ECO220Y1 Lecture Notes - Lecture 4: Null Hypothesis

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There are two ways to make a mistake. The null hypothesis is true, but we mistakenly reject it. The null hypothesis is false, but we fail to reject it. These are known as a type i error and type ii error , respectively. One way to keep the names straight is to remember that we start by assuming the null hypothesis is true, so a type i error is the first kind of error we could make. Normally we are going to reject the null, so in favour of type i error. Depends on the context of the research/investigation. The level that you choose is the maximum probability of a type i error that you are prepared to tolerate. Then we can"t possibly make a type i error. You can"t get a false positive from a sick person. A type i error can happen only when. H 0 is true. the letter to the probability of this mistake.

Related Questions

1	Which of the following statements about Type I and Type II errors is correct
a	Type I: Reject a true alternative hypothesis. Type II: Do not reject a false alternative.
b	Type I: Reject a true null hypothesis. Type II: Do not reject a false null hypothesis.
c	Type I: Reject a false null hypothesis. Type II: Reject a true null hypothesis.
d	Type I: Do not reject a false null hypothesis. Type II: Reject a true null hypothesis.

2	You are reading a report that contains a hypothesis test you are interested in. The writer of the report writes that the p-value for the test you are interested in is 0.0749, but does not tell you the value of the test statistic. From this information you can:


a	Not reject the hypothesis at a Probability of Type I error = .05, but reject the hypothesis at a Probability of Type I error = 0.10

b	Reject the hypothesis at a Probability of Type I error = .05, and reject at a Probability of Type I error = 0.10

c	Not reject the hypothesis at a Probability of Type I error = 0.05, and not reject at a Probability of Type I error = 0.10

d	Reject the hypothesis at a Probability of Type I error = .05, but not reject at a Probability of Type I error = 0.10


3	The random sample below is obtained to test the following hypothesis about the population mean.
	H?: ? ?	1500
	H?: ? >	1500
	620	1711	366	2528	2678	1661	442	725	1938
	409	330	2480	542	369	2124	549	2074	1665
	1873	873	2143	2061	1177	2509	1264	2397	1523
	1837	1958	1041	1639	2199	2232	387	2270	2136
	1111	1883	2612	2230	1597	1726	694	1990	1354
	2090	909	2128	1608	747	1121	2220	2390	2347
	1041	316	655	632	2064	1901	532	552	846
	2704	1410	2165	1065	937	1452	2539	410	656
	1169	527	809	2364	2350	2210	1459	2391	856
	2711	1985	2382	2289	1927	518	2177	437	1151
	2018	1580	607	2715	2188	1691	1394	2610	1186
	695	2428	2246	858	2036	1681	2449	1578	1971
	1846	1729	2389	1737	1913	1863	2072	2593	2287
	2220	2230	551	458	2626	2731	488	2551	1736
	1373	307	1803	2647	2679	1508	1468	1443	516
	1002	2116	2616	817	2522	460	1879	1999	1837

	The level of significance of the test is ? = 0.05. Compute the relevant test statistic.
	This is a(n) _______ (two-tail, upper-tail, lower-tail) test. The test statistic is TS = _______.
a	Two-tail test		TS =	1.81
	Do not reject H?: ? ? 1500. Conclude that the population mean is not greater than 1500.
b	Upper tail test.		TS =	1.52
	Do not reject H?: ? ? 1500. Conclude that the population mean is not greater than 1500.
c	Upper tail test.		TS =	1.81
	Reject H?: ? ? 1500. Conclude that the population mean is greater than 1500.
d	Lower tail test.		TS =	1.98
	Do not reject H?: ? ? 1500. Conclude that the population mean is no greater than 1500.

4	Consider the following hypothesis test.
	H?: ? ?	30
	H?: ? >	30
	A random sample of n = 15 yielded the following observations
	51	38	26	16	28
	57	20	33	35	23
	21	47	56	54	36
	Use ? =	0.05
	TS = ______	CV = ______	State the decision rule.
a	1.68	1.761	Do not reject H?. Conclude the mean is not greater than 30.
b	1.68	1.64	Reject H?. Conclude the mean is greater than 30.
c	1.847	2.145	Do not reject H?. Conclude the mean is not less than 30.
d	1.847	1.761	Reject H?. Conclude the mean is less than 30.

