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class 2 - May 22 > chapter 9 > Flashcards

chapter 9 Flashcards

1
Q

Explain the Null Hypothesis

A

making a tentative assumption about a pop parameter

- the result that is hoped to be proven false

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2
Q

Explain the Alternative Hypothesis

A
  • opposite of what is stated in the Null hypothesis
  • the result that is hoped to be true
  • given by < > or not =
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3
Q

What is hypothesis testing

A

a method of testing whether or not a claim is valid

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4
Q

What are Two types of Claims

A
  1. Proportions - data given by percentages, %

2. Means - data given by data measurements, M

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5
Q

What does developing the Null Hypothesis involve?

A

collecting a sample and using the sample results to provide evidence for drawing a conclusion

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6
Q

What are we really doing when we are testing the hypothesis

A

Ha is often what the test is attempting to establish

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7
Q

Ex Hyp Test: WHat is the Ha and Ho

Current system ahs a M of 24 miles we are looking for this new item to be more than 24 miles

A

Ho M is < or = 24

Ha M > 24

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8
Q

Ex. Hyp test: What is the Ha and Ho

New teaching method developed is believed to be better than current one

A

Ho - new method is not better

Ha - new method is better

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9
Q

Ex Hyp test: what is the Ha and Ho

New sales force bonus plan developed to increase sales

A

Ho - new bonus plan does not increase sales

ha - new bonus plan does increase sales

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10
Q

If you disprove Ho you

A

prove Ha

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11
Q

if you fail to disprove Ho then

A

Nothing

- it is impossible to provide Ho true nor is it possible to disprove Ha

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12
Q

Ho: M>= M0
Ha: M< Mo
What type of tailed test is this

A

one tailed test

the line goes to the right of the bell curve

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13
Q

Ho: M<= Mo
Ha: M> Mo
What type of tailed test is this

A

one tailed

the line goes to the left of the bell curve

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14
Q

Ho: M = Mo
Ha: M does not = Mo
WhaT type of test is this

A

two tailed test

the lines goes on either end of the bell curve

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15
Q

What is a type I error

A

probability of rejecting a true Ho

- the prob of committing a type I error is just a significance level a

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16
Q

What are common choices for type I error /a

A
  • 0.05 & 0.01

- this controls the probability of making this type of error

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17
Q

If the cost of making a type I error is not too high,

A

larger values of a are typically used

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18
Q

What does a significance test control

A

only controlling type I error

- most applications only control type I error

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19
Q

Due to the uncertainty associated with making a type II error we should say

A

Do not reject Ho instead of accept Ho

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20
Q

Whenever the prob of making type II error has NOT been determined and controlled use

A

Do not reject No or Reject Ho

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21
Q

Is controlling type II errors common

A

no

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22
Q

If proper controls have been established for Type II errors, it can be3 appropriate to use

A

accept Ho

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23
Q

What are the steps for calcualting the prob of a Type II error

A
  1. gather a sample and calculate the sample average and the pop SD
  2. suppose you know the true average is 58%
  3. calculate the prob of type II error with a claim at the 1% significance level
  4. state the Ho and Ha
  5. calcualte the z score for the claim
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24
Q

What are the steps for calculating the prob of a Type II error

A
  1. gather a sample and calculate the sample average and the pop SD
  2. suppose you know the true average is 58%
  3. calculate the prob of type II error with a claim at the 1% significance level
    - find the area of 0.01 which is a z-score of -2.33
  4. solve for CV
    CV = M+(-2.33)(SE)
    - put this number on the curve at the cv line
    - the mean for this curve is the M you are trying to find (H0: M)
  5. standardize the number from step 4 the cv
    - calculate the z-score for this number M as the actual known mean
    - find out what the area is for this z-score
    1- this area is the prob of making the type 2 error `
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25
Q

What is the power of the test

A

prob of correctly rejecting Ho when it is false

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26
Q

what is the formula for power - which type of error is this used for

A

1-B

- used to find the prob of making a type II error

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27
Q

what is 1 in the power

A

1 is the prob of correctly rejecting HO

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28
Q

what is B in the power test

A

prob of making type II error

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29
Q

what do you use in order to calculate the power test

A

use table 9.7

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30
Q

the prob of a type 2 error depends on what value

A

depends on the value of the pop mean

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31
Q

for the power test, for values of M near M0, the prob of making teh type II error

A

can be high

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32
Q

What is the graph for the power called

A

the power curve

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33
Q

the power curve extends over what values

A

values of M for which the hypothesis is false

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34
Q

the height of a power curve at any value of M indicates what

A

the prob of CORRECTLY rejecting HO when Ho is false

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35
Q

Common confidence levels state their significance level and critical value z -score

.90
.95
.99

A

Confidence Significance CV
.90 .10 1.645
.95 .05 1.96
.99 .01 2.575

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36
Q

applications of hypothesis tests that only control for Type I errors are called

A

significance tests

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37
Q

What is the p-value

A

the area for the z-score

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38
Q

definition for p-value

A

a probability that provides a measure of the evidence against the null hypothesis provided by the sample.

