Question

Based on previous research and sound theoretical considerations, an experimental psychologist believes that memory for pictures is superior to memory for words. To test this hypothesis, the psychologist performs an experiment in which students from a introductory psychology class are used as subjects. Eight randomly selected students view 30 slides with nouns printed on them, and another group of eight randomly selected students view 30 slides with actual pictures of the same nouns. Each slide contains either one noun or one picture and is viewed for 4 seconds. After viewing the slides, students are given a recall test. The number of correctly recalled items is recorded. The data collected are given below.

# of pictures recalled: 18 21 14 25 23 19 26 15

# of nouns recalled: 12 9 21 17 16 10 19 22

a. Describe (1) the independent variable and its levels, and (2) the dependent variable and its scale of measurement.

b. Describe the null and alternative hypotheses for the study described.

c. Using Excel, conduct a statistical test of the null hypothesis at p = .05. Be sure to properly state your statistical conclusion.

d. Provide an interpretation of your statistical conclusion in part C.

e. What type of statistical error might you have made in part C?

f. Obtain the 95% confidence interval using the obtained statistic.

g. Provide an interpretation of the confidence interval obtained in part f.

h. Does the confidence interval obtained support your statistical conclusion? Explain your answer.

Answer 1

a) In the above question, we are trying to see the impact of the type of slide shown (noun or pictures) on the memory of the students. So, here independent variable becomes the "type of Slides shown" and its levels are 'Nouns' and "pictures'.

Dependent variable would be the 'memory' in the form of 'number of correctly recalled items'. Its scale of measurement is ratio as there is a presence of absolute zero in the sense that there could be a student who can not recall any item.

b) Null hypothesis and Alternative hypothesis:

Null hypothesis means that there is no significant difference between the memory for pictures and memory of words

Alternative hypothesis means that memory for pictures is superior than memory of words ( thats why it is right tailed)

c) Since, we have two groups for comparison, we will apply t-test for difference between two groups. The formula for t-statistic is given below:

where are means of two samples respectively, and are the sample variances for both samples respectively with n1 and n2 being the sample sizes

We calculate sample variances by using the following formula

Using the above formula, we calculate

and means as

Now putting these values in the t formula, we get

t = 1.86

t calculated = 1.86, we compare this with t tabulated at 5% level of significance and 14 degrees of freedom (8+8-2)

t tabulated is 1.76 (One tailed value)

Conclusion: We see that t calculated is more than t tabulated, so we reject the null hypothesis at 5% level of significance.

d) Conclusion in part c) means that memory for pictures is superior than memory of words.

e) Type of statistical error would be type 1 error which means rejecting H0 when it is true.

f) 95% confidence interval for obtained statistic would be

Putting the values in the above, we

confidence interval as (0.244, 8.505)

g) Interpretation: The confidence interval obtained above means out of 100 samples, 95 times the unknown population parameter would lie in the confidence interval