Stats 4 - HT for Proportion (including calculation of the Critical Region)

Question 1

What is a hypothesis?

Answer 1

A statement made about the value of the population parameter that we wish to test by collecting evidence in the form of a sample

Question 2

What is the null hypothesis?

Answer 2

H0 the default position- nothing has changed unless proven otherwise
* the value that you’d expect

eg: the coin is fair p=0.5

Question 3

Wha is the alternate hypothesis?

Answer 3

H1: there has been some change in population parameter

eg: the coin is biased towards heads p>0.5

Question 4

What is a test statistic?

Answer 4

• the evidence from the sample
  Test statistic X is what we observed
  Eg: the number of heads seen in 10 throws

a distribution

Question 5

what is the level of significance ?

Answer 5

the maximum probability where we could reject the null hypothesis (or, equivalently, represents the chance of incorrectly rejecting H0)

Question 6

what is a hypothesis test?

Answer 6

using statistical techniques to test a particular claim ot theory

Question 7

what is the p value?

Answer 7

the probability that you obtain a value as extreme as the test statistic

Question 8

what are the main steps in carrying out a hypothesis test for a population proportion?

Answer 8

1. define the null & alternative hypotheses
2. determine if it is a 1-tail or a 2-tail test
3. always assume H0
4. describe the associated binomial model
5. identify/calculate the test statistic (TS)
6. if the TS is on the LHS, find “at most”
   if the TS is on the RHS, find “at least”
7. calculate the p-value
8. compare p-vale and significance level
9. accept or reject H0
10. interpret the conclusions in context

Question 9

Answer 9

Question 10

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Question 11

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Question 12

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Question 13

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Question 14

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Question 15

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Question 16

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Question 17

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Question 18

Answer 18

Question 19

What is the critical region?

Answer 19

The range of values of the test statistic that would lead you to rejecting H0 (null hypothesis)

Question 20

What is the critical value?

Answer 20

The values on the boundary of the critical region

Question 21

Answer 21

Question 22

What is the actual significance level?

Answer 22

The actual probability of being in the critical region

Question 23

What is the actual significance level?

Answer 23

Question 24

Answer 24

Question 25

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Question 26

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Question 27

Answer 27