Question

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 1.6 and the standard deviation is 0.45. A study took a random sample of 42 people who lived in low income neighborhoods and found their mean PAL to be 1.49. Using a one-sample z test, what is the z-score for this data? (Answer to 2 decimal places)

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.)

Answer 1

Ho :   µ =   1.6
Ha :   µ ╪   1.6
      
Level of Significance ,    α =    0.01
population std dev ,    σ =    0.45
Sample Size ,   n =    42
Sample Mean,    x̅ =   1.49
      

Standard Error , SE =   σ/√n =   0.0694
      
Z-test statistic=   (x̅ - µ )/SE =    -1.58

critical z value, z*   = ±2.58 [Excel formula =NORMSINV(0.05/2 ]