Question

for the following question(s): a school counselor tests the level of depression in fourth graders in a particular class of 20 students. the counselor wants to know whether the kind of students in this class differs from that of fourth graders in general at her school. on the test, a score of 10 indicates severe depression, while a score of 0 indicates no depression. from reports, she is able to find out about past testing. fourth graders at her school usually score 5 on the scale, but the variation is not known. her sample of 20 fifth graders has a mean depression score of 4.4. suppose the counselor tested the null hypothesis that fourth graders in this class were less depressed than those at the school generally. she figures her t score to be 2.8. what decision should she make regarding the null hypothesis? group of answer choices postpone any decisions until a more conclusive study could be conducted fail to reject it there is not enough information given to make a decision reject it

Answer 1

Based on the information provided, the correct choice is:

fail to reject it

Here are the key points:

• The mean depression score for the sample of 20 4th graders was 4.4.

• The counselor tested the null hypothesis that these 4th graders were less depressed than the general 4th grader population.

• The t score calculated was 2.8.

To reject the null hypothesis and conclude the sample differs from the population, we would need a high enough t score. But the t score of 2.8 is not conclusively high enough here.

Some additional considerations:

• The general 4th grader population mean is 5, so the sample mean of 4.4 is a bit lower, but not drastically. This suggests the sample may not differ hugely from the population.

• There is no information on the variation or standard deviation for either the sample or population. Without this, we can't determine if a t score of 2.8 actually signifies a statistically significant difference.

• The sample size of 20 is decent but not very large. Larger sample sizes provide more conclusive results.

• No p-value is given, making it hard to judge if the t score of 2.8 is high enough to reject the null hypothesis. By convention, p<0.05 is often used but we don't have the p-value here.

So overall, there is not enough definitive evidence provided to conclusively reject the null hypothesis. The t score of 2.8 alone is probably not high enough, given the considerations around sample size, variation, and lack of a p-value. More data and analysis would be needed to make a firm decision either way.

Therefore, the correct choice is: "fail to reject it". There is not enough information given in this question and results to conclusively reject the null hypothesis.

Explanation: