Description
Mathematics consists of a lot of concepts expressed in terms of symbols, formulas and other mathematical notation. For example, the exponent rule xmxn = xm+n. But what is this really saying?When multiplying the same base you add the exponents. The point is you should try to verbalize the meaning.
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HiPFA for the solution.
Product Rule of Exponents
The rule of exponent, 𝑥 𝑚 . 𝑥 𝑛 = 𝑥 𝑚+𝑛 is known as the product rule. When the two exponents of
the same base are multiplied together then the base remains the same and the power is summed
up. This is a shortha...
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MCAD Hypothesis Test for a Difference in Two Population Means Worksheet
Learn by DoingIn this activity you will learn to use StatCrunch to perform a two-sample t-test.Some features of this activ ...
MCAD Hypothesis Test for a Difference in Two Population Means Worksheet
Learn by DoingIn this activity you will learn to use StatCrunch to perform a two-sample t-test.Some features of this activity may not work well on a cell phone or
tablet. We highly recommend that you complete this activity on a
computer.Here are the directions and grading rubric for the discussion board exercises. A list of StatCrunch directions is provided at the bottom of this page.ContextDo undergraduates sleep less than graduate students?A student conducted a study of sleep habits at a large state
university. His hypothesis is that undergraduates will party more and
sleep less than graduate students. He surveyed random samples of 75
undergraduate students and 50 graduate students. Subjects reported the
hours they sleep in a typical night.For this hypothesis test, he defined the population means as follows:
μ
1
is the mean number of hours undergraduate students sleep in a typical night.
μ
2
is the mean number of hours graduate students sleep in a typical night.VariablesHours: typical number of hours a student sleeps each night Program: undergraduate or graduate Program is the explanatory variable, and the data is categorical. Hours is the response variable, and the data is quantitative.DataTwo sample T hypothesis test:μ1 : Mean of undergraduateμ2 : Mean of graduateμ1 - μ2 : Difference between two meansH0 : μ1 - μ2 = 0HA : μ1 - μ2 < 0(without pooled variances)Hypothesis test results:
DifferenceSample Diff.Std. Err.DFT-StatP-value
μ1 - μ2-0.233333330.18963708106.32776-1.23042040.1106
PromptState the null and alternative hypotheses. Include a clear description of the populations and the variable.Explain why we can safely use the two-sample T-test in this case.Use StatCrunch to carry out the test. Copy and paste the content of in the StatCrunch output window (text and the table) in your initial post. State a conclusion in the context of this problem.ANSWER(S): (hint)Since we want to check whether the data supports the claim that
undergraduate students sleep less, on average, than graduate students,
we are testing:
H
0
:
μ
1
−
μ
2
=
0
H
a
:
μ
1
−
μ
2
<
0
We can safely use the two-sample T-test in this case since:
Both samples are random, and therefore independent.The sample sizes (75 and 50) are quite large, and therefore we can
proceed regardless of whether the populations are normal or not.
T = -1.23; P-value = 0.111Here is the StatCrunch output depicting these values.Two sample T hypothesis test:
μ
1
: Mean of undergraduate
μ
2
: Mean of graduate
H
0
:
μ
1
−
μ
2
=
0
H
a
:
μ
1
−
μ
2
<
0
(without pooled variances)
Hypothesis test results:
Difference
Sample Diff.
Sd. Err.
DF
T-Stat
P-Value
μ1 - μ2
-0.23333333
0.18963708
106.32776
-1.2304204
0.1106
The P-value (0.111) is greater than 0.05. This indicates that
the observed data is not unusual if undergraduate and graduate students,
on average, have the same mean for sleep hours. Therefore, the data do
not provide evidence to reject
H
0
. So we cannot conclude that undergraduate students sleep less, on average, than graduate students.
9 pages
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Northern Star Online Statistics and Trigonometry & Circular Functions Exercises
FST Chapter 4
The questions are from the Chapter Review on pages 303-307 of our textbook, which have been scanned and can be found in the attached Word.doc. **Helpful tip: There are answers to the odd numbered questions in the back of the textbook, which have also been scanned and included in the attached Word.doc. Use these to help you make sure you are on the right track for the questions on the assignment.
