PR 680 Lecture Notes - Lecture 54: Null Hypothesis

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periwinklemammoth360

16 Mar 2020

School

Ball State University

Department

Public Relations

Course

PR 680

Professor

Dr. Sungwon Chung

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Document Summary

Degrees of freedom is a term most often used in statistics classes and it"s a pretty important term because it"s used in a lot different calculations. Although people might think it"s easy to calculate, it helps to understand what it"s like in case you forget the equation. The symbol used for degrees of freedom is (df), which is the only symbol really used. The best way to explain it is to use an example because the formal definition is just the amount of values within a system that are free to vary. The dictionary definition of degrees of freedom says that each of a certain number of independently variable factors affect the range of something that exists, and any of the directions that a motion can occur independently. It"s not a very clear definition so with the example, let"s say you have a distribution of a number. Three numbers of anything, let"s say 5 apples, 10 apples, and 15 apples.

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Introduction: A Chi-square test is used to compare observed data with expected data according to a hypothesis. For instance, if you were crossbreeding 2 heterozygous pea plants, you would expect to see a 3:1 phenotypic ratio in the offspring. In this case, if you were to breed 400 pea plants, you would expect to see 300 plants showing the dominant trait and 100 showing the recessive trait. But what happens if you observe only 260 plants with the dominant trait and 140 plants with the recessive trait? Does this mean something is wrong with Mendelian genetics or is this difference in expected results just due to chance (random sampling error)? These are the questions that can be answered using Chi-square statistics. The results of this statistical test is used to either reject or accept (fail to reject) the null hypothesis. The null hypothesis states there is no significant difference between the observed results and the expected results. This means that if the null hypothesis is accepted, the difference in observed and expected results was just a matter of chance and so the observed results basically "fit" with what was expected. Degrees of freedom (df) = number of independent outcomes (Y) being compared less 1 df = Y-1 At the 95% confidence interval we are 95% confident that there is a significant difference between the observed and expected results, therefore rejecting the null hypothesis. Probability Value - Is the decimal value determined from the X2 table and is the probability of accepting the null hypothesis. A 0.05 probability value equates to a 95% confidence interval.

The Chi-squared test formula is: Example: If we cross two pea plants that are heterozygous yellow pods, we would expect a 3:1 phenotypic ratio. So let's say we actually did the cross and got 280 plants with green pods and 120 plants with yellow pods. Question: Is this a 3:1 phenotypic ratio? This is the value of Chi-squared Test. We have a total of 400 plants and we expect a 300 green:100 yellow phenotypic ratio If the calculated Chi-squared value is less than the critical value listed in the Chi-squared table, then we accept the null hypothesis. This means that there is no significant difference between the observed and the expected values. Our degrees of freedom (df) = 2 outcomes - 1, or df = 1. Now we go the X2 table below and using the df = 1 and probability value of 0.05, our critical value is 3.84. Since our calculated X2 value is 5.33, and is larger than the critical value, we reject the null hypothesis and can say (at 95% confidence) that there is a significant difference between our observed and expected values.

The parent generation is yellowed podded and green podded pea plants. You cross a yellow podded pea plant with a green podded pea plant and you get 100% yellow podded plants in the F1 Generation (Phenotypic ratio 4 : 0, yellow to green). What will be the expected phenotypic ratio when you allow the F1 generation to reproduce?

Fill out the Punnett square.

If we actually did the cross and got 1150 yellow and 350 green. Would this be a consistent with what was expected?

Learning Outcomes Questions

1. Why would you run a Chi-squared test?

To determine if our data is consistent with expected results.
		a To determine if our data is consistent with expected results. b To determine if our data exactly matches the expected results.
		c To determine the expected results.
	d	To compare the phenotypic ratios to the genotypic ratios.

2. Determine the degrees of Freedom of the phenotypic ratio for this genetic cross.

a. 1

b. 2

c. 3

d. 4

e. 5

3. Using the data given, what is the result of your Chi-squared analysis? x2= ___.

	a.	2.22
	b	2.71
	c	4.36
	d	187.78
	e	448.27

4. Using the results of your Chi-squared analysis, do we fail to reject or reject the null hypothesis?

a.		Fail to reject the null
b.		Reject the null
c.		It cannot be determined from the data given

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Problem: Divisibility and Divisibility Rules There are many rules to determine if a number is divisible by other smaller numbers. In basic arithmetic courses, you learned divisibility and discussed a few common divisibility rules. Your task is to determine if the given number is divisible by 9 but is not divisible by 11 Given number: 7,176,825,942,116,027,211 Note: You want to use divisibility rules. Do not attempt to use long division and do not just use your calculator 1. Research the topic of divisibility 2. Research the divisibility rules for 9 and 11. 3. Using the divisibility rules found, determine how the given number is divisible by 9 and is not divisible by 11. "Note:I am telling you that the number IS divisible by 9 and IS NOT divisible by 11. Do not try to show the opposite of this statement. 4. Include the following information in a report, in this order: a. Explain (in a few sentences) the topic of divisibility, including any correct terms that apply b. Explain in your own words the divisibility rule of 9. C. Give an example using another number to help the explanation. d. Show how the given number is divisible by 9. Work out all your steps. e. Explain in your own words the divisibility rule of 11 f. Give an example using another number to help the explanation. g. Show how the given number is not divisible by 11. Work out all your steps. 5. You must locate a minimum of 2 sources to help you complete this project. More than two sources, though not required, can be used if it helps to give detail to the project. a. You must use at least one book or E-book (other than your textbook). Do not use the dictionary for your definition. b. You must use at least one website. Do not use Wikipedia c. Your sources should explain the topics of the problem (divisibility and divisibility rules) and have examples that help you with the problem. Your sources should be relevant to the project and not just be a math source because it has math in the context d. 6. Correctly cite, in MLA format, the sources that you located to complete the assignment. If you need help for citations in MLA format, you can try using the website EasyBih Be sure to do the entire project typed neatly 7. Papers will be compared for similarity Plagiarism is against the academic honesty policy and will receive a zera. Note: A detailed Grading Rubric is provided on Canvas and on the assignment submission link The due date for the project is listed on Canvas. The Math/Analytical Project must be submitted through Canvas. Directions for submitting can be found in the Course Syllabus and on Canvas.

