Exercise I: One hundred subjects in a psychological study had a mean score of \( M=35 \) on a test instrument designed to measure anger. The standard deviation of the \( n=100 \) test scores was \( \sigma=10 \). Find: a. A \( 99 \% \) confidence interval for the mean of the population the sample was selected. b. A \( 95 \% \) confidence interval for the mean of the population the sample was selected.

You wish to test the following claim \( \left(H_{a}\right) \) at a significance level of \( \alpha=0.002 \). \[ \begin{array}{l}H_{a}: \mu_{1}=\mu_{2} \\ H_{a}: \mu_{1}>\mu_{2}\end{array} \] You believe both populations are normally distributed, but you do not know the standard deviations for either. However, you also have no reason to believe the variances of the two populations are not equal. You obtain a sample of size \( n_{1}=20 \) with a mean of \( M_{1}=51.3 \) and a standard deviation of \( S D_{1}=13.2 \) from the first population. You obtain a sample of size \( n_{2}=23 \) with a mean of \( M_{2}=38.8 \) and a standard deviation of \( S D_{2}=8.7 \) from the second population.

20. Some researchers claim that herbal supplements such as ginseng or ginkgo biloba enhance human memory. To test this claim, a researcher selects a sample of \( n=25 \) college students. Each student is given a ginkgo biloba supplement daily for 6 weeks and then all of the participants are given a standardized memory test. Scores on the normalized test are \( \mu=70 \) and standard deviation of 15 . The sample of 25 students had a mean score of \( M=75 \). (8 points) a. Do the data indicate a significant effect of the herb on memory? Use a two-tailed test with \( \alpha=0.05 \). (Show all steps.)

3. Box and Whisker Plot: Draw a box and whisker plot for the data provided and identify any outliers. \( 12,17,13,14,12,16,18,29,15,14,12,17,13,14,12,16,18,29,15,14,12,17,13 \), \( 14,12,16,18,29,15,14 \)

2. Scatter Plot and Correlation: Consider the following data points representing the number of hours studied \( (x) \) and the marks obtained \( (y) \) : \[ (1,50),(2,55),(3,60),(4,65),(5,75) \] wa scatter plot and determine whether the relationship between hours studied and marks ositive, negative, or none.

g) Of the " \( r \) " values below which would be reasonable for the scatterplot above? Explai your reasoning. \( r=-.94 \quad r=-.32 \quad r=.32 \quad r=.94 \)