Experiments on learning in animals sometimes measure how long it takes a mouse to find its way
through a maze. The mean time is 23 seconds for one particular maze. A researcher thinks that
playing rap music will cause the mice to complete the maze faster. She measures how long each
of 10 mice takes with the rap music as a stimulus. She wants to test Ho: ? = 23 Ha: ? < 23
with a 10% level of significance. Assume the population standard deviation is known to be ? =
3.4. NOTE: For parts (a) and (e) take z* to 3 decimal places as given in the bottom of Table D.
Take calculated z values to 2 decimal places, using Table A. Take to 1 decimal place. Take
probabilities to four decimal places. Answers submitted with any other number of decimal places
will be marked wrong. (a) We reject Ho if z < ? _____. (b) We reject if Ho if x? <
_______ . (c) What is the probability of a Type II error when ? = 21? _______ (d) What is
the power of the test against when ? = 21? ________ Now suppose we decrease the level of
significance to 0.01. (e) We reject Ho if z < ?_______ . (f) We reject if Ho if < x?
?_______. (g) What is the probability of a Type II error when ? = 21? ______ (h) What is
the power of the test against when ? = 21? ______ (i) Based on your results in (c), (d), (g) and
(h), what is the relationship between ? and ? and the power of a test?(choose from choices below)
a)For a fixed n and ?, a decrease in ? will result in an increase in ? and a decrease in the
power. b)For a fixed n and ?, a decrease in ? will result in an increase in ? and in the
power. c)For a fixed n and ?, changing ? will have no effect on ? or on the power.
d)For a fixed n and ?, a decrease ? will result in an increase in the power but will have no
effect on the value of ?. e)For a fixed n and ?, a decrease in ? will result in a decrease in
? and an increase in the power.
Solution
http://www.marin.edu/~npsomas/Math115/Ch6/6.2_HW_.
Experiments on learning in animals sometimes measure how long it tak.pdf
1. Experiments on learning in animals sometimes measure how long it takes a mouse to find its way
through a maze. The mean time is 23 seconds for one particular maze. A researcher thinks that
playing rap music will cause the mice to complete the maze faster. She measures how long each
of 10 mice takes with the rap music as a stimulus. She wants to test Ho: ? = 23 Ha: ? < 23
with a 10% level of significance. Assume the population standard deviation is known to be ? =
3.4. NOTE: For parts (a) and (e) take z* to 3 decimal places as given in the bottom of Table D.
Take calculated z values to 2 decimal places, using Table A. Take to 1 decimal place. Take
probabilities to four decimal places. Answers submitted with any other number of decimal places
will be marked wrong. (a) We reject Ho if z < ? _____. (b) We reject if Ho if x? <
_______ . (c) What is the probability of a Type II error when ? = 21? _______ (d) What is
the power of the test against when ? = 21? ________ Now suppose we decrease the level of
significance to 0.01. (e) We reject Ho if z < ?_______ . (f) We reject if Ho if < x?
?_______. (g) What is the probability of a Type II error when ? = 21? ______ (h) What is
the power of the test against when ? = 21? ______ (i) Based on your results in (c), (d), (g) and
(h), what is the relationship between ? and ? and the power of a test?(choose from choices below)
a)For a fixed n and ?, a decrease in ? will result in an increase in ? and a decrease in the
power. b)For a fixed n and ?, a decrease in ? will result in an increase in ? and in the
power. c)For a fixed n and ?, changing ? will have no effect on ? or on the power.
d)For a fixed n and ?, a decrease ? will result in an increase in the power but will have no
effect on the value of ?. e)For a fixed n and ?, a decrease in ? will result in a decrease in
? and an increase in the power.
Solution
http://www.marin.edu/~npsomas/Math115/Ch6/6.2_HW_
