Compute the mean and standard deviation for the following sample of $n=5$ scores: $70,72,71,80$, and 72. Hint: To simplify the arithmetic, you can subtract 70 points from each score to obtain a new sample. Then, compute the mean and standard deviation for the new sample. Finally, make the correction for having added 70 points to each score to find the mean and standard deviation for the original sample.

Compute the sample mean and standard deviation for each index.

Calculate $S S$, variance, and standard deviation for the following sample of $n=5$ scores: 2, 9, 5, 5, 9.

a. Use the technology of your choice to obtain boxplots for the data sets, using the same scale. b. compare the data sets by using your results from part (a), paying special attention to center and variation. L. Petersen et al. evaluated the effects of integrated treatment for patients with a first episode of psychotic illness in the paper "A Randomised Multicentre Trial of Integrated Versus Standard Treatment for Patients with a First Episode of Psychotic Illness". Part of the study included a questionnaire that was designed to measure client satisfaction for both the integrated treatment and a standard treatment. The data on the WeissStats site are based on the results of the client questionnaire.

Sample annual salaries (in thousands of dollars) for employees at a company are listed.

42 36 48 51 39 39 42 36 48 33 39 42 45

(a) Find the sample mean and the sample standard deviation.

(b) Each employee in the sample receives a 5% raise. Find the sample mean and the sample standard deviation for the revised data set.

(c) To calculate the monthly salary, divide each original salary by 12. Find the sample mean and the sample standard deviation for the revised data set.

(d) What can you conclude from the results of (a), (b), and (c)?

The quantitative data set under consideration has roughly a bell-shaped distribution. Apply the empirical rule to solve each exercise. The data set has size 60. Approximately how many observations lie within three standard deviations to either side of the mean?

Sample annual salaries (in thousands of dollars) for employees at a company are listed.

$$48, 45,62,59,32,32,48,45,62,26,59,48,49.$$

Each employee in the sample is given a $5\%$ raise. Find the sample mean and sample standard deviation for the revised data set.

The quantitative data set under consideration has roughly a bell-shaped distribution. Apply the empirical rule to solve each exercise. The data set has mean 15 and standard deviation 2. Approximately what percentage of the observations lie between 13 and 17?

Apply Chebyshev's rule to solve. A quantitative data set has size 80. At least how many observations lie within two standard deviations to either side of the mean?

For the following sample of $n=6$ scores: $0,11,5,10,5,5$

a. Sketch a histogram showing the sample distribution. b. Locate the value of the sample mean in your sketch, and make an estimate of the standard deviation (as done in the previous example). c. Compute $S S$, variance, and standard deviation for the sample. (How well does your estimate compare with the actual value of $s$ ?)

The quantitative data set under consideration has roughly a bell-shaped distribution. Apply the empirical rule to solve each exercise. The data set has size 80. Approximately how many observations lie within two standard deviations to either side of the mean?

You are applying for two jobs, and you estimate the probability of getting an offer for the first job is 0.70 while the probability of getting an offer for the second job is 0.80. Assume the job offers are independent. Compute the probability of getting offers for both jobs. How does this probability compare to the probability of getting each individual job offer?

You are applying for two jobs, and you estimate the probability of getting an offer for the first job is 0.70 while the probability of getting an offer for the second job is 0.80. Assume the job offers are independent. Compute the probability of getting an offer for either the first or the second job. How does this probability compare to the probability of getting each individual job offer? Does it seem worthwhile to apply for both jobs? Explain.

You are applying for jobs at two companies. Company A offers starting salaries with $\mu$ = 31, 100 and $\sigma$ = 100. Company B offers starting salaries with $\mu$ = 31, 00 and $\sigma$ = 5000. From which company are you more likely to get an offer of 3, 100 or more? Explain your reasoning.