The admissions officer at a small college compares the scores on the Scholastic Aptitude Test (SAT) for the school's male and female applicants. A random sample of 6 male applicants results in an SAT score of 1200, with a standard deviation of 100. The mean SAT score for all male applicants is 1100. The admissions officer wants to test if the mean SAT score for male applicants is significantly different from 1100.

What is the null hypothesis for this test?

1) The null hypothesis is that the mean SAT score for male applicants is equal to 1100.
2) The null hypothesis is that the mean SAT score for male applicants is less than or equal to 1100.
3) The null hypothesis is that the mean SAT score for male applicants is greater than or equal to 1100.
4) The null hypothesis is that the mean SAT score for male applicants is not equal to 1100.

The null hypothesis in a hypothesis test represents the default assumption, typically stating no effect or no difference. In this case, the admissions officer wants to test if the mean SAT score for male applicants is significantly different from 1100, which is the population mean. Option 1 correctly states that the null hypothesis is that the mean SAT score for male applicants is equal to 1100. This means that the admissions officer assumes there is no significant difference between the sample mean and the population mean of 1100.

The null hypothesis is formulated as a statement of equality, indicating that there is no effect or difference. By assuming that the mean SAT score for male applicants is equal to 1100, the admissions officer is essentially setting a baseline to compare the sample data against. If the sample data significantly deviates from this baseline, it would suggest that there is evidence to reject the null hypothesis in favor of an alternative hypothesis.

In hypothesis testing, the null hypothesis is typically framed as the hypothesis of no effect or no difference, and the alternative hypothesis is what the researcher wants to test for evidence of an effect or difference. Therefore, the null hypothesis is crucial in determining whether there is sufficient evidence to support a claim or hypothesis about the population parameter being tested. In this case, the null hypothesis serves as the reference point for evaluating the significance of the mean SAT score for male applicants. Therefore, the correct option is 1) The null hypothesis is that the mean SAT score for male applicants is equal to 1100.