A prominent cancer researcher believes that women who smoke are more likely to develop breast cancer than those who do not smoke. In their study, 4050 non-smokers and 4200 smokers aged between 35 and 65 were tracked over a 20 year period. They found that 448 of the group of non-smokers and 547 of the group of smokers had received a diagnosis with breast cancer at some time during the period. The researcher agrees that a 1% level of significance should be used to test the validity of the claim.

1. If the hypotheses are written in the form of the proportion of non-smokers minus the proportion of smokers, state the direction of the alternative hypothesis used to test the researcher's claim. 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. Calculate the test statistic for the Z test, reporting your answer correct to two decimal places.

3. Use the tables in the text to determine the p-value for the test (4 decimal places).

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

5. Hence, on the basis of this test, does the researcher's claim appear to be valid? Type yes or no.