Every user of statistics should understand the distinction between statistical significance and practical importance. A sufficiently large sample will declare very small effects statistically significant. Consider the study of elite female Canadian athletes that investigated whether elite athletes are deficient in their nutritional intake. A total of n athletes from eight Canadian sports centers participated in the study. Female athletes were consuming an average of 2403.7 kcal/day with a standard deviation of 880 kcal/day. Suppose a nutritionist is brought in to implement a new health program for these athletes. This program should increase mean caloric intake but not change the standard deviation. Given the standard deviation and how caloric deficient these athletes are, a change in the mean of 50 kcal/day to 2453.7 is of little importance. However, with a large enough sample, this change can be significant. To see this, calculate theP-value for the test of

H0:μ=2403.7
Ha:μ>2403.7

in the following situation:

A sample of 100 athletes; their average caloric intake is x= 2453.7.

(Fill in the blanks below and roundzto to 2 decimal places and round P to 4 decimal places.)

For n=100, z=____ P=P(Z >___) =