Final Module (6 & 7) Flashcards

1
Q

2-tailed test hypothesis test

A

H0: 𝑋 = 𝜇
Ha: 𝑋 ≠ 𝜇

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2
Q

1-tailed test hypothesis test

A

H0: 𝑋 = 𝜇
Ha: 𝑋 > 𝜇 OR Ha: 𝑋 < 𝜇

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3
Q

Z-score

A

measures how many standard deviations away from the mean your measurement is

𝑧 = 𝑋 − 𝜇 / 𝜎

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4
Q

Significance level (𝛼)

A

percentage of the data you want to be above or below you measurement in order for it to be significantly different from the mean

(most often: 𝛼 = 5%)

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5
Q

Confidence level equation

A

1 - 𝛼

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6
Q

p-value

A

the area of the tail beyond your measurement

  • the probability of obtaining the value as extreme or more extreme as the given value, provided that H0 is true
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7
Q

How to Calculate the p-value?

A

1) Z-table or T-table
2) Excel using 1- normal or 1- standard normal dist

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8
Q

𝑝 ≤ 𝛼

A

reject H0, your value is significantly different from the mean

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9
Q

𝑝 > 𝛼

A

fail to reject H0

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10
Q

Sample mean is a random variable with

A

standard deviation, this is called standard error

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11
Q

Assumptions of Z-test
(What if not all of these assumptions are met?)

A
  • Sample data follow a normal distribution
  • All observations are independent
  • Sample size is more than 30
  • Population standard deviation is known

If these are not met then use a t-test

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12
Q

Types of two samples

A
  • well-separated distributions
  • overlapping distributions
  • different variances
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13
Q

The confidence interval of two samples

A

𝑋 ± 𝑡-critical * 𝑠 /√𝑛

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14
Q

Hypothesis Tests for Variances

A
  • Hypothesis test for single variance – use 𝜒2 distribution
  • Hypothesis test for equality of two variances – use F-distribution
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15
Q

𝝌𝟐 (chi-squared) distribution

A

distribution of the sum of 𝑘 independent standard normal random variables

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16
Q

F-distribution

A

distribution of a ratio of two random variables which are distributed according to 𝜒2-distributions with parameters 𝑘1 and 𝑘2.

17
Q

The denominator for the t-statistic depends on whether

A

the variances of the samples can be assumed to be the same so we need a separate test for variances
- There is a equation for equal and unequal t-statistic

18
Q

F-test

A

can be used to test if two variances are equal or if one variance if greater than the other

(left tail if you divide smaller by larger variance, right tail if you divide larger by smaller variance)

19
Q

𝜒2 test

A

can be used to test if the variance of a population is equal to a specified value, based on the sample data