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39
Q

what does a smaller p-value indicate

A

more evidence against the H0

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40
Q

using the p-value, when do you reject the HO

A

if p-value is <= a

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41
Q

what is the p-value also called

A

the observed level of significance

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42
Q

How do you calculate the hyp test for p-value approach

A
  1. calculate the z score for the sample mean (x bar)
    z= x bar - M0 / se
  2. find the area for the z-score (p-value)
  3. if p-value is larger than the critical value is a= 0.01
    do not reject HO

if p-value is smaller than CV - reject Ho

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43
Q

the p-value approach and CV approach will always lead to what conclusion

A

the same conclusion

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44
Q

what is the advantage of the p-value approach

A

tells us how significant the results are

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45
Q

if we only use the CV approach, what can we say

A

we only know that the results are significant at the stated level of significance

46
Q

what is the rule for computing the p-value in the lower tailed test

A

compute the prob that z is less or equal to the value of the test statistic (area in the lower tail)

47
Q

what is the rule for computing the p-value in the upper tailed test

A

compute the prob that z is greater than or equal to the value of the test statistic (upper tail area)

48
Q

how do you calculate the hyp test using CV for two tailed test

A
  1. a / 2 (example a = 0.05) then it’s 0.025
  2. find z -score for 0.025
    • z = -1.96 and z = 1.96
  3. calculate the z-score for the test statistic ie z = 1.53
  4. compare the two z scores by drawing on the bell curve
    if the test statistic is is less than -1.96 or greater than 1.96 reject Ho
    if it is in between the two values, reject Ho
49
Q

how do you calculate the hyp test using p-value for two tailed test

A
  1. calculate the z-score for the test statistic (using sample mean x bar)
  2. calculate the area for that z-score
  3. add
50
Q

p-value test reject Ho if

A

p-value is less than or equal to a

51
Q

critical value approach - reject Ho if

A

need to know what type of tailed test it is

52
Q

critical value approach in the lower tailed test, reject HO if

A

z for test statistic is is less than or equal to -z for the cv

53
Q

critical value approach in the upper tailed test, reject Ho if

A

if Z for test statistic is greater than or equal to z for the cv

54
Q

critical value approach in the two tailed test, reject Ho if

A

if z for test statistic is less than or equal to the -za/2 for the cv OR if z for test stat is greater than or equal to z a/2

55
Q

Confidence interval approach to Hyp test for single tailed test

A

if the confidence interval contains the hypothesis value Mo DO not reject HO

56
Q

if the confidence interval does not contain the hyp value Mo for single tailed test

A

reject Ho

57
Q

for a two tailed hyp test for an interval reject HO if

A

the confidence interval does not include Mo

58
Q

by controlling the sample size the user can also control what

A

the prob of making a type 2 error

59
Q

level of significance determines what

A

the prob of making a type I error

60
Q

controlling the sample size controls what

A

the prob of making a type II error

61
Q

sample size for hyp test how do you calculate c

A

c = Mo - Za x SE
or
C = Ma + Zb x SE

both equations must provide the same value for C

62
Q

what is the formula to determine the required Sample size to control type 1 and type 2 errors

A

N = (za +zb)squared x Qsquared / (Mo + Ma) squared

63
Q

for a given level of significance a, increasing the sample size will

A

reduce B

64
Q

for a given sample size decreasing a will

A

increase B

65
Q

for a given sample size increasing a will

A

decrease B

66
Q

When the prob of type II error is not controlled, this suggests

A

that one should not choose unnecessarily small values for the level of significance a

67
Q

When the prob of type II error is not controlled, this suggests

A

that one should not choose unnecessarily small values for the level of significance a

68
Q

for a given samples size, choosing a smaller level of signficance means

A

more exposure to a type 2 error

69
Q

smaller values of a (significance level) have the disadvantage of

A

increasing the prob of making a type II error

70
Q

for a given samples size, choosing a smaller level of significance means

A

more exposure to a type 2 error

71
Q

smaller values of a (significance level) have the disadvantage of

A

increasing the prob of making a type II error

72
Q

conclusions of the hypothesis testing and interpretation of the results are dependent upon what

A

a clear and sound definition of the pop parameter being tested (often M or Q)

73
Q

conclusions of the hypothesis testing and interpretation of the results are dependent upon what

A

a clear and sound definition of the pop parameter being tested (often M or Q)

74
Q

with type I and Type 2 errors, a and B are what

A

probabilities of TYpe 1 and type 2 errors and not the errors

75
Q

How can we control (or minimize) type 1 and type 2 errors

A

with a fixed sample size, but not both of them at the same time
- they are conflicting objectives that cannot be achieved simultaneously unless additional data re added by increasing the sample size

76
Q

Ideally we would like a and B to be what

A

as small as possible

77
Q

when the sample size becomes larger and larger and reaches infinity, both a and B become

A

zero, which is the smallest possible value

- this is what happens when the sample is the whole population

78
Q

A local pizza store knows the mean amount of time it takes them to deliver an order is 45 minutes after the order is placed. The manager has a new system for processing delivery orders, and they want to test if it changes the mean delivery time. They take a sample of delivery orders and find their mean delivery time is 48 minutes.
What are appropriate hypotheses for their significance test?

