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BASICS OF HYPOTHESIS TESTING Flashcards

1
Q

A claim or a statement about a property of a population

A

Hypothesis

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2
Q

The assumption about the population parameter

A

Hypothesis

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3
Q

Conjecture which may or may not be true

It could either be rejected or not rejected

A

Hypothesis

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4
Q

A standard procedure for testing a claim about a property of population

A

Hypothesis Test (Test of Significance)

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5
Q

the general goal of hypothesis testing

A

The general goal of hypothesis testing is to rule out chance or something
error a plausible explanation or the result of a research study, in that
case, the result is said to be statistically significant.

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6
Q

Hypothesis testing is one of 2 common forms of _____________

A

statistical inference

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7
Q

Identify a target population or study population, the population of interest.
You do _______________sampling then collect data from the
sample.

A

random or probability

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8
Q

From the collected data, ____________are determined or
calculated. And there used to make an inference or generalizations
about the ____________

A

sample statistics; population of interests

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9
Q

The goal of hypothesis testing has a form of ____________, is to
make a statements or generalizations regarding unknown ___________ based on sample data.

A

statistical inference; parameter

values

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10
Q

Statement that the value of a population parameter (e.g. proportion, mean,
or standard deviation) is equal to some claimed value (To the hypothesized
value)

A

Null Hypothesis (Ho)

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11
Q

β†’ Uses equal symbol (=)
β†’ Statement of equality
β†’ A claim of no difference or of equality

A

Null Hypothesis (Ho)

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12
Q

the researchers in general hope to reject in favor of the other hypothesis

A

Null Hypothesis (Ho)

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13
Q

Either reject it or do not reject it

A

Null Hypothesis (Ho)

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14
Q

A statement that the parameter has a value that somehow differs from the
null hypothesis;

A

Alternative Hypothesis (Ha,HA, or H1)

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15
Q

use contradictory statement
β†’ Uses one of these symbols: , β‰ 
β†’ Also, at least (less than or equal) & at most (greater than or equal)

A

Alternative Hypothesis (Ha,HA, or H1)

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16
Q

what is the sign of at least

A

(less than or equal)

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17
Q

what is the sign of at most

A

(greater than or equal)

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18
Q

Identify the null and alternative hypotheses using the given claims:
The proportion of drivers who admit to driving under the influence of
alcohol is less than 0.5.

A
  • P < 0.5 (claim)
  • P β‰₯ 0.5
  • Ho: p = 0.5
  • Ha: p < 0.5
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19
Q

Identify the null and alternative hypotheses using the given claims:
The average number of calories of a low–calorie meal is at most 300.

A
  • Β΅ ≀ 300 (claim)
  • Β΅ > 300
  • Ho: Β΅ = 300
  • Ha: Β΅ > 300
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20
Q

Identify the null and alternative hypotheses using the given claims:
The standard deviation of IQ scores of hospital employees is 15.

A
  • Ho: Οƒ = 15 (claim)

* Ha: Οƒ β‰  15

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21
Q

A value used in making a decision (to whether or not to reject the null
hypothesis) about the null hypothesis and is found by converting the sample
statistic to a score with the assumption that the null hypothesis is true.

A

TEST STATISTIC

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22
Q

z test for mean can be used when n is ____, or when the population is
__________ and Οƒ is known. Otherwise, used t test equation
instead.

A

β‰₯ 30, normally distributed

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23
Q

The tails in a distribution are the extreme regions bounded by____________

A

critical value

24
Q

Directional / One tailed

A

Left-tailed or Right-tailed

25
Q

Non-directional

A

two-tailed

26
Q

We can identify it by the _______________hypothesis wether you have a
right-tailed, left-tailed, or two-tailed test

A

alternative

27
Q

Alternative hypothesis uses the symbols:

A

> , < , or, β‰ 

28
Q

what tail is Less than (

A

Left-tailed

29
Q

what tail is Greater than (>)

A

Right-tailed test

30
Q

what tail has Inequality (β‰ )

A

two-tailed test
(meaning the Ξ± is divided in the
opposite tails)

31
Q

Consider the claim that the XSORT (in vitro fertilization) method of gender
selection increases the likelihood of having a baby girl. Preliminary results from
a test of the XSORT method of gender selection involved 14 couples who gave
birth to 13 girls and 1 boy. Use the given claim and the preliminary results to
calculate the value of the test statistic and test the claim at Ξ± = 0.05.

