please help if you can with this problem!

• A school psychologist is looking at assessment scores from the end-of-semester finals. She takes the entire set of scores from the school and finds the mean to be =80, with a population standard deviation of 25 points. She selects a sample of 25 students and gets a sample mean of 95 points.She wants to know the probability of getting a sample mean of 95 points or above from this data set.

Draw out the curve and shade in what she is looking for.

What is the probability of the sample mean being 95 or above?

• A researcher wanted to see if giving a selective serotonin reuptake inhibitor (anti-depressant) would decrease the number of self-injurious behaviors found in adolescents. They gave the anti-depressant to a group of 8 participants and found a sample mean of 40.

Suppose the =45 and a population SD=5, what is thez score for the sample mean?

What is the SEM for this particular sample?

• A group of doctors are deciding whether or not to perform an operation. Suppose the null hypothesis, H₀, is: the surgical procedure will go well. Which is the error with the greater consequence?

• The probability of winning the grand prize at a particular carnival game is 0.005. Michele wins the grand prize. Is this considered a rare or common event? Why?

• The National Institute of Mental Health published an article stating that in any one-year period, approximately 9.5 percent of American adults suffer from depression or a depressive illness. Suppose that in a survey of 100 people in a certain town, seven of them suffered from depression or a depressive illness. If you were conducting a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult American population, what would the null and alternative hypotheses be?