5	In a recent study, a major fast food restaurant had a mean service time of 165 seconds. The company embarks on a quality improvement effort to reduce the service time and has developed improvements to the service process. The new process will be tested in a sample of stores. The new process will be adopted in all of its stores, if it reduced mean service time by more than 45 seconds compared to the current mean service time. To perform the hypothesis test, the sample of 48 stores yields the following data (seconds).





	90	96	133	108	136	110	119	138
	129	98	101	92	135	124	115	90
	132	125	110	124	126	138	94	130
	108	96	140	135	102	114	109	137
	138	104	108	134	92	107	96	119
	105	111	96	136	126	116	98	131

	Use ? =	0.05
	\|TS\| = ______	\|CV\| = ______
a	1.548	1.678	Do not reject H?. The mean service time is not reduced by more than 45 seconds. Do not adopt the new process.

b	1.871	1.678	Reject H?. The mean service time is reduced by more than 45 seconds. Adopt the new process.

c	1.871	1.640	Do not reject H?. The mean service time is not reduced by more than 45 seconds. Do not adopt the new process.

d	1.548	1.640	Reject H?. The mean service time is reduced by more than 45 seconds. Adopt the new process.

Suppose that, instead of taking this test, you could either have worked and earned income or partied and had a pleasurable time. Your opportunity cost of taking the test is the

	a.	forgone working or partying, depending on which was your next best choice.
	b.	forgone work.
	c.	forgone working and partying.
	d.	test because you are taking it.

1 points

QUESTION 2

A trend is

	a.	a measure of closeness on a scatter diagram.
	b.	a general tendency for a variable to rise or fall.
	c.	the maximum value of a variable.
	d.	the difference between the maximum value of a variable and the minimum value of the variable.

1 points

QUESTION 3

A time-series graph measures

	a.	time on the y-axis and the variable or variables in which we are interested on the x-axis.
	b.	time on the x-axis and the variable or variables in which we are interested on the y-axis.
	c.	the value of one variable against the value of another variable.
	d.	the value of an economic variable for different groups in a population at a point in time.

1 points

QUESTION 4

Canada has nationalized health care, so that everyone, regardless of their ability to pay, has some access to health care. Based on this observation, Canada has decided that "everyone, regardless of their ability to pay" is the answer to what microeconomic question?

	a.	Why will we offer health care?
	b.	How will health care be produced?
	c.	For whom will health care be produced?
	d.	What type of health care will be produced and in what quantity?

1 points

QUESTION 5

As a shoe factory adds more workers, shoe production grows, reaches a maximum, and then shrinks. In a diagram that has the number of workers on the horizontal axis and the number of shoes on the vertical axis, the relationship between the number of workers and the number of shoes starts as ________ and then, after the maximum point, is ________.

	a.	positive; negative
	b.	negative; positive
	c.	linear; negative
	d.	positive; linear

1 points

QUESTION 6

Microeconomics includes the study of the

	a.	choices made by individuals and businesses.
	b.	recessions and inflation in the global economy.
	c.	aggregate effects on the national economy.
	d.	reasons why the government changes interest rates.

1 points

QUESTION 7

When Fresh Express Salads decides to mechanically pick all of its lettuce, it directly answers the ________ question.

	a.	when
	b.	for whom
	c.	how
	d.	what

1 points

QUESTION 8

Proponents of cuts in income tax rates argue that when income tax rates are cut, workers have an incentive to increase their work hours. This argument is based on the assumption that

	a.	the opportunity cost of working is negative.
	b.	the marginal cost of each additional work hour is not important to most workers.
	c.	workers are irrational.
	d.	workers make decisions based on the marginal benefit of each hour worked compared to the marginal cost of work.

1 points

QUESTION 9

A choice made by comparing all relevant alternatives systematically and incrementally is

	a.	an opportunity cost.
	b.	a benefit.
	c.	a sunk cost.
	d.	a choice on the margin.

1 points

QUESTION 10

A normative statement

i. can be tested as to whether it is true or false.

ii. is considered negative.

iii. depends on a person's values.

	a.	i, ii, and iii
	b.	iii only
	c.	i and iii
	d.	ii and iii

1 points

QUESTION 11

Normative statements

i. describe how the world is.

ii. describe how the world ought to be.

iii. depend on people's values and cannot be tested.

	a.	iii only.
	b.	i only.
	c.	ii and iii.
	d.	ii only.