A

β†’ H0: p = 0.5
β†’ H1: p > 0.5 (right-tailed)
β–ͺ The CLAIM is on the ALTERNATIVE HYPOTHESIS (Ha)

𝑝̂= π‘ π‘Žπ‘šπ‘π‘™π‘’ π‘π‘Ÿπ‘œπ‘π‘œπ‘Ÿπ‘‘π‘–π‘œπ‘› = 13/14 = 0.929
z= 3.21

If the test statistic (zstat) is within the critical region = REJECT H0β€œ
β†’ zstat = 3.21 is within the critical region or beyond the z Critical = 1.645.
Therefore, we reject H0.
P-VALUE METHOD:
β€œIf P-value ≀ Ξ± = REJECT H0”
β†’ P-value β‡’ 1 – P(Z<3.21) = 1 - 0.9993 = 0.0007
β†’ 0.0007 < 0.05 (Ξ±) = reject H0

There is not enough evidence to support the claim that the XSORT
method of gender selection increases the likelihood of having a baby girl.”

32
Q

what is the decision if the test statistic (zstat) is within the critical region

A

= REJECT H0

33
Q

If P-value ≀ Ξ±, what is the decision

A

= REJECT H0

34
Q

it is the β€œObserved Significance Level”

35
Q

what is the p-value of zstat = -1.82

A

P-value = 0.0344

36
Q

what is the p-value of zstat = 2.23

A

P-value = 1 – 0.9871 = 0.0129

37
Q

what is the decision if P-value ≀ Ξ±,

38
Q

what is the decision if P-value > Ξ±

A

do not reject H0 / fail to reject H0 / retain H0

39
Q

what is the decision If the test statistic falls within the critical region,

40
Q

what is the decision If the test statistic does not fall within the critical region

A

do not reject H0 / fail to reject H0 / retain H0

41
Q

mistake of rejecting the null hypothesis when it is actually true.

A

Type I error

42
Q

mistake of failing to reject the null hypothesis when it is actually false

A

Type II error

43
Q

H0: New drug is no better than standard treatment
β€’ H1: New drug is better than standard treatment
what is the type I error?

A

Concluding that the new drug is better than the standard (HA)
when in fact it is not (H0).

44
Q

H0: New drug is no better than standard treatment
β€’ H1: New drug is better than standard treatment
what is the type II error?

A

Failing to conclude that the new drug is better (HA) when in
fact it is

45
Q

A survey claims that 9 out of 10 doctors recommend aspirin for their patients
with headaches. To test this claim, a random sample of 100 doctors is obtained.
Of these 100 doctors, 82 indicate that they recommend aspirin. Use Ξ± = 0.05
to test if the claim is accurate.

A
  • Claim: p = 0.9 (p=proportion)
  • 9 out of 10 – 90%
  • counter claim: p ο‚Ή 0.9
46
Q

The probability that the test statistic will fall in the critical region when the null
hypothesis is actually true

A

SIGNIFICANCE LEVEL

47
Q
  • Also called as the rejection region

* Related and corresponds to 

A

CRITICAL REGION

48
Q

It encompasses all values beyond the critical value that will cause us to reject
the null hypothesis

A

CRITICAL REGION

49
Q

If you have an alpha= 0.05, there is_____ in the right tail and ______ in the left
tail (area under the curve)

50
Q

If the test statistic falls under either tail

A

reject null hypothesis

51
Q

Any value that separates the critical region from the test statistic that do not
lead to rejection of the null hypothesis

A

CRITICAL VALUE

52
Q

Boundary between the non-rejection and rejection region

A

CRITICAL VALUE

53
Q

Depends on the nature of the null hypothesis, whether it is left, right, or two-tailed test

A

CRITICAL VALUE

54
Q

What is the critical z value given H1: p β‰  0.5 and Ξ± = 0.01?

55
Q

The standard deviation of heights of adult women is greater than 6.0 cm.

A

Οƒ > 6.0

56
Q

What is the critical z value given H1: p < 0.5 and Ξ± = 0.05?

57
Q

A survey claims that 9 out of 10 doctors recommend aspirin for their patients
with headaches. To test this claim, a random sample of 100 doctors is
obtained. Of these 100 doctors, 82 indicate that they recommend aspirin.
Use =0.0.5 to test if the claim is accurate.

A

State the H0 and H1.
β€’ Answer:
β†’ H0: p = 0.9
β†’ H1: p β‰  0.9

β†’ Two-tailed test

State the level of significance, Ξ± and determine critical value.
Ξ±.
β€’ Answer:
β†’ Ξ± : 0.05
β€’ Z critical Value
β†’ Β±1.96

Compute the test statistic and find the P-value.
z = -2.67
P Value
P= P(Z β‰₯ z) = 0.0038

Decision: Reject H0
Conclusion: There is enough evidence to reject the claim that 90% of
doctors recommend aspirin for their patients with headaches

BIOSTATS (4 decks)

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