1. One sample has SS=100 and a second sample has SS=124.a. If n=8 for both samples, find each of the sample variances, and calculate the pooled variance. Because the samples are the same size, you should find that the pooled variance is exactly halfway between the two sample variances.b. Now assume the n=8 for the first sample and n=4 for the second. Again, calculate the two sample variances and the pooled variance. You should find that the pooled variance is closer to the variance for the larger sample.2. Two separate samples receive different treatments. After treatment, the first sample has n=10 with SS=500, and the second sample has n=6 with SS=340.a. Compute pooled variance for the two samples.b. Calculate the estimated standard error for the sample mean difference.c. If the sample mean difference is 8 points, is this enough to reject the null hypothesis using a two-tailed test with α=.05?3. In a recent study, Piff, Kraus, Cote, Cheng and Keitner (2010) found that people from lower social economic classes tend to display greater prosocial behavior than their higher class counterparts. In one part of the study, participants played a game with an anonymous partner. Part of the game involved sharing points with the partner. The lower economic class participants were significantly more generous with their points compared with the upper class individuals. Results similar to those found in the study, show that n=12 lower class participants shared an average of M=5.2 points with SS=11.91, compared to an average of M=4.3 with SS=9.21 for the n=12 upper class participants.a. Are the data sufficient to conclude that there is a significant mean difference between the two economic populations? Use a two-tailed test with α=.01.b. Construct an 90% confidence interval to estimate the size of the population mean difference.4. Recent research has demonstrated that music-based physical training for elderly peopld can improve balance and walking efficiency and reduce the risk of falls (Trombetti et al., 2011). As part of the training, participants walked in time to music and responded to changes in the music’s rhythm during a 1-hour per week exercise program. After 6 months, participants in the training group increased their walking speed and their stride length compared to individuals in the control group. The following data are similar to the results obtained in the study.Exercise Group Control GroupStride length Stride length24, 25, 22, 24 26, 23, 20, 2326, 17, 21, 22 20, 16, 21, 1722, 19, 24, 23 18, 23, 16, 2023, 28, 25, 23 25, 19, 17, 16a. Do the results indicate a significant difference in the stride length for the two groups? Use a two-tailed test with α=.05.5. Research has shown that people are more likely to show dishonest and self-interested behaviors in darkness than in a well-lit environment (Zhong, Bohns, & Gino, 2010). In one experiment, participants were given a set of 20 puzzles and were paid $0.50 for each one solved in a 5-minute period. However, the participants reported their performance and there was no obvious method for checking their honesty. Thus, the task provided a clear opportunity to cheat and receive undeserved money.