1 points

QUESTION 12

In order to determine whether to major in economics, a rational individual compares the ________ of the decision.

	a.	positive benefits and normative costs
	b.	normative benefits and positive costs
	c.	marginal benefit and marginal cost
	d.	opportunity cost and the sunk cost

1 points

QUESTION 13

If x increases whenever y decreases, then x and y are

	a.	positively related.
	b.	negatively related.
	c.	not related.
	d.	related but whether positively or negatively related depends on whether the x variable or the y variable is plotted on the vertical axis.

1 points

QUESTION 14

Rational choice

	a.	is what you must give up get what you want.
	b.	is made by comparing different incentives.
	c.	making the choice.
	d.	provides the answer to only the "how" question.

1 points

QUESTION 15

Scarcity results from the fact that

	a.	choices made in self-interest rare not always in the social interest.
	b.	not all goals are desirable.
	c.	people's wants exceed the resources available to satisfy them
	d.	we cannot answer the major economic questions.

1 points

QUESTION 16

When Delta decides to quit flying to Lithuania, it directly answers the ________ question.

	a.	what
	b.	why
	c.	for whom
	d.	how

1 points

QUESTION 17

A normative statement

	a.	says what is currently believed about the way the world operates.
	b.	depends on someone's values.
	c.	cannot use the word "should."
	d.	must be tested to determine if it is correct.

1 points

QUESTION 18

Which of the following statements best describes the study of economics? Economics studies how

	a.	to organize production so that scarcity does not occur.
	b.	to create incentives so that scarcity does not exist.
	c.	firms make profits.
	d.	we make choices in the face of scarcity.

1 points

QUESTION 19

Which of the following best defines economics?

	a.	Economics teaches how to limit our wants.
	b.	Economics is concerned with prices and quantities of goods and services, both at the individual level and at the industry level.
	c.	Economics helps you earn as much money as possible.
	d.	Economics studies how to choose the best alternative when coping with scarcity.

1 points

QUESTION 20

In economics, cost is ________, and benefit is ________.

	a.	the amount of money that you pay for something; the amount of money that someone else is willing to pay you
	b.	what you are willing to pay on the margin; what the government pays you when you are unemployed or retired
	c.	what you must give up to get something; what you are willing to give up to get it
	d.	the amount of money that you pay on the margin; the amount of money that you receive on the margin

1 points

QUESTION 21

If Jessie studies economics for two hours instead of going to the movies with her friends, then

	a.	the opportunity cost of studying is the missed movie.
	b.	Jessie is ignoring a sunk cost
	c.	Jessie is not responding to any incentives.
	d.	Jesse definitely is making a rational choice.

1 points

QUESTION 22

Going skiing will cost Adam $80 a day. He also loses $40 per day in wages because he has to take time off from work. Adam still decides to go skiing.

	a.	The $80 price of skiing is a sunk cost and so did not affect Adam's decision.
	b.	He loses a total of $120 per day, so his decision is irrational.
	c.	His decision is rational if Adam's marginal benefit of spending a day skiing is greater than his marginal cost.
	d.	Adam's lost $40 per day in wages is a sunk cost and so did not affect his decision.

1 points

QUESTION 23

If a curve falls and then rises, it

	a.	has a maximum.
	b.	has a linear relationship.
	c.	has a minimum.
	d.	has a constant slope relationship.

1 points

QUESTION 24

In 2003, Michael Jordan decided to retire from professional basketball. Which of the following was an opportunity cost of his decision?

	a.	the avoidance of pain and injury from playing one more year
	b.	the time he could spend with his family while retired
	c.	the lost salary from playing one more year
	d.	the value of new employment opportunities that would await him

1 points

QUESTION 25

Which of the following statements is a normative statement?

	a.	Military spending as a percent of government spending decreased by 5 percent in the 1990s.
	b.	Every American household should have health care insurance coverage.
	c.	Welfare reform has decreased the amount the government spends on welfare.
	d.	The price of computers fell last year.

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ECO220Y1 Lecture Notes - Lecture 4: Null Hypothesis

ECO220Y1 Full Course Notes

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