An Office Manager Has Several Computers Running Distributed

An Office Manager Has Several Computers Running Distributed Programs

An office manager has several computers running distributed programs. Because of the demands on the system, the machines may crash at various times during the day and require a hard reset. The probability distribution for the number of times a randomly selected machine crashes during a day, X, is given in the table. Fill in the blanks. 1.

The mean for the number of crashes by a single machine during a day is _(Answer 1)_. (Give your answer to two decimal places.) 2. The variance for the number of crashes by a single machine during a day is _(Answer 2)_. (Give your answer to four decimal places.) 3. The standard deviation for the number of crashes by a single machine during a day is _(Answer 3)_. (Give your answer to two decimal places.) 4. Suppose n = 2 machines are selected at random and the statistic T represents the total number of crashes for the two machines. Then mean of T is _(Answer 4)_.

5. The variance of T is _(Answer 5)_. (Give your answer to four decimal places.) 6. The standard deviation of T is _(Answer 6)_. (Give your answer to four decimal places.) A researcher plans a study in which a crucial step is offering participants a food reward. It is important that the three food rewards be equal in appeal. Thus, a pre-study was designed in which participants were asked which of the rewards they preferred.

Of the 60 participants, 16 preferred cupcakes, 26 preferred candy bars, and 18 favored dried apricots. Do these scores suggest that the different foods are differentially preferred by people in general? (Use the .05 significance level.) a. Use the five steps of hypothesis testing. b. Sketch the distribution involved. c. Explain your findings.

2. A high school principal wanted to know if the racial makeup of her teachers mirrored that of the student body. The student body broke down into 47% White, 28% Latino, 15% African American, and 10% other. Of the 65 teachers, 42 were White, 4 were Latino, 15 were African American, and 4 were Other. Do these results suggest that the racial makeup of the faculty members is different from that of the students? (Use the .05 significance level.) Use the five steps of hypothesis testing and explain your findings.

3. Please make up and discuss research examples corresponding to the various techniques introduced throughout this course. Describe a plausible study for each of the following statistical procedures, indicating how it would apply and what results you would predict. Also include information about the number of participants you would assess and how you would go about estimating effect size and statistical power (when relevant). a. correlation b. multiple regression c. t test for independent means d. t test for dependent means e. ANOVA f. chi square for goodness of fit g. chi-square test for independence

Paper For Above instruction

The given assignment encompasses multiple complex statistical problems ranging from probability distributions, hypothesis testing, and descriptive as well as inferential statistics for categorical data across different scenarios. The first part involves calculating the mean, variance, and standard deviation for the crashes experienced by computers in a day, assuming the probability distribution is provided. Subsequently, it entails analyzing the combined crashes for two machines, determining the mean, variance, and standard deviation for the total number of crashes using properties of expected value and variance for independent random variables.

The second section involves conducting a chi-square goodness-of-fit test to evaluate whether participants’ food preferences are uniformly distributed. This includes formulating hypotheses, calculating expected frequencies, and computing the chi-square statistic, followed by interpreting the results to assess if the observed preferences significantly differ from a uniform distribution at the 0.05 significance level. Additionally, visualizing the chi-square distribution helps in understanding the likelihood of the observed data under the null hypothesis.

The third part tasks the researcher with evaluating the racial composition of faculty against the student body using chi-square tests of independence. This involves calculating the expected counts based on proportions and total counts, then performing the chi-square test to determine if the differences are statistically significant — indicating whether faculty demographics reflect those of the students or not.

Finally, the assignment requests the applicant to creatively fabricate research scenarios exemplifying each statistical technique introduced in the course. These include correlation, multiple regression, t-tests (independent and dependent), ANOVA, and chi-square tests (goodness-of-fit and independence). For each, a hypothetical study description, appropriate sample size, effect size estimation, and power considerations are required to demonstrate comprehension and applied understanding of these methodologies.

References

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