In a psychology testing experiment 25 subjects are selected randomly and their r
ID: 3127741 • Letter: I
Question
In a psychology testing experiment 25 subjects are selected randomly and their reaction time in seconds to a particular stimulus is measured. Past experience suggests that the variance in reaction times to these types of stimuli is 4 seconds and that the distribution of reaction times is approximately normal. The average time for the 25 subjects is 6.4 seconds. Researchers would like to estimate the average reaction time. Calculate a 90% confidence interval for the average reaction time.
Solve: Carry out the work in two phases:
1. (3 points) Check the conditions for the interval that you plan to use.
2. (5 points) Calculate the confidence interval.
Our point estimate, =
The standard error,
critical value =
Explanation / Answer
1.
Here, the subjects are selected randomly, so that is satisfied.
It is also approximately normal, and we know the population variance.
Hence, the conditions are satisfied.
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2.
Point estimate = sample mean = X = 6.4 s [ANSWER]
SE = sigma/sqrt(n) = sqrt(4)/sqrt(25) = 0.4 [ANSWER]
alpha/2 = (1 - confidence level)/2 = 0.05
z(alpha/2) = critical z for the confidence interval = 1.644853627 [ANSWER, CRITICAL VALUE]
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Note that
Margin of Error E = z(alpha/2) * s / sqrt(n)
Lower Bound = X - z(alpha/2) * s / sqrt(n)
Upper Bound = X + z(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.05
X = sample mean = 6.4
z(alpha/2) = critical z for the confidence interval = 1.644853627
s = sample standard deviation = 2
n = sample size = 25
Thus,
Margin of Error E = 0.657941451
Lower bound = 5.742058549
Upper bound = 7.057941451
Thus, the confidence interval is
( 5.742058549 , 7.057941451 ) [CONFIDENCE INTERVAL]
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