Chapter 18 Hypothesis Testing Using The Binomial

Question 1

What are the null and alternative hypotheses?

Answer 1

The null hypothesis, H0, is the default position that nothing special has occurred. The alternative hypothesis, H1, is that there has been a change from the position described by the null hypothesis.

The alternative hypothesis may be 1-tail or 2-tail according to whether the direction of change is or is not specified.

Question 2

What is the significance level in hypothesis testing?

Answer 2

The significance level is the level at which you say there is enough evidence to reject the null hypothesis in favor of an alternative hypothesis.

Question 3

What is the importance of data collection in hypothesis testing?

Answer 3

Collect suitable data using a random sampling procedure that ensures the items are independent.

Question 4

What is the test statistic in hypothesis testing?

Answer 4

The test statistic is the measure that will be used to decide whether the test is significant. In the case of a binomial test, it is the number of successes.

Question 5

What are the options after conducting the test?

Answer 5

1. Work out the p-value and compare it with the significance level.
2. Work out the critical region and value for the significance level and compare it with the test statistic.

Question 6

How can the outcome of a hypothesis test be described?

Answer 6

1. The evidence is not strong enough to reject the null hypothesis in favor of the alternative hypothesis.
2. There is not enough evidence to conclude that the probability/proportion has changed/increased/decreased.
3. There is sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis.
4. There is sufficient evidence to conclude that the probability/proportion has changed/increased/decreased.

Question 7

What should be added after describing the outcome of a hypothesis test?

Answer 7

You should then add a comment relating to the situation you are investigating.