Which of the following are true?

The probability of making a Type I error is conditional on the Null Hypothesis being true.

A Type II error cannot occur if the decision is do not reject the null hypothesis

Type I and Type II errors can occur together.

The decision rule is usually formulated so that there is a low probability of making a Type I error

A wholesaler buys pre-packed sugar in bags with an advertised mean weight of 5 kgs. He wishes to conduct a hypothesis test to check the validity of the advertised weight. Which of the following alternative hypotheses is appropriate?

Ha:= 5 kg (equal to)

Ha:< 5 kg (less than)

Ha: 5 kg (not equal to)

Ha:> 5 kg (more than)

The Colgate company believes its toothpaste is more effective than its leading rival, Aim, in fighting tooth decay. A small scale clinical trial was held with 30 patients using Colgate and 21 using Aim. The results showed that the mean and variance of the number of cavities for Colgate was 10.2 and 9.85, respectively, with the results for Aim being 11.4 and 8.42.

It is assumed that the population variances are the same and the distribution of the number of cavities for both groups closely approximates a normal distribution. Use alpha = 0.05.

1. If the hypotheses are to be written in the form of the average of Aim minus the average of Colgate, what is the direction of the alternative hypothesis used to test Colgate's belief. Type the letters gt(greater than), ge (greater than or equal to), lt (less than), le(less than or equal to) or ne (not equal to) as appropriate in the box.

2. Determine the standard error for the difference between means, reporting your answer to three decimal places.

3. Calculate the test statistic, reporting your answer to two decimal places.

4. Is the null hypothesis rejected for this test? Type yes or no.

5. Regardless of your answer for 4, if the null hypothesis was rejected, can we conclude that Colgate's belief is valid at the 5% level of significance? Type yes or no.

QUESTION 8

1.The Australian Medical Association believed that the Health Minister's recent statement claiming that 75% of doctors supported the reforms to Medicare was incorrect. It thought that the actual support for the reforms was lower than this. The Association's President suggested the best way to test this was to survey 150 members, selected through a random sample, on the issue. She indicated that the Association would be prepared to accept a Type I error probability of 0.05.

1. State the direction of the alternative hypothesis for the test. Type gt (greater than), ge (greater than or equal to), lt (less than), le (less than or equal to) or ne (not equal to) as appropriate in the box.

2. State, in absolute terms, the critical value as found in the tables in the textbook.

3. Determine the lower boundary of the region of non-rejection in terms of thesample proportionof respondents (as a % to two decimal places) in favour of the reforms. If there is no (theoretical) lower boundary, type lt in the box.

4. Determine the upper boundary of the region of non-rejection in terms of thesample proportionof respondents (as a % to two decimal places) in favour of the reforms. If there is no (theoretical) upper boundary, type gt in the box.

5. If 102 of the survey participants indicated support for the reforms, is the null hypothesis rejected for this test? Type yes or no.

6. Disregarding your answer for 5, if the null hypothesis was rejected, could the Association claim that the Health Minister's assertion is incorrect at the 5% level of significance?