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365 Data Science - Statistics > Hypothesis Testing > Flashcards

Hypothesis Testing Flashcards

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1
Q

When making decisions you need a Yes or No answer. What is the correct way to do this?

A

Use a test.

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2
Q

What are the 4 steps in Data Driven Decision Making?

A
  1. Formulate a Hypothesis
  2. Find the right test for the hypothesis
  3. Execute the test
  4. Make a decision based on the result
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3
Q

What is a Hypothesis?

A

A hypothesis is an idea that can be test

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4
Q

What is the Null Hypothesis denoted as?

A

H0

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5
Q

What is the Alternative Hypothesis denoted as?

A

H1 or HA

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6
Q

Which hypothesis is the one to be tested?

A

The null hypothesis - H0

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7
Q

When would you accept the null hypothesis?

A

If the mean is close enough to the true mean

Reject if the mean is too far from the true mean

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8
Q

As a researcher what hypothesis are you challenging?

A

The null hypothesis

In statistics the null hypothesis is the statement we are trying to reject

Therefore, the null is the present state of affairs while the alternative is our personal opinion.

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9
Q

You want to check if your height is above average, compared to your classmates. State the null and alternative hypotheses of this test.

A

H0: My height is lower or equal to the average height in the class. H1: My height is higher than the average height in the class.

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10
Q

You want to test if the Obama administration issued fewer executive orders than the Bush administration. State the null and alternative hypotheses of this test.

A

H0: The Obama administration issued at least as many executive orders as the Bush administration. H1: The Obama administration issued fewer executive orders than the Bush administration.

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11
Q

True or False - We always include the equality sign (=) in the null hypothesis

A

True

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12
Q

What does significance level mean?

A

It is the probability of rejecting the null hypothesis, it it is true.

Denoted as alpha

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13
Q

What are typical values for alpha?

A

0.01, 0.05, 0.1

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14
Q

If the sample mean is close to the hypothesized mean then Z will be close to what number?

A

Zero

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15
Q

It the sample mean is close to the hypothesized mean then Z will be exactly what number?

A

Zero

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16
Q

How big should Z be to reject the null hypothesis?

A

It depends on the Confidence Interval we desire. If the test is two sided then we can check the Z score table.

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17
Q

What is a One Side Test vs A Two Sided Test?

A

Two sided tests are used when we need to know if H1 is significantly more or less than H0.

One sided test are used when we need to only know one direction

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18
Q

What are the 2 types of errors in hypothesis testing?

A
  1. Type I error - False Positive
  2. Type II error - False Negative
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19
Q

What is a Type I error?

A

When you reject the true null hypothesis - A False Positive

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20
Q

What is the probability of making a Type I error (false positive)?

A

The probability is alpha

21
Q

What is a Type II error?

A

A False Negative

22
Q

What is the probability of making a Type II error (false negative)?

A

The probability is beta - beta depends on sample size (n) and the magnitude of the effect (variance)

23
Q

What is the probability of rejecting a false null phypothesis?

A

Probability is 1-beta (one minus beta)
It is also called “The power of the test”

24
Q

Type I error or false positive comprises:

A

accepting a null hypothesis that is false

25
Q

What is another way to call the probability of rejecting a null hypothesis that is false?

A

Power of the test

26
Q

You are taking a pregnancy test. The null hypothesis of this test is: I am not pregnant. In reality, you are not pregnant, but the test says you are. Which type of error occurred?

A

Type I error

27
Q

What is a Z-score?

A

A Z-score is the standardized variable associated with the test

28
Q

Lowercase z is also know as?

A

The critical value - taken from the table - “z-stat”

29
Q

What is decision rule when you have a negative valued Z-score?

A

-4.67 < a negative z-stat <=> 4.67 > a positive z-stat

Decision Rule:
Reject if: absolute value of Z-score > positive z-stat

30
Q

Is the P-value the most common way to test hypotheses?

A

Yes

31
Q

Why use the P-value?

A

Instead of testing at preassigned levels of significance we can find the smallest level at which we can still reject the null hypothesis, given the observed sample statistic.

32
Q

How do you use P-value?

A

You should reject the null hypothesis if the P-value < alpha

33
Q

How do you calculate the P-value?

A

One-sided test
= 1- the number from the table

Two-sided test
= (1- number from table)*2

34
Q

Where are P-values used?

A

The p-value is a universal concept that works with every distribution

The closer to 0.000 the p-value the more significant is the result you’ve obtained

35
Q

When do you reject the null hypothesis using the P-value?

A

When the P-value is lower than the level of significance - you reject the null hypothesis

36
Q

You have a z-score of 2.31. What is the p-value of this test?

A

not enough information

37
Q

You have a z-score of 2.31 for a one-tailed test. What is the p-value of this test?

A

0.010

38
Q

What do we do when the p-value is lower than the level of significance?

A

Reject the null hypothesis.

39
Q

T or F;
If we have a p-value of 0.001 and a significance level of 1% we reject the null hypothesis.

A

True

40
Q

The null hypotheses actually states the opposite statement

A

True

Task: estimate if our competitor has a higher open rate

H0 : mu open rate <= 40%
H1 : mu open rate > 40%

41
Q

How are the T & Z -scores calculated?

A

T or Z = sample mean - null hypothesis mean / standard error

42
Q

What is a Dependent sample?

A

A sample where you test the same people again. A before and after situation.
Examples: drug development test

43
Q

What does D0 stand for?

A

It stand for the Hypothesized population mean difference.

mu B - mu A

44
Q

As a rule of thumb, what t-score do researchers believe to be sufficiently significant for a T-test?

A

2

45
Q

The power of a hypothesis test is:

A

The probability of not making a Type II error

46
Q

If the probability of a Type II error is equal to 10%, and the significance level is 5%, what is the power of the test?

A

.90

The power of a test is the probability of rejecting the null hypothesis when it is false. It is equal to (1- the Probability of Type II Error). In this case, this is (1-.10) or 90%.

47
Q

Which of the following statements about the p-value is least accurate?

A

The p-value indicates the probability of making a Type ll error

Explanation of correct answer
The power of a test represents the probability of avoiding, a Type ll error. It does not denote the probability of making a Type Il
error.

48
Q

The probability of correctly rejecting the null hypothesis when it is false is known as:

A

The power of the test

Explanation of correct answer.
The power of a test is the probability of rejecting the null hypothesis when it is false.

365 Data Science - Statistics (5 decks)

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