Question

Please show every step

6) A police study tested eyewitness memory a week after a non-stressful interrogation of a cooperative suspect and a stressful interrogation of an uncooperative and belligerent suspect. The numbers of details recalled were recorded and the summary statistics are givern below: Groupn Non-stress 4053.3 11.6 Stress 4045.3 13.2 We want to construct a 95% confidence interval for the difference of mean amount of details recalled based on stressful or non-stressful interrogation methods. a) Are the samples independent or dependent? b) What are the conditions for constructing a 95% confidence interval? c) Construct the confidence interval d) State your conclusion in the context of the problem.

Answer 1

a)

Here we have two independent samples.

b)

Since sample sizes are greater 30 so conditions for constructing a 95% confidence interval has been satisfied.

c)

Here we have following information:

The pooled standard deviation:

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So standard error for difference in population mean is

Degree of freedom for t is df=40+40-2=78, so t-critical value using excel function "=TINV(0.05,78)" is 1.991. So required confidence interval for will be

So required confidence interval is (2.468, 13.532).

d)

Since confidence interval does not contain zero so we can conclude that there is a significant difference between the population means.