Print these pages out, show your work and circle your answers for each question below. You must show your work to earn full credit on each answer. If your answer is not correct I will look at your work to see if I can award partial credit. You may attach your work to this as long as you clearly mark which problem is being worked. If you type anything in, please use a dark color that is easy to distinguish from the black font of the question.
When you are finished you should scan or take photos of the pages and send back to me. Please take any photos of the assignment in bright light so that your answers and work show up clearly.
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MCAD Hypothesis Test for a Difference in Two Population Means Worksheet
Learn by DoingIn this activity you will learn to use StatCrunch to perform a two-sample t-test.Some features of this activ ...
MCAD Hypothesis Test for a Difference in Two Population Means Worksheet
Learn by DoingIn this activity you will learn to use StatCrunch to perform a two-sample t-test.Some features of this activity may not work well on a cell phone or
tablet. We highly recommend that you complete this activity on a
computer.Here are the directions and grading rubric for the discussion board exercises. A list of StatCrunch directions is provided at the bottom of this page.ContextDo undergraduates sleep less than graduate students?A student conducted a study of sleep habits at a large state
university. His hypothesis is that undergraduates will party more and
sleep less than graduate students. He surveyed random samples of 75
undergraduate students and 50 graduate students. Subjects reported the
hours they sleep in a typical night.For this hypothesis test, he defined the population means as follows:
μ
1
is the mean number of hours undergraduate students sleep in a typical night.
μ
2
is the mean number of hours graduate students sleep in a typical night.VariablesHours: typical number of hours a student sleeps each night Program: undergraduate or graduate Program is the explanatory variable, and the data is categorical. Hours is the response variable, and the data is quantitative.DataTwo sample T hypothesis test:μ1 : Mean of undergraduateμ2 : Mean of graduateμ1 - μ2 : Difference between two meansH0 : μ1 - μ2 = 0HA : μ1 - μ2 < 0(without pooled variances)Hypothesis test results:
DifferenceSample Diff.Std. Err.DFT-StatP-value
μ1 - μ2-0.233333330.18963708106.32776-1.23042040.1106
PromptState the null and alternative hypotheses. Include a clear description of the populations and the variable.Explain why we can safely use the two-sample T-test in this case.Use StatCrunch to carry out the test. Copy and paste the content of in the StatCrunch output window (text and the table) in your initial post. State a conclusion in the context of this problem.ANSWER(S): (hint)Since we want to check whether the data supports the claim that
undergraduate students sleep less, on average, than graduate students,
we are testing:
H
0
:
μ
1
−
μ
2
=
0
H
a
:
μ
1
−
μ
2
<
0
We can safely use the two-sample T-test in this case since:
Both samples are random, and therefore independent.The sample sizes (75 and 50) are quite large, and therefore we can
proceed regardless of whether the populations are normal or not.
T = -1.23; P-value = 0.111Here is the StatCrunch output depicting these values.Two sample T hypothesis test:
μ
1
: Mean of undergraduate
μ
2
: Mean of graduate
H
0
:
μ
1
−
μ
2
=
0
H
a
:
μ
1
−
μ
2
<
0
(without pooled variances)
Hypothesis test results:
Difference
Sample Diff.
Sd. Err.
DF
T-Stat
P-Value
μ1 - μ2
-0.23333333
0.18963708
106.32776
-1.2304204
0.1106
The P-value (0.111) is greater than 0.05. This indicates that
the observed data is not unusual if undergraduate and graduate students,
on average, have the same mean for sleep hours. Therefore, the data do
not provide evidence to reject
H
0
. So we cannot conclude that undergraduate students sleep less, on average, than graduate students.
9 pages
Mathematics 37 Lab 6
• Find the mean and standard deviation of a discrete random variable. • Mean and standard deviation of a discrete rand ...
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MAT 351 Dynamics of Public Opinion About Political Ideologies Project
Hi,I need detailed solutions for both parts of the final project.**The final project, a guideline for how to solve the pro ...
