An education researcher would like to test whether 2nd graders retain or lose knowledge during the summer when they are presumably not in school. She asks nine 2nd graders to take a comprehension exam at the end of the school year (May), and then asks those same students to come back after the summer (late August) to retake a different but equivalent exam, to see if their level of comprehension has changed. Using the data below, test this hypothesis using an alpha level of .05. May August
90 100
65 80
78 92
50 60
89 90
92 98
75 70
90 96
65 87
a) What is the appropriate test? Is it a one or two tailed test?
b) State the null hypothesis (in words and using means).
c) State the alternative hypothesis (in words and using means).
d) Find the critical value.
e) Calculate the obtained value by hand. What does your decision mean?

Given tan∅=4/3 and π< ∅< (3π)/2; find cos2∅ a. -24/25 b. 24/25 c. -24/7 d. -7/25

The table shows population statistics for the ages of best actor and best supporting actor winners at an awards ceremony. the distributions of the ages are approximately bell-shaped. compare the z-scores for the actors in the following situation. best actor best supporting actor muequals42.0 muequals49.0 sigmaequals7.3 sigmaequals15 in a particular year, the best actor was 59 years old and the best supporting actor was 45 years old. determine the z-scores for each. best actor: z equals best supporting actor: z equals (round to two decimal places as needed.) interpret the z-scores. the best actor was (more than 2 standard deviations above more than 1 standard deviation above less than 1 standard deviation above less than 2 standard deviations below) the mean, which (is not, is) unusual. the best supporting actor was (less than 1 standard deviation below more than 1 standard deviation above more than 2 standard deviations below more than 1 standard deviation below) the mean, which (is is not) unusual.

What unit of been sure would be appropriate for the volume of a sphere with a radius of 2 meters