Hypothesis Testing: One population

Question 1

What is type 1 error? (alpha)

Answer 1

The error that H0 is rejected when H0 is actually true.

Question 2

What is type 2 error? (beta)

Answer 2

The error that H0 has failed to be rejected when H0 is actually false.

Question 3

How do you calculate the significance level of a type 1 error when mean and variance is known? (a < X < b)

Answer 3

Use Z statistic.
error = P(X < a) + P(X > b)
(We want outside critical region area)

Question 4

How can type 1 (alpha) error be reduced?

Answer 4

1. Widening the critical region.
2. Increase sample size
   - -> But will increase type 2 error.

Question 5

How do you calculate the significance level of a type 2 error when mean and variance is known? (a < X < b)

Answer 5

Test for 95% significance
alpha/2 = 0.025
z1 = 1.96
z2 = -1.96
Use Z statistic to find X values.
Use true mean for z3 and z4.
beta = P(X < b) - P(X < a)
(We want the critical region area)

Question 6

What is the P-value?

Answer 6

Smallest level of significance that would lead to rejection of the null hypothesis. (Same as alpha type 1 error).

Question 7

What statistical test is used when mean and variance are both known?

Answer 7

Z statistic

Question 8

What statistical test is used when mean is known but variance is unknown?

Answer 8

T statistic.

Question 9

How do you calculate the P value for a;

1. 2 tailed test
2. upper tailed test
3. lower tailed test

Answer 9

1. = 2(1 - P(z0))
2. = 1 - P(z0)
3. = P(z0)

Question 10

What statistical test is used when only variance is known?

Answer 10

Chi-squared test.

Question 11

What bounds does the P value hold for rejecting or failing to reject the null hypothesis?

Answer 11

P < alpha, reject H0 at alpha level of significance

P > alpha, fail to reject H0