sampling and simulation | Practice Problems, Examples & Solutions

Common Sampling Techniques

Elementary Statistics

refer to Data Set 12 in Appendix $B$ and we the amounts of electricity consumed (in $k W b$ ) in the author's home. Let each subgroup consist of the six amounts within the same year, so that there are eight subgroups with six amounts in each subgroup.
Energy Consumption: Notation After finding the values of the mean and range for each year, find the values of $\bar{x}$ and $\bar{R}$ Then find the values of LCL and UCL for an $R$ chart and for an $\bar{x}$ chart.

Statistical Process Control

Control Charts for Variation and Mean

08:11

Elementary Statistics

we the data in the following table, which lists carbon dioxide concentrations (in parts per million) for each year from 1880 to 2009 , will projected values used for the last four years. Atmospheric carbon dioxide is believed to be the result of human activity and a major contributor to the greenhouse effect that is at least partly responsible for global warming.
TABLE CANT COPY
Carbon Dioxide: Notation After finding the values of the mean and range for each decade, find the values of $\bar{x},$ and $\bar{R}$ Also find the values of $L C L$ and UCL for an $R$ chart, and find the values of LCL and UCL for an $\bar{x}$ chart.

Statistical Process Control

Control Charts for Variation and Mean

02:00

Elementary Statistics

Product Specs Consider process data consisting of the amounts of Coke (in oz) in randomly selected cans of regular Coke. Recent $\bar{x}$ and $R$ control charts show that the process of filling cans of Coke is within statistical control. Does being within statistical control indicate that cans of Coke labeled 12 ounces actually have amounts of Coke that are reasonably dose to 12 oz? Why or why not?

Statistical Process Control

Control Charts for Variation and Mean

Surveys and Questionnaire Design

10 Practice Problems

03:30

Elementary Statistics

Constructing Control Charts for $p$. We the given process data to construct a control chart for $p$. In each case, we the three out-of-control criteria listed in Section $14-2$ and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply.
In each of 20 recent and consecutive years, 10,000 people were randomly selected and the numbers of births they generated were found, with the results given below. How might the results be explained? (The listed values are based on data from the U.S. Department of Health and Human Services, and they are the most recent values available at the time of this writing.)
157 160 164 167 167 162 158 154 150 146 144 142 143 142 144 141 139 141 140 140

Statistical Process Control

Control Charts for Attributes

03:18

Elementary Statistics

Constructing Control Charts for $p$. We the given process data to construct a control chart for $p$. In each case, we the three out-of-control criteria listed in Section $14-2$ and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply.
$p$ Chart for College Enrollment In each of 15 recent and consecutive years, 1000 high school completer were randomly selected and the number who enrolled in college was determined, with the results listed below. Does the $p$ chart indicate that such college enrollments are high enough? (The values are based on data from the U.S. National Center for Education Statistics, and they are the most recent values available at the time of this writing.)
$\begin{array}{rlllllllllll}601 & 625 & 619 & 626 & 619 & 619 & 650 & 670 & 656 & 629 & 633 & 618 & 652 & 639 & 667\end{array}$

Statistical Process Control

Control Charts for Attributes

01:05

Elementary Statistics

Determining Whether a Process Is in Control.examine the given control chart for $p$ and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply.
(FIGURE CANNOT COPY)

Statistical Process Control

Control Charts for Attributes

Simulation Techniques and the Monte Carlo Method

14 Practice Problems

0:00

Mathematical Statistics with Applications

Refer to Exercises 13.31 and $13.47 .$ Because method 4 is the most expensive, it is desired to compare it to the other three. Construct confidence intervals for the differences $\mu_{1}-\mu_{4}, \mu_{2}-\mu_{4}$ and $\mu_{3}-\mu_{4}$ so that the simultaneous confidence coefficient is at least. 95 .

The Analysis of Variance

Simultaneous Confidence Intervals for More Than One Parameter

0:00

Mathematical Statistics with Applications

Refer to Example $13.9 .$ The six confidence intervals for $\mu_{i}-\mu_{i^{\prime}}$ were obtained by using an approximate (due to the limitation of the information in Table 5 , Appendix 3 ) value for $t_{.00417}$ Why do some of the intervals differ in length?

The Analysis of Variance

Simultaneous Confidence Intervals for More Than One Parameter

02:16

Elementary Statistics

Statistical Literacy and Critical Thinking
Monitoring Aspirin The labels on a bottle of Bayer aspirin indicate that the tablets contain $325 \mathrm{mg}$ of aspirin. Suppose manufacturing specifications require that tablets have between $315 \mathrm{mg}$ and $335 \mathrm{mg}$ of aspirin, so a tablet is considered to be a defect if the amount of aspirin is not within those limits. If the proportion of defects is monitored with a $p$ chart and is found to be within statistical control, can we conclude that almost all of the tablets meet the manufacturing specifications? Why or why not?

Statistical Process Control

Control Charts for Attributes