Please include explanation for answers!

1.Public health officials claim that people living in low income neighborhoods have different Physical Activity Levels (PAL) than the general population. This is based on knowledge that in the U.S., the mean PAL is 1.63 and the standard deviation is 0.52. A study took a random sample of 50 people who lived in low income neighborhoods and found their mean PAL to be 1.53. Using a one-sample z test, what is the z-score for this data? (Answer to 2 decimal places)

2.What is the critical value of z in the previous question? Report the critical value CLOSEST to your calculated z-score. (Answer to 2 decimal places.)

3.The strength of one's immune system can be evaluated in several ways. One of the most popular methods involves measuring the concentration of adenosine triphosphate (ATP) in the blood. In women, the mean blood ATP level is 390 ng/mL, and the standard deviation is 115 ng/mL. It has been hypothesized that women with Major Depressive Disorder (MDD) have decreased immune function. A recent study found that a random sample of 96 women with MDD had an average blood ATP level of 355 ng/mL. Using a one-sample z test, what is the p-value of this result? (HINT: This involves a one-tailed hypothesis test.)

4.In a recent study on gender differences in education, a sample of 7 boys had a mean score of 18.5 and a standard deviation of 4.1 on a Standardized Math Test. A sample of 11 girls had a mean score of 19.9 and a standard deviation of 3.6 on the same test. What is the t-statistic for this data? (Use the sample of boys as Group 1.)