Hypothesis Testing

Question 1

What is a test statistic?

Question 2

What is the null hypothesis?

Question 3

What is the alternate hypothesis?

Question 4

A single observation is taken from a binomial distribution B( 6, p). The observation is used to test Ho: p = 0.35 against H1:p is bigger than 0.35.
a. Using a 5 per cent significance level, find the critical region for this test.

Answer 4

5

Question 5

A single observation is taken from a binomial distribution B( 6, p). The observation is used to test Ho: p = 0.35 against H1:p is bigger than 0.35.
b. State the actual significance level of this test.

Answer 5

2.23 per cent

Question 6

The standard treatment for a particular disease has a 2/5 probability of success. A researcher has produced a new drug which has been successful with 11 out of 20 patients. He claims the new drug is more effective than the standard treatment. Test at a 5% significance level, the claim made by the researcher.

Answer 6

1. The test statistic is the number of patients in the trial for how the drug was successful. The parameter was the probability of success for each patient.
2. Model
3. null and alternative hypothesis.
4. Calculate the probability of 11/20 being successful and find the significance level for that.
5. Compare the significance level and write a conclusion.

Question 7

In Enrico’s restaurant, the ratio of non-vegetarian to vegetarian means is found to be 2 to 1. In Manuel’s restaurant in a random sample of 10 people ordering meals, 1 ordered the vegetarian meal. Using a 5% significance level test whether the proportion of people eating a vegetarian meal is different in both those restaurants.

Answer 7

1. Name the test statisstic and parmater.
2. Hypothesis and model.
3. Test wether the probability is less than one and compare the significance levels.