Question

Eyewitness Accuracy of Police Does stress affect the recall ability of police eyewitnesses? This issue was studied in an experiment that tested eyewitness memory a week after a nonstressful interrogation of a cooperative suspect and a stressful interrogation of an uncooperative and belligerent suspect. The numbers of details recalled a week after the incident were recorded, and the summary statistics are given below (based on data from “Eyewitness Memory of Police Trainees for Realistic Role Plays,” by Yuille et al., Journal of Applied Psychology, Vol. 79, No. 6). Use a 0.01 significance level to test the claim in the article that “stress decreases the amount recalled.”

Nonstress: n = 40,\(\bar x\)= 53.3, s = 11.6

Stress: n = 40,\(\bar x\)= 45.3, s = 13.2

Short answer

There is enough evidence to conclude that stress decreases the amount of information recalled by an eyewitness.

Step-by-step solution

Given information

The mean value, sample size and standard deviation values are given for the amount of information recalled by 2 samples of eyewitnesses after a non-stressful interrogation and after a stressful interrogation.

Hypotheses

It is claimed that stress decreases the amount of information recalled by an eyewitness.

Corresponding to the given claim, the following hypotheses are set up:

Null Hypothesis: The amount of information recalled after a non-stressful interrogation is equal to the amount of information recalled after a stressful interrogation.

\({H_0}:{\mu _1} = {\mu _2}\)

Alternative Hypothesis: The amount of information recalled after a stressful interrogation is less than the amount of information recalled after a non-stressful interrogation.

\({H_1}:{\mu _1} > {\mu _2}\)

The test is right-tailed.

Sample sizes, sample means and pooled variance

Sample Means:

Let\({\bar x_1}\)denote the mean amount of information recalled after a non-stressful interrogation.

The value of\({\bar x_1}\)is equal to 53.3.

Let\({\bar x_2}\)denote the mean amount of information recalled after a stressful interrogation.

The value of\({\bar x_2}\)is equal to 45.3.

Sample Sizes:

Let\({n_1}\)denote the sample size corresponding to the non-stressful interrogation.

The value of\({n_1}\)is equal to 40.

Let\({n_2}\)denote the sample size corresponding to the stressful interrogation.

The value of\({n_2}\)is equal to 40.

Pooled Variance:

Let\({s_1}\)denote the standard deviation of the amount of information recalled after a non-stressful interrogation.

The value of\({s_1}\)is equal to 11.6.

Let\({s_2}\)denote the standard deviation of the amount of information recalled after a stressful interrogation.

The value of\({s_2}\)is equal to 13.2.

The value of the pooled variance is computed below:

\(\begin{aligned} s_p^2 &= \frac{{\left( {{n_1} - 1} \right)s_1^2 + \left( {{n_2} - 1} \right)s_2^2}}{{\left( {{n_1} - 1} \right) + \left( {{n_2} - 1} \right)}}\\ &= \frac{{\left( {40 - 1} \right){{\left( {11.6} \right)}^2} + \left( {40 - 1} \right){{\left( {13.2} \right)}^2}}}{{\left( {40 - 1} \right) + \left( {40 - 1} \right)}}\\ &= 154.4\end{aligned}\)

Calculate test statistic, critical value and p-value

The test statistic value is computed as follows:

\(\begin{aligned} t &= \frac{{\left( {{{\bar x}_1} - {{\bar x}_2}} \right) - \left( {{\mu _1} - {\mu _2}} \right)}}{{\sqrt {\frac{{s_p^2}}{{{n_1}}} + \frac{{s_p^2}}{{{n_2}}}} }}\;\;\;{\rm{where}}\;{\mu _1} - {\mu _2}\;is\;0\\ &= \frac{{\left( {53.3 - 45.3} \right) - 0}}{{\sqrt {\frac{{154.4}}{{40}} + \frac{{154.4}}{{40}}} }}\\ &= 2.879\end{aligned}\)

The value of the degrees of freedom is equal to:

\(\begin{aligned} df &= {n_1} + {n_2} - 2\\ &= 40 + 40 - 2\\ &= 78\end{aligned}\)

Referring to t-table:

The critical value of t for \(\alpha = 0.01\) and 78 degrees of freedom for a right-tailed test is equal to 2.3751.

The corresponding p-value is equal to 0.0026.

Since the test statistic (2.879) is greater than the critical value and the p-value is less than 0.01, the null hypothesis is rejected.

Conclusion

There is enough evidence to conclude thatstress decreases the amount of information recalled by an eyewitness.