Hypothesis testing

Question 1

Parameters

Answer 1

Null hypothesis H₀
Alternative hypothesis H₁

Question 2

Forms of H₁

Answer 2

H₁ : μ < μ₀ - one tail
H₁ : μ > μ₀ - one tail
H₁ : μ ≠ μ₀ - two tail

Question 3

Rejectance and acceptance regions

Answer 3

If the sample mean is in the acceptance region you accept H₀ else you reject it

Question 4

Finding the rejection region

Answer 4

1. Determine p based on significance level
2. Find corresponding z value
3. set z equal to [c - μ] / [σ/√n]
4. solve for c

z value may be negative depending on bell curve and context

Question 5

Test statistic approach steps

Answer 5

1. Lay out parameters
2. Set up like normal distribution
3. Solve for phi value
4. Reject or accept H₀ by comparing value and significance level

Question 6

Discrete variables

Answer 6

Reject null hypothesis for one tail test if probability is less than the significance level

Reject null hypothesis for two tail test if probability is less than half the significance level

Question 7

Binomial AS reminder

Answer 7

To input binomial notation into calculator use nCr

Question 8

Binomial distribution approximated to normal distribution steps

Answer 8

1. Layout all parameters
2. Show np > 5 and nq > 5
3. State mean and variance using np and npq respectively
4. State normal distribution
5. State probability (cont correction)
6. Solve for z
7. Compare with signficance level
8. State conclusion

Question 9

Poisson distributionapproximated to normal distribution steps

Answer 9

1. Lay out all parameters
2. Ensure λ is large, > 15
3. Set poisson and normal parameters
4. Set probability
5. Solve for z
6. Compare with significance level
7. State conclusion

Question 10

Type 1 and Type 2 errors

Answer 10

Type 1 error is when a true null hypothesis is rejected, for normal distribution P(Type 1 error) = significance level of the test
Type 2 error is when a false null hypothesis is accepted, for normal distribution P(Type 2 error) = P(accept H₀ | H₀ false)

Question 11

Probability of type 1 and type 2 errors with binomial distribution

Answer 11

Type 1:
1. set binomial parameters
2. set type 1 error parameter
3. solve binomially using condition given
4. answer is the probability

Type 2:
1. set binomial parameters
2. set type 2 error parameter
3. solve binomially using condition given and the probability given for the type 2 error
4. answer is the probability

Question 12

Probability of type 1 and type 2 errors with poisson distribution

Answer 12

Type 1:
1. set hypothesis testing parameters
2. set type 1 error parameter
3. solve using poisson distribution and condition given
4. answer is the probability

Type 2:
1. set hypothesis testing parameters
2. set type 2 error parameter
3. solve using poisson distribution and condition given, change the λ value to what is given
4. answer is the probability

Question 13

Solving steps for large samples

Answer 13

1. lay out hypothesis testing parameters
2. set p and z value according to significance level
3. solve for x̄
4. use x̄ to place into equation when solving for z, [x̄ - μ] / [σ/√n]
5. place z value into another probability notation
6. solve for the phi value, the probability
7. state conclusion by comparing probaility with significance level