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.