly explain how one determines which of the three possibilities is to be used.

d. Describe the possible Type I error for this situation--make sure to state the error in terms of the percent of Kansas college students with education loans.

e. Describe the possible Type II error for this situation--make sure to state the error in terms of the percent of Kansas college students with education loans.

f. Determine the appropriate critical value(s) for this situation.

g. Determine/calculate the value of the sample test statistic.

h. Detemine the P-value.

i. Based upon your work above, is there statistically sufficient evidence in this sample to support that more than 75% of Kansas college students have education loans? Briefly explain your reasoning.

8. It is claimed that the national average for the price of gasoline is $3.42 per gallon. Listed below are gas prices from a sample of 32 gas stations from Kansas. At the 5% significance level, follow the steps below to conduct a hypothesis test determine if the average price of gasoline in Kansas is significantly different than the national average of $3.42.

3.15 3.27 3.14 3.38 3.49 3.12 3.22 3.31

3.58 3.76 3.26 3.59 3.73 3.12 3.62 3.52

3.08 3.28 2.98 3.33 3.48 3.18 3.28 3.28

3.48 3.46 3.48 3.11 3.48 2.88 3.23 3.48

a. Give the null and alternative hypotheses for this test in symbolic form.

H0:

H1:

b. Determine the value of the test statistic.

c. Determine the appropriate critical value(s).

d Detemine the P-value.

e. Is there sufficient evidence to support the claim that average price of gasoline in Kansas is significantly different than the national average of $3.42.

9. Captoril is a drug to lower systolic blood pressure. When seven randomly selected subjects were treated with this drug, their systolic pressure reading (in MM Hg) were measured before and after the drug was taken. Using a 1% significance level, is there sufficient evidence to support the claim that Captoril is effective in lowering the systolic blood pressure? Perform an appropriate hypothesis test showing necessary statistical evidence to support your final given conclusion.

PreTest PostTest

200 160

175 171

198 177

170 167

193 176

209 183

155 145

10. Multiple Choice:

For each of the following data sets, choose the most appropriate response from the choices below the table.

Data Set #1 Data Set #2

x y x y

7.4 23.9 -1 -4

23.9 75.1 -2 -10

16.6 55.7 2 5

21.8 68.5 3 4

7 22 -3 -19

13.5 48.3 6 -10

20.9 67.7 7 -20

9.7 30.5 -1 -4

10.4 36 0 1

A. A strong positive linear relation exists A. A strong positive linear relation exists

B. A strong negative linear relation exists B. A strong negative linear relation exists

C. A curvilinear relation exists C. A nonlinear relation exists

D. No relation exists D. No relation exists

11. Create a paired data set with five data points (i.e., five x-values and five corresponding y-values) with a strong (but not perfect) positive linear correlation. Determine the correlation coefficient value for your data.

x y

12. To answer the following, use the list below that contains information on the age of 12 female staffs in FHSU and their corresponding pulse rate.

Ages Pulse rates

42 98

34 80

49 98

27 63

42 84

18 49

41 80

21 55

21 56

19 53

19 61

30 74

a. Construct a scatterplot for this data set in the region to the right (ages as the independent variable, and pulse rate as the dependent.)

b. Based on the scatterplot, does it look like a linear regression model is appropriate for this data? Why or why not?

c. Add the line-of-best fit (trend line/linear regression line) to your scatterplot. Give the equation of the trend line below.

d. Determine the value of the correlation coefficient. Explain what the value tells you about the data pairs?

e. Does the value of the correlation coefficient tell you there is or is not statistically significant evidence that a linear correlation exists between the variables? Explain your position. (HINT: application of table A-6 is needed!)

f. What is the predicted pulse rate of a female staff who is 50 years old.

g. What is the predicted age of a female staff whose pulse rate is 64?

Show More

Show Less

Was this answer helpful?

Describe your issueThe assistant will guide you

Chat 1:1 with a tutorLicensed Experts are available 24/7

100% satisfaction guaranteeGet all the answers you need

Related Calculus and Above Questions

A researcher wishes to test the claim that there is a

A researcher wishes to test the claim that there is a difference in the distribution of ages of elementary school, high school, and community college teachers. Teachers are randomly selected from each… read more

Do you offer a program that can help me get through

do you offer a program that can help me get through statistics? a monthly plan I can ask questions on … read more

A simple random sample of 81 SAT scores in a certain

A simple random sample of 81 SAT scores in a certain district has a mean of 1200 and a standard deviation of 400. District officials claim that their students' scores on average are at least 1300. A g… read more

I need assistance understanding and completing this question

i need assistance understanding and completing this question Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test… read more

1. What is the appropriate critical value of the following

1. What is the appropriate critical value for each of the following confidence levels and sample sizes? (Remember that in regard to confidence level this implies two-tails) (a) Critical z-value for an… read more

1. What is the appropriate critical value of the following

1. What is the appropriate critical value for each of the following confidence levels and sample sizes? (Remember that in regard to confidence level this implies two-tails) (a) Critical z-value for an… read more

1. Determine the two chi-squared (χ2) critical values for the

1. Determine the two chi-squared (χ2) critical values for the following confidence levels and sample sizes. a. 95% and n=36 b. 99% and n=18 2. We are also interested in estimating the population stand… read more

For the problems that require a written response, please use

For the problems that require a written response, please use proper English and complete sentences. Your definitions and explanations should be explicit and meaningful from a statistical viewpoint. Wh… read more

1. Assume that the data has a normal distribution and the

1. Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis. ALPHA = 0.05 for a left-tailed test. -… read more

1. The lengths of human pregnancies are normally distributed

1. The lengths of human pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. What is the probability that a pregnancy lasts at least 300 days? (Points : 6)… read more