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Hi,I need detailed solutions for both parts of the final project.**The final project, a guideline for how to solve the project, as well as the book for the course have been attached**Thanks :)
yearly gross and net income, Math Project Help
Assignment Directions: a. Develop a budget for the fictitious Brown family. b. Create a chart of the famil ...
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Assignment Directions: a. Develop a budget for the fictitious Brown family. b. Create a chart of the family budget. Include the following: yearly gross and net incomebanking, housing, transportation, savings, insurance, transportation, and leisure activitiesadditional expenses you identify as ordinary and necessary that are not listed in the narrativeidentify fixed and variable expensescited resources to just additional ordinary and necessary expenses you identifiedYou have the following information:Mr. Brown is a city worker earning $16.54 per hour for a 40 hour week, 52 weeks per year. He also earns overtime at the standard overtime rate. This year he worked 500 hours overtime. He also earns a yearly bonus of $2000 for his satisfactory performance evaluation. What as his total combined income?Mrs. Brown is a social worker with a salary of $26000 per year. She also works 10 hours per week part-time on weekends at a retail store in the mall an hourly rate of $7.50 and a commission of 10% of sales. Her yearly sales were $25,000. What is her total combined income?Joe, their teenage son, works 20 hours per week part-time earning $6.50 per hour. Joe has a responsibility to pay for his own student class dues of $10 per semester, his own entertainment, and his own clothes and personal items. Create a projected budget for Joe that includes a detailed list of possible expenditures.Sandy, their pre-teen daughter, is too young to work, but receives and allowance of $10 per week for completing her chores at home. Create a typical budget for a pre-teen using her allowance as income.Their house mortgage payment is $992 monthly. Maintenance for the home averages $200 monthly.The family lives in an area with mass transportation available.Family medical insurance is available through Mr. Brown's employer for $150 per month. There are routine co-payments for each visit to the doctor. The Brown family was fortunate that no family member was ill, but each member of the family had a health check-up with a co-pay of $35.00 for each visit. Mr. Brown has a monthly prescription with a co-pay of $15.00.The family's income tax rate is 25%.Mrs. Brown's hourly rate (her part-time work) is put into savings, which earns 10 % interest compounded annually. How much will be in the account at the end of one year?The family owes $5000 on credit card accounts with an annual interest rate of 12%, which is 1% monthly. The required minimum monthly payment is $75.00. How long will it take to repay the balance if the minimum amount is paid? How much must they pay each month to pay off the balance in 5 years? ***Hint: Locate a credit card calculator online to configure this amount. Provide the link to the calculator that you used.Mr. and Mrs. Brown need to save 5% of their net income for retirement. Include this in your chart.Identify fixed and variable expenses for the Brown family. *Remember, after you calculate expenses from the information provided and include additional expenses you identify as ordinary and necessary, you must create a chart of the family budget.You may create your project in a word document, a chart, a brochure, or a PowerPoint. For other expenses that you identify as necessary, use local research information (e.g., local sale advertisemens or flyers, etc.) to determine the expenses. Explain and/or cite the sources you used to calculate the additional expenses you identify as ordinary and necessary. Be specific in your explanations and citations. *The grades for Senior Capstone Math and Senior Capstone Science will be averaged for a final grade.
Northern Star Online Statistics and Trigonometry & Circular Functions Exercises
FST Chapter 4
The questions are from the Chapter Review on pages 303-307 of our textbook, which have been scanned an ...
Northern Star Online Statistics and Trigonometry & Circular Functions Exercises
FST Chapter 4
The questions are from the Chapter Review on pages 303-307 of our textbook, which have been scanned and can be found in the attached Word.doc. **Helpful tip: There are answers to the odd numbered questions in the back of the textbook, which have also been scanned and included in the attached Word.doc. Use these to help you make sure you are on the right track for the questions on the assignment.
Print these pages out, show your work and circle your answers for each question below. You must show your work to earn full credit on each answer. If your answer is not correct I will look at your work to see if I can award partial credit. You may attach your work to this as long as you clearly mark which problem is being worked. If you type anything in, please use a dark color that is easy to distinguish from the black font of the question.
When you are finished you should scan or take photos of the pages and send back to me. Please take any photos of the assignment in bright light so that your answers and work show up clearly.
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