In a Psychology testing experiment, 20 subjects are selected randomly and their

Question

In a Psychology testing experiment, 20 subjects are selected randomly and their reaction time in seconds to a particular stimulus is measured. Past experience suggests that the population standard deviation of reaction times to these types of stimuli is 5 seconds and that the distribution of reaction times is approximately normal. The average time for the 20 subjects is 6.9 seconds. Researchers would like to estimate the average reaction time.   Calculate a 99% confidence interval for the average reaction time.   

Carry out the work in two phases:

          1.Check the conditions for the interval that you plan to use.

2.Calculate the confidence interval.

Our estimate, =

The standard error,

critical value =

Explanation / Answer

Conditions to be met:

1) The sample is a simple random sample. In this case, it is a random sample.

2) The population is normally distributed

3) The population standard deviation is known.

The 99% confidence interval is given by: estimate ± margin error

Estimate = mean = 6.9 seconds

Population standard deviation = = 5

n = 20

Critical value = z/2 = z0.01/2 = 2.576

Standard error = /n = 1.118

Margin error = critical value*standard error = 2.576*1.118 = 2.879968

99% confidence interval is given by: 6.9 ± 2.879968

99% confidence interval : (4.02, 9.779)

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