Question

An experiment on memory was performed, in which 16 subjects were randomly assigned to one of two groups, called "Sentences" or "Intentional". Each subject was given a list of 50 words. Subjects in the "Sentences" group were told to form multiple sentences, each using at least two words from the list, and to keep forming sentences until all the words were used at least once. Subjects in the "Intentional" group were told to spend five minutes memorizing as many of the 50 words as possible. Subjects from both groups were then asked to write down as many words from their lists as they could recall. We are interested in drawing inference on the difference in the population average number of words recalled for subjects in the "sentences" group vs. subjects in the "intentional" group. The data is in the table below. Number of words recalled "Sentences" group 31 37 32 30 26 29 24 32 "Intentional" group | 31 | 32 | 37 | 33 | 30 | 36 | 34 | 31 (For these questions, round all numeric answers to three decimal places) a. Enter the values for the following statistics: Xsentences = 30.125 Ssentences = 3.980 Xintentional = 33 Sintentional = 2.507 (Xsentences - Xintentional) = -2.875 standard error of (Xsentences - Žintentional) = 1.662 b. Construct an approximate 95% confidence interval for usentences - Mintentional Lower bound = Upper bound =

Answer 1

We know that

(X_bar_sentences - X_bar_intentional ​​​​​) = - 2.875

Standard error = SE (X_bar_sentences - X_bar_intentional​​​​​​) = 1.662

n1 = 8 ,n2 = 8

Df = n1 + n2 - 2

= 8 + 8 - 2

Df = 14

So 95% confidence interval for t

Therefore t_{$\alpha$/2,df} = t_0.025,14 = 2.145

Hence the 95% of confidence interval using formula is given by

CI=(X_bar_sentences- X_bar_intentional​​​​​) $\pm$ t_0.025,14 SE(X_bar_{sentences -} X_bar_intentional ​​​​​)

CI = - 2.875 $\pm$ 2.145 * 1.662

= - 2.875 $\pm$ 3.565

CI = - 2.875 - 3.565 and CI = - 2.874 + 3.565

= - 6.439 CI = 0.691

So 95 % confidence interval is (-6.439,0.691)

Lower bound = - 6.439

Upper bound = 0.691