1. The command "rnorm" generates random numbers from a normal distribution. The numbers are based on the normal distribution.
   1. Please show me how to create a vector of 10 numbers using the mean of 100 and a standard deviation of 1. Find the mean and standard deviation of the vector. (please cut and paste the computation formulas)
   2. Repeat the process from above, but change the standard deviation from 1 to 10. Find the mean and standard deviation of the new vector. Characterize the change. (What happened?) What does that say about scores with larger variations?Please cut and paste the output here.
   3. Repeat the process from above, but now change the number of output elements from 10 to 100. Characterize the change.(What happened?) What does that say about sample size?
2. A researcher wants to know if people on vacation, engage in an "inner dialogue" less than when working.The researcher selects a starts by obtaining a sample of 10 individuals who sare about to go on a week's vacation and agree to note (on an app) each time they "hear" themselves mentally talking. Each person in the sample is asked to keep a log for the week. The daily average instances (based on the week) appears below.

Please show me how to create a vector with the following observations

50, 40, 46, 49, 40, 58, 45, 47, 46, 43

Complete a one-sample t-test where the population mean is 50. (please cut and paste the computation formulas.)

1. What is the t-value?

2. What is the p-value?

3. What is the interpretation of the Null Hypothesis Significance Test?

4. This is a one-tailed t-test. In which direction (as compared to the mean)?

5. Could this experiment be converted to a two-tailed t-test? If so, state the hypothesis.

1. From the experiment in (2), the researcher also obtains data from a second sample (of the same size) from individuals during a regular week of work. The daily average instances (based on a week of data) of inner dialogue appear below.

Please show me how to create a vector with the following observations

53, 40, 51, 50,43, 62, 49, 47, 51, 39

Please show me how to create a two-sample independent t-test of your first vector against the second. (please cut and paste the computation formulas.)

1. What is the t-value?
2. What is the p-value?
3. What is the interpretation of the Null Hypothesis Significance Test?
4. This is a one-tailed t-test. In which direction (as compared to the mean)?
5. Could this experiment be converted to a two-tailed t-test? If so, state the hypothesis

1. Please redo the t-test above, but instead of a two-sample, independent t-test, please show how to compute the t-test as apaired samples t-test. (Assume that the same people are measured during vacation and then again at a later time during a workweek. Please cut and paste the computation formulas.)
   1. What is the t-value?
   2. What is the p-value?
   3. What is the interpretation of the Null Hypothesis Significance Test?
   4. Compared to the two-sample, independent t-test, what changed? What explains the change?