WJEC AS-Level Mathematics - Hypothesis Testing

Various quick questions on this topic.

What is a Hypothesis in terms of Statistics?
It is a statement about the population parameter, which we would test by collecting evidence through samples.
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What is the Test Statistic, and how is it denoted?
The Test Statistic can be denoted as any algebraic symbol, as it is simply the amount of times something happened within a sample.
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What is the Null Hypothesis, and how is it denoted?
The null hypothesis is our initial assumption, and we will assume it to be correct until proven false. It is denoted by H0, hence, Null Hypothesis.
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What is the Alternative Hypothesis, and how is it denoted?
This hypothesis is what we would say if our null hypothesis was wrong. It is denoted as H1.
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If we were to flip a coin 8 times to see if it were biased towards heads, and X being the amount of times we flip heads, what would the X be called, and what would the Null and Alternative Hypothesis's be?
X is the Test Statistic, the Null Hypothesis is P(H) = 0.5, and the Alternative Hypothesis is P(H) > 0.5
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If we did not specify the bias from the last question, how would we state our Alternative hypothesis?
P(H) =/= 0.5
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What is the critical region?
The range of values that would cause us to reject the Null Hypothesis in favour of our Alternative Hypothesis.
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What is the Level of Significance?
The threshold between regular values and the critical region.
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What is the Critical Value?
The value of the Test Statistic that corresponds to the threshold, essentially meaning that this is the number of times something must happen in order to make us reject the Null Hypothesis.
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What is the generally accepted thresholds?
5%/0.05, or 1%/0.01, depending on the problem. 5% is the most applicable.
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How would we find the critical value?
Binomial tables, either through a calculator or the easier to eliminate incorrect answers with, the paper table.
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What is the One Tailed Test?
A test that looks for the increase or decrease in the value of a parameter. The test has a critcal region spanning 5% of the probability.
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When is the One Tailed Test used?
Whenthe Null Hypothesis is expressed as H0: Theta = m, as either H1: Theta > m, or H1: Theta < m
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What is a Two Tailed Test?
This test is like the One Tailed Test, but we use it when we are unsure of the direction of bias. The usual 5% threshold is shared between two critical regions, thus the threshold at either end becomes 2.5%
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Other cards in this set

Card 2

Front

What is the Test Statistic, and how is it denoted?

Back

The Test Statistic can be denoted as any algebraic symbol, as it is simply the amount of times something happened within a sample.

Card 3

Front

What is the Null Hypothesis, and how is it denoted?

Back

Preview of the front of card 3

Card 4

Front

What is the Alternative Hypothesis, and how is it denoted?

Back

Preview of the front of card 4

Card 5

Front

If we were to flip a coin 8 times to see if it were biased towards heads, and X being the amount of times we flip heads, what would the X be called, and what would the Null and Alternative Hypothesis's be?

Back

Preview of the front of card 5
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