Question

Two groups of children were shown a commercial. One group​ (the A/V​ group) was shown the ad with both audio and​ video; the second group​ (the video-only​ group) was shown only the video portion of the commercial. Following the​ viewing, the children were asked to recall 10 specific items from the ad. The number of items recalled correctly by each child is summarized in the accompanying table. The researchers theorized that​ "children who receive an audiovisual presentation will have the same level of mean recall of ad information as those who receive only the visual aspects of the​ ad." Complete parts a through f below.

e. The researchers reported the p-value of the test as p-value 0.56. Interpret this result. Choose the correct answer below. Since this p-value f. What conditions are required for the inference to be valid? Select all that apply. ▼ | the given value of α, there is Vevidence to reject Ho A. Both population variances must be the same. B. The samples must be random and independent. □ C. Both populations being sampled from are normal. D. The samples must be dependent. E. Both population variances must be different.

Answer 1

Part a)

The null and alternative hypotheses for testing the researcher’s theory are given as below:

Correct answer: C

H₀: µ₁ = µ₂; H_a: µ₁ ≠ µ₂

[Here, we want to check whether the means for number of items recalled are same for the both group or not.]

Part b

Here, we have to use two sample t test for the population mean. The test statistic formula is given as below:

t = (X1bar – X2bar) / sqrt[S_p²*((1/n1)+(1/n2))]

Where S_p² is pooled variance

S_p² = [(n1 – 1)*S1^2 + (n2 – 1)*S2^2]/(n1 + n2 – 2)

We are given

X1bar = 3.74

X2bar =3.35

S1 = 1.99

S2 = 2.15

n1 = 20

n2 = 20

S_p² = [(20 – 1)*1.99^2 + (20 – 1)*2.15^2]/(20 + 20 – 2)

S_p² = 4.2913

t = (X1bar – X2bar) / sqrt[S_p²*((1/n1)+(1/n2))]

t = (3.74 – 3.35) / sqrt[4.2913*((1/20)+(1/20))]

t = 0.39/ 0.6551

t = 0.5953

Degrees of freedom = n1 + n2 – 2 = 20 + 20 – 2 = 38

Level of significance = α = 0.10

Critical values = -1.686 and 1.686

(by using t-table or excel)

P-value = 0.5551

(by using t-table or excel)

P-value > α = 0.10

So, we do not reject the null hypothesis

We fail to reject null hypothesis H₀ that mean recall of ad information by the A/V group is same as the video only group.

There is insufficient evidence to conclude that mean recall of ad information by the A/V group is different from the video only group.

Part c

Correct Rejection region

D. t > 1.686 or t < -1.686

(See part b, value obtained from t-table)

Part d

Correct answer: A

Since there is insufficient evidence to indicate the mean recall of ad information by the A/V group is different from the video only group at α = 0.10, fail to reject H₀.

Part e

Since this p-value is greater than given value of α, there is insufficient evidence to reject H₀.

Part f

Answers: A and C

Both population variances must be the same and both populations being sampled from normal distribution.