Question

Loftus and Palmer study (1974) demonstrated the influence of language on eyewitness memory. Participants watched a film of a car accident and were asked questions about what they saw. One group was asked “About how fast the cars were going when they smashed into each other?” Another group was asked the same question, except the verb was changed to “hit” instead of “smashed into”. The ‘smasher into” group reported significantly higher estimates of speed than the hit group. Suppose a researcher repeats this study with two samples of college students and obtains the following results:

Estimated Speed
Smashed into	hit
n = 15	n = 15
M = 40.8	M = 34.0
SS = 510	SS = 414

Is there a significantly higher estimated speed for the “smashed into” group? Use a one-tailed test with α = .01.

a) The t-statistic is

b) Your decision is:

c)The estimated Cohen's d is:

d)The critical t value is

Answer 1

s1^2 = SS/n1 - 1 = 510/14 = 36.43

s2^2 = SS/n2 - 1 = 414/14 = 29.57

H₀:

H₁:

a) The test statistic t = (M1 - M2)/sqrt(s1^2/n1 + s2^2/n2)

                                 = (40.8 - 34)/sqrt(36.43/15 + 29.57/15)

                                 = 3.242

b) df = (s1^2/n1 + s2^2/n2)^2/((s1^2/n1)^2/(n1 - 1) + (s2^2/n2)^2/(n2 - 1))

        = (36.43/15 + 29.57/15)^2/((36.43/15)^2/14 + (29.57/15)^2/14)

        = 27

P-value = P(T > 3.242)

            = 1 - P(T < 3.242)

            = 1 - 0.9984

            = 0.0016

Since the P-value is less than the significance level(0.0016 < 0.01), so we should reject the null hypothesis.

At 0.01 significance level, we can conclude that there is a significantly higher estimated speed for the "smashed into" group.

c) Cohen's d = (M1 - M2)/sqrt((s1^2 + s2^2)/2)

                     = (40.8 - 34)/sqrt((36.43 + 29.57)/2)

                      = 1.1837

d) At 0.01 significance level the critical value is t_0.99,27 = 2.473