Question

In a study of memory recall, eight students from a large psychology class were selected at random and given 10 minutes to memorize a list of 20 nonsense words. Each was asked to list as many of the words as he or she could remember both 1 hour and 24 hours later. The data are as shown in the accompanying table. Use these data to estimate the difference in mean number of words remembered after 1 hour and after 24 hours. Build and interpret a 90% confidence interval. It is safe to assume an approximate normal distribution.

1 Hour: 14 12 18 7 11 9 16 15

24 Hrs: 10 4 14 6 9  6 12 12

#1. all Hypothesis Tests must include all four steps, clearly labeled;

#2. all Confidence Intervals must include all output as well as the CI itself

#3. include which calculator function you used for each problem.

Anyone that could help answer this I would greatly appreciate it with an explanation please! Thanks!

Answer 1

Suppose, random variables X and Y denote number of

We have to use two sample z-test statistic.

Corresponding test statistics is given by

Here,

First sample size

Second sample size

We know,

Estimated difference in mean number of words remembered after 1 hour and after 24 hours is 3.625.

Based on given data, 90% confidence interval of difference in mean number of words remembered after 1 hour and after 24 hours is (0.970021, 6.279979).

This confidence interval interpretates that if we calculate confidence intervals in this manner based on different sets of sample values, on average 90% of those confidence intervals contain the true value of difference in mean number of words remembered after 1 hour and after 24 hours in population.