1. What is the appropriate critical value for each of the following

1. What is the appropriate critical value for each of the following confidence levels and sample sizes? (Remember that in regard to confidence level this implies two-tails) (a) Critical z-value for an… read more

I need help with an intro to statistics quiz. It is 20 questions

I need help with an intro to statistics quiz. It is 20 questions multiple choice. It has to be done today and I have 2 hours.… read more

A sample of 25 different payroll departments found that the

A sample of 25 different payroll departments found that the employees worked an average of 310.3 days a year with a standard deviation of 23.8 days. What is the 95% confidence interval for the average… read more

Please help me with this test! I have no idea! :( 5.The

Please help me with this test! I have no idea! :( 5.The test statistic in a two tailed test is z=-1.63. Find the P-value. 6. Assume that a hypothesis test of the given claim will be conducted. Identif… read more

1. Assume you need to build a confidence interval for a population

1. Assume you need to build a confidence interval for a population mean within some given situation. Naturally, you must determine whether you should use either the t-distribution or the z-distributio… read more

1. Find the mean for the given sample data. Unless indicated

1. Find the mean for the given sample data. Unless indicated otherwise, round your answer to one more decimal place than is present in the original data values. The students in Hugh Logan's math class… read more

2)Which of the following hypothesis tests use a z test statistic? A)

2)Which of the following hypothesis tests use a z test statistic? A) Matched Pairs B) Single Proportion C) Two Proportions D) Goodness-of-Fit E) Single Mean: σ Known F) Independence G) Two Variances H… read more

Find the mean for the given sample data. Unless indicated otherwise,

Find the mean for the given sample data. Unless indicated otherwise, round your answer to one more decimal place than is present in the original data values. The students in Hugh Logan's math class to… read more

Disclaimer: Information in questions, answers, and other posts on this site ("Posts") comes from individual users, not JustAnswer; JustAnswer is not responsible for Posts. Posts are for general information, are not intended to substitute for informed professional advice (medical, legal, veterinary, financial, etc.), or to establish a professional-client relationship. The site and services are provided "as is" with no warranty or representations by JustAnswer regarding the qualifications of Experts. To see what credentials have been verified by a third-party service, please click on the "Verified" symbol in some Experts' profiles. JustAnswer is not intended or designed for EMERGENCY questions which should be directed immediately by telephone or in-person to qualified professionals.

Ask-a-doc Web sites: If you've got a quick question, you can try to get an answer from sites that say they have various specialists on hand to give quick answers... Justanswer.com.

JustAnswer.com...has seen a spike since October in legal questions from readers about layoffs, unemployment and severance.

Web sites like justanswer.com/legal

...leave nothing to chance.

...leave nothing to chance.

Traffic on JustAnswer rose 14 percent...and had nearly 400,000 page views in 30 days...inquiries related to stress, high blood pressure, drinking and heart pain jumped 33 percent.

Tory Johnson, GMA Workplace Contributor, discusses work-from-home jobs, such as JustAnswer in which verified Experts answer people’s questions.

I will tell you that...the things you have to go through to be an Expert are quite rigorous.

Wonderful service, prompt, efficient, and accurate. Couldn't have asked for more. I cannot thank you enough for your help.

Freshfield, Liverpool, UK

This expert is wonderful. They truly know what they are talking about, and they actually care about you. They really helped put my nerves at ease. Thank you so much!!!!

Los Angeles, CA

Thank you for all your help. It is nice to know that this service is here for people like myself, who need answers fast and are not sure who to consult.

Hesperia, CA

I couldn't be more satisfied! This is the site I will always come to when I need a second opinion.

Kernersville, NC

Just let me say that this encounter has been entirely professional and most helpful. I liked that I could ask additional questions and get answered in a very short turn around.

Woodstock, NY

Thank you so much for taking your time and knowledge to support my concerns. Not only did you answer my questions, you even took it a step further with replying with more pertinent information I needed to know.

Elkton, Maryland

He answered my question promptly and gave me accurate, detailed information. If all of your experts are half as good, you have a great thing going here.

Dallas, TX

< Previous | Next >

Mr. Gregory White

Master's Degree

114 satisfied customers

M.A., M.S. Education / Educational Administration

SusanAthena

Master's Degree

102 satisfied customers

Tutor for Algebra, Geometry, Statistics. Explaining math in plain English.

Dr Arthur Rubin

Doctoral Degree

97 satisfied customers

Ph.D. in Mathematics, 1978, from the California Institute of Technology, over 20 published papers

JACUSTOMER-yrynbdjl-

Master's Degree

42 satisfied customers

I have a MS in Mathematics and I have taught Mathematics for 10 years at the college level.

Don

Master's Degree

29 satisfied customers

M.S. Astronautical Engineering. Math/Sci/Comp Tutor

Kofi

PhD in Statistics

7,345 satisfied customers

Masters in Mathematics and Statistics

Sandhya_sharma

Master's Degree

5,309 satisfied customers

I hold M.Sc and M.Phil degrees in math and have several years of teaching experience.

< Previous | Next >

Disclaimer: Information in questions, answers, and other posts on this site ("Posts") comes from individual users, not JustAnswer; JustAnswer is not responsible for Posts. Posts are for general information, are not intended to substitute for informed professional advice (medical, legal, veterinary, financial, etc.), or to establish a professional-client relationship. The site and services are provided "as is" with no warranty or representations by JustAnswer regarding the qualifications of Experts. To see what credentials have been verified by a third-party service, please click on the "Verified" symbol in some Experts' profiles. JustAnswer is not intended or designed for EMERGENCY questions which should be directed immediately by telephone or in-person to qualified professionals.