Unit 8: hypothesis testing

Question 1

The significance level of a test is the probability of rejecting the null hypothesis, given the null
hypothesis is true.

Answer 1

true

Question 2

If we reject the null hypothesis, then we know that the null hypothesis is false

Answer 2

False. There
is an important difference between the result of the test and the (unknown) underlying reality.
Whatever the result of the hypothesis test, we still do not know the underlying reality

Question 3

If we reject the null hypothesis, then we know that the alternative hypothesis is false.

Answer 3

false

Question 4

If we do not reject the null hypothesis, then we know that the null hypothesis is true.

Answer 4

false

Question 5

If we do not reject the null hypothesis, then we know that the alternative hypothesis is true.

Answer 5

false

Question 6

A p-value is a probability.

Answer 6

true

Question 7

We reject the null hypothesis when the p-value is less than or equal to the significance level

Answer 7

true

Question 8

The p-value of a test is the probability, given H0 is true, of obtaining the observed value of the test statistic or a value with even greater evidence against H0 and in favour of Ha.

Answer 8

true

Question 9

The p-value of a test depends on sample data and on the null and alternative hypotheses.

Answer 9

true

Question 10

The p-value of a two-sided test will be greater than 1 if the null hypothesis is true.

Answer 10

False.

A p-value is a probability and as such cannot be greater than 1.

Question 11

The p-value of a test will be less than 0.05 if the null hypothesis is false.

Answer 11

False. The p-value
can be any value between 0 and 1, whether or not the null hypothesis is true. Keep in mind
that there is a fundamental difference between the conclusion from a test and the (unknown)
underlying reality.
(b) The p-value of a test

Question 12

The p-value of a test is the probability that the null hypothesis is true

Answer 12

false

Question 13

If the p-value of a hypothesis test with a two-sided alternative is equal to exactly 1, then we
can be certain the null hypothesis is true.

Answer 13

false

Question 14

If the p-value of a hypothesis test with a two-sided alternative is equal to exactly 1, then we
can be certain the null hypothesis is false.

Answer 14

false

Question 15

If the p-value of a test is less than 0 that means there is extremely strong evidence against the
null hypothesis.

Answer 15

False. A p-value is a probability and as such it cannot be less than 0. If we
find a negative p-value, that means we made a mistake.

Question 16

If we wish to carry out inference procedures on the mean of a normally distributed population where sigma is known, we should use the t distribution.

Answer 16

false

Question 17

Both the t distribution and the standard normal distribution have a median of 0.

Answer 17

true

Question 18

The t distribution has more area in the tails than the standard normal distribution.

Answer 18

true

Question 19

The t distribution is a discrete probability distribution.

Answer 19

false (continuous)

Question 20

The t distribution has a standard deviation of 1.

Answer 20

false