Show transcribed image text Problem: Divisibility and Divisibility Rules There are many rules to determine if a number is divisible by other smaller numbers. In basic arithmetic courses, you learned divisibility and discussed a few common divisibility rules. Your task is to determine if the given number is divisible by 9 but is not divisible by 11 Given number: 7,176,825,942,116,027,211 Note: You want to use divisibility rules. Do not attempt to use long division and do not just use your calculator 1. Research the topic of divisibility 2. Research the divisibility rules for 9 and 11. 3. Using the divisibility rules found, determine how the given number is divisible by 9 and is not divisible by 11. "Note:I am telling you that the number IS divisible by 9 and IS NOT divisible by 11. Do not try to show the opposite of this statement. 4. Include the following information in a report, in this order: a. Explain (in a few sentences) the topic of divisibility, including any correct terms that apply b. Explain in your own words the divisibility rule of 9. C. Give an example using another number to help the explanation. d. Show how the given number is divisible by 9. Work out all your steps. e. Explain in your own words the divisibility rule of 11 f. Give an example using another number to help the explanation. g. Show how the given number is not divisible by 11. Work out all your steps. 5. You must locate a minimum of 2 sources to help you complete this project. More than two sources, though not required, can be used if it helps to give detail to the project. a. You must use at least one book or E-book (other than your textbook). Do not use the dictionary for your definition. b. You must use at least one website. Do not use Wikipedia c. Your sources should explain the topics of the problem (divisibility and divisibility rules) and have examples that help you with the problem. Your sources should be relevant to the project and not just be a math source because it has math in the context d. 6. Correctly cite, in MLA format, the sources that you located to complete the assignment. If you need help for citations in MLA format, you can try using the website EasyBih Be sure to do the entire project typed neatly 7. Papers will be compared for similarity Plagiarism is against the academic honesty policy and will receive a zera. Note: A detailed Grading Rubric is provided on Canvas and on the assignment submission link The due date for the project is listed on Canvas. The Math/Analytical Project must be submitted through Canvas. Directions for submitting can be found in the Course Syllabus and on Canvas.

1. The marginal product of labor is:

A. equal to the demand for labor.

B. the payment made to workers for their contribution to the output they produce.

C. the change in a firm's revenue as a result of hiring one more worker.

D. the additional output a firm produces as a result of hiring one more worker.

2. What does the phrase "internalizing an external cost" mean?

A. limiting the extent to which domestic firms can outsource production

B. prohibiting economic activities that create externalities

C. finding a way to address cross-border pollution

D. forcing producers to factor into their production costs the cost of the externalities created in the production of their output

3. The highest-valued alternative that must be given up to engage in an activity is the definition of

A. implicit cost

B. opportunity cost.

C. utility.

D. economic sacrifice.

4. What is market failure?

A. It refers to the inability of the market to allocate resources efficiently up to the point where marginal social benefit equals marginal private cost.

B. It refers to a situation where an entire sector of the economy (for example, the airline industry) collapses because of some unforeseen event.

C. It refers to a breakdown in a market economy because of widespread corruption in government.

D. It refers to the inability of the market to allocate resources efficiently up to the point where marginal social benefit equals marginal social cost.

5. Suppose a competitive firm is paying a wage of $12 an hour and sells its product at $3 per unit. Assume that labor is the only input. If the last worker hired increases output by three units per hour, then to maximize profits the firm should

A. lay off some of its workers.

B. does not change the number of workers it currently hires.

C. hire additional workers.

D. There is not enough information to answer the question.

6. When the price of summer tank tops falls and you buy more of them because they are relatively less expensive, this is called

A. the deadweight loss effect.

B. the income effect.

C. the substitution effect.

D. the elasticity effect.

7. An externality is

A. a benefit realized by the purchaser of a good or service.

B. a benefit or cost experienced by someone who is not a producer or consumer of a good or service.

C. a cost paid for by the producer of a good or service.

D. anything that is external or not relevant to the production of a good or service.

8. Firms pay famous individuals to endorse their products because

A. apparently demand is affected not just by the number of people who use a product but also by the type of person that uses the product. '

B. famous people only consume high-quality products.

C. famous people obviously know what are the best goods and services.

D. the firms are irrational and are wasting advertising expenditures.

9. If a consumer receives 20 units of utility from consuming two candy bars, and 25 units of utility from consuming three candy bars, the marginal utility of the second candy bar is

A. 25 utility units.

B. 20 utility units.

C. 5 utility units.

D. unknown as more information is needed to determine the answer.

10. When there is a negative externality, the private cost of production ________ the social cost of production.

A. is less than

B. is greater than

C. eliminates

D. is equal to

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PR 680 Lecture Notes - Lecture 54: Null Hypothesis

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