A

​

H 0:μ=45 minutes
H a:μ not =45 minutes
​

79
Q

A ketchup company regularly receives large shipments of tomatoes. For each shipment that is received, a supervisor takes a random sample of 500 tomatoes to see what percent of the sample is bruised and performs a significance test. If the sample shows convincing evidence that more than 10%, percent of the entire shipment of tomatoes is bruised, then they will request a new shipment of tomatoes.

What are appropriate hypotheses for the company’s significance test?

A

Ha:p: > .10

80
Q

the average running time for a computer was 36 hours. It is believed that a new program reduced the average hours per week. What is the hypothesis

A

HO:M>= 36
Ha: M< 36

81
Q

The average cost of heating per month for a business is $700. Because of the weather change, it is believed that there is a decrease in the average cost per month.

what is the null and alternative hypothesis

A

Ho:M > 700
Ha: M <700

82
Q

A manufacturing process fills cans with 8.2 oz of liquid. the manufacturer does not want over or under filling to happen. What is the null and alternative hypothesis

A

HO:M = 8.2
Ha:M does not = 8.2

83
Q

The average rate of pay for a labourer with 2 years of experience is $25/hr. Because of the high demand for labourers, it is believed there has been a significant increase in the average wage of labourers. What is the null and alternative hypothesis

A

HO: M < or = 25
Ha: M >25

84
Q

A friend thinks the average grade on a final exam is at least 75. You take a sample to test this belief. What is the null and alternative hypothesis

A

HO: m >= 75
Ha: m does not <75%

85
Q

In the past 25% of people who visit the job site went to see the demo phase. Recently the co undertook some extensive advertising showing the demo of their projects. They are interested in determining whether the advertising actually increased the proportion of visitors who visited the demo phase at job sites. what is the null and alternative hyp

A

HO:p<= 75%
Ha: P>75%

86
Q

The average tire produced by CDNT has been 40,000 miles. Mgmt thinks that due to new production process, the life expectancy of their tires has increased.
what is the null and alternative hyp,

A

Ho: m<=40000
Ha:m>40,000

87
Q

A company fills liquid detergent bottles with 12 oz. any over or under filling causes a machine to be readjusted and the department shuts down. To determine if the machine is running properly, the null and alternative hyp is

A

Ho: M = 12
Ha: M does not = 12

88
Q

A school is thinks that at least 35% of all students will need to attend tutoring classes after school.
what is the correct null and alternative hyp

A

Ho:p >= 35
Ha: p< 35

89
Q

If you were looking at increasing a mean from its current avg. lets say of 5 what is the null and alternative hyp

A

HO: M <=5
Ha: M> 5

90
Q

if you are expecting an avg to be AT LEAST 10%. what is the null and alternative hyp

A

HO:M>= .10
Ha: M<10

91
Q

if you are expecting an avg to be 80 OR LESS. What is the mull and alternative hyp

A

Ho: M <= 80
Ha: M > 80

92
Q

If you are expecting a proportion to be AT LEAST 30%. waht is the null and alternative hyp

A

Ho: p >=.30
Ha: p

93
Q

the p-value must be a number between

A

zero and 1

94
Q

what type of error occurs if you fail to reject HO when it is not true

A

Type 2

95
Q

THe prob of committing a Type I error when the null hypothesis is true is

A

the level of significance

96
Q

In hypothesis testing, the smaller the type I error, the (what type 2 error)

A

the larger the type 2 error will be

97
Q

In hype testing the tentative assumption about the pop parameter is

A

the null hypothesis HO

98
Q

for a lower tailed test, the p-value is the prob of obtaining a value for the test statistic at least as

A

small as the that provided by the sample

99
Q

the p-value is a prob that measures the support (or lack of support) for the

A

null hypothesis HO

100
Q

the p-value is a

A

probability

101
Q

for a two -tailed test, the p-value is the prob of obtaining a value for the test statistic as

A

unlikely as that provided by the sample

102
Q

the level of significance is a maximum allowable

A

probability of a type 1 error

103
Q

the power curve provides the prob of

A

correctly rejecting the null hypothesis

104
Q

a type II error is committed when

A

a true alternative hypothesis is mistakenly rejected

105
Q

the error of rejecting a true null hypothesis is

A

a type I error

106
Q

In hype testing, if the null hypothesis is rejected when the altnernative is true

A

the correct decision has been made

107
Q

as the test statistic becomes larger, the p-value

A

gets smaller

108
Q

the p-value ranges between

A

zero to one

109
Q

if a hyp is rejected at the 5% level of significance, it will be (rejected/accepted) at the 1% level

A

may be rejected or not rejected at the 1% level

110
Q

if a hype is NOT rejected at the 5% level of significance, it will be (rejected/accepted) at the 1% level

A

will also not be rejected at the 1% level

class 2 - May 22 (9 decks)

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