In: Statistics and Probability
In a maze running study, a rat is run in a T maze and the result
of each run recorded. A reward in the form of food is always placed
at the right exit. If learning is taking place, the rat will choose
the right exit more often than the left. If no learning is taking
place, the rat should randomly choose either exit. Suppose that the
rat is given n = 100 runs in the maze and that he chooses
the right exit x = 63 times. Would you conclude that
learning is taking place? (Use α = 0.01.)
State the null and alternative hypotheses.
H0: p ≠ 0.63 versus Ha: p = 0.63H0: p = 0.63 versus Ha: p ≠ 0.63 H0: p = 0.5 versus Ha: p > 0.5H0: p = 0.5 versus Ha: p ≠ 0.5H0: p < 0.5 versus Ha: p > 0.5
Find the test statistic and the p-value. (Round your test
statistic to two decimal places and your p-value to four
decimal places.)
z | = | |
p-value | = |
State your conclusion.
The p-value is less than alpha, so H0 is rejected. There is insufficient evidence to indicate that learning is taking place.The p-value is greater than alpha, so H0 is not rejected. There is sufficient evidence to indicate that learning is taking place. The p-value is less than alpha, so H0 is rejected. There is sufficient evidence to indicate that learning is taking place.The p-value is greater than alpha, so H0 is not rejected. There is insufficient evidence to indicate that learning is taking place.
please answer step by step
Solution:
Given: the rat is given n = 100 runs in the maze and that he chooses the right exit x = 63 times.
Sample proportion is:
Part a) State the null and alternative hypotheses.
learning is taking place that means proportion is more than 50% or > 0.5
thus
H0: p = 0.5 versus Ha: p > 0.5
Part b) Find the test statistic and the p-value.
P-value = P( Z> z )
P-value = P( Z> 2.60)
P-value = 1 - P( Z< 2.60)
Look in z table for z = 2.6 and 0.00 and find corresponding area.
P( Z< 2.60) = 0.9953
Thus
P-value = 1 - P( Z< 2.60)
P-value = 1 - 0.9953
P-value = 0.0047
Part c) State your conclusion.
Decision Rule:
Reject H0, if P-value < 0.01 level of significance, otherwise we
fail to reject H0
Since P-value = 0.0047 < 0.01 level of significance, we reject
H0.
The p-value is less than alpha, so H0 is rejected. There is sufficient evidence to indicate that learning is taking place.