
Concept explainers
You are going to use the random number generator to generate different types of samples from the data. This table displays six sets of quiz scores (each quiz counts 10 points) for an elementary statistics class.
Table 1.6
#1 | #2 | #3 | #4 | #5 | #6 |
5 | 7 | 10 | 9 | 8 | 3 |
10 | 5 | 9 | 8 | 7 | 6 |
9 | 10 | 8 | 6 | 7 | 9 |
9 | 10 | 10 | 9 | 8 | 9 |
7 | 8 | 9 | 5 | 7 | 4 |
9 | 9 | 9 | 10 | 8 | 7 |
7 | 7 | 10 | 9 | 8 | 8 |
8 | 8 | 9 | 10 | 8 | 8 |
9 | 7 | 8 | 7 | 7 | 8 |
8 | 8 | 10 | 9 | 8 | 7 |
Instructions: Use the Random Number Generator to pick samples.
1. Create a stratified sample by column. Pick three quiz scores randomly from each column.
Number each row one through ten.
On yotu calculator, press Math and anow over to PRB.
For column 1, Press 5:randlnt( and enter 1,10). Press ENTER. Record the number. Press ENTER 2 more times (even the repeats). Record these numbers. Record the three quiz scores in column one that conespond to these three numbers.
Repeat for columns two through six.
These 18 quiz scores aje a stratified sample.
2. Create a cluster sample by picking two of the columns. Use the column numbers: one through six. Press MATH and arrow over to PRB.
Press 5:randlnt( and enter 1,6). Press ENTER. Record the number. Press ENTER and record that number.
The two numbers are for two of the columns.
The quiz scores (20 of them) In these 2 columns are the cluster sample.
3. Create a simple random sample of 15 quiz scores.
Use the numbeiing one through 60.
• Press MATH. Arrow over to PRB. Press 5:randlnt( and enter 1, 60).
Press ENTER 15 times and record the numbers.
Record the quiz scores that correspond to these numbers.
These 15 quiz scores are the systematic sample.
Create a systematic sample of 12 quiz scores. Use the numbering one through 60.
Press MATH. Arrow over to PRB. Press S:randlnt( and enter 1, 60).
Press ENTER. Record the number and the first quiz score. From that number, count ten quiz scores and record that quiz score. Keep counting ten quiz scores and recording the quiz score until you have a sample of 12 quiz scores. You may wrap around (go back to the beginning).

Trending nowThis is a popular solution!

Chapter 1 Solutions
Introductory Statistics
Additional Math Textbook Solutions
Introductory Statistics
Elementary Statistics (13th Edition)
Calculus: Early Transcendentals (2nd Edition)
Elementary Statistics: Picturing the World (7th Edition)
Basic Business Statistics, Student Value Edition
- 4. Linear Regression - Model Assumptions and Interpretation A real estate analyst is studying how house prices (Y) are related to house size in square feet (X). A simple linear regression model is proposed: The analyst fits the model and obtains: • Ŷ50,000+150X YBoB₁X + € • R² = 0.76 • Residuals show a fan-shaped pattern when plotted against fitted values. Questions: a) Interpret the slope coefficient in context. b) Explain what the R² value tells us about the model's performance. c) Based on the residual pattern, what regression assumption is likely violated? What might be the consequence? d) Suggest at least two remedies to improve the model, based on the residual analysis.arrow_forward5. Probability Distributions – Continuous Random Variables A factory machine produces metal rods whose lengths (in cm) follow a continuous uniform distribution on the interval [98, 102]. Questions: a) Define the probability density function (PDF) of the rod length.b) Calculate the probability that a randomly selected rod is shorter than 99 cm.c) Determine the expected value and variance of rod lengths.d) If a sample of 25 rods is selected, what is the probability that their average length is between 99.5 cm and 100.5 cm? Justify your answer using the appropriate distribution.arrow_forward2. Hypothesis Testing - Two Sample Means A nutritionist is investigating the effect of two different diet programs, A and B, on weight loss. Two independent samples of adults were randomly assigned to each diet for 12 weeks. The weight losses (in kg) are normally distributed. Sample A: n = 35, 4.8, s = 1.2 Sample B: n=40, 4.3, 8 = 1.0 Questions: a) State the null and alternative hypotheses to test whether there is a significant difference in mean weight loss between the two diet programs. b) Perform a hypothesis test at the 5% significance level and interpret the result. c) Compute a 95% confidence interval for the difference in means and interpret it. d) Discuss assumptions of this test and explain how violations of these assumptions could impact the results.arrow_forward
- 1. Sampling Distribution and the Central Limit Theorem A company produces batteries with a mean lifetime of 300 hours and a standard deviation of 50 hours. The lifetimes are not normally distributed—they are right-skewed due to some batteries lasting unusually long. Suppose a quality control analyst selects a random sample of 64 batteries from a large production batch. Questions: a) Explain whether the distribution of sample means will be approximately normal. Justify your answer using the Central Limit Theorem. b) Compute the mean and standard deviation of the sampling distribution of the sample mean. c) What is the probability that the sample mean lifetime of the 64 batteries exceeds 310 hours? d) Discuss how the sample size affects the shape and variability of the sampling distribution.arrow_forwardA biologist is investigating the effect of potential plant hormones by treating 20 stem segments. At the end of the observation period he computes the following length averages: Compound X = 1.18 Compound Y = 1.17 Based on these mean values he concludes that there are no treatment differences. 1) Are you satisfied with his conclusion? Why or why not? 2) If he asked you for help in analyzing these data, what statistical method would you suggest that he use to come to a meaningful conclusion about his data and why? 3) Are there any other questions you would ask him regarding his experiment, data collection, and analysis methods?arrow_forwardBusinessarrow_forward
- What is the solution and answer to question?arrow_forwardTo: [Boss's Name] From: Nathaniel D Sain Date: 4/5/2025 Subject: Decision Analysis for Business Scenario Introduction to the Business Scenario Our delivery services business has been experiencing steady growth, leading to an increased demand for faster and more efficient deliveries. To meet this demand, we must decide on the best strategy to expand our fleet. The three possible alternatives under consideration are purchasing new delivery vehicles, leasing vehicles, or partnering with third-party drivers. The decision must account for various external factors, including fuel price fluctuations, demand stability, and competition growth, which we categorize as the states of nature. Each alternative presents unique advantages and challenges, and our goal is to select the most viable option using a structured decision-making approach. Alternatives and States of Nature The three alternatives for fleet expansion were chosen based on their cost implications, operational efficiency, and…arrow_forwardBusinessarrow_forward
- Why researchers are interested in describing measures of the center and measures of variation of a data set?arrow_forwardWHAT IS THE SOLUTION?arrow_forwardThe following ordered data list shows the data speeds for cell phones used by a telephone company at an airport: A. Calculate the Measures of Central Tendency from the ungrouped data list. B. Group the data in an appropriate frequency table. C. Calculate the Measures of Central Tendency using the table in point B. 0.8 1.4 1.8 1.9 3.2 3.6 4.5 4.5 4.6 6.2 6.5 7.7 7.9 9.9 10.2 10.3 10.9 11.1 11.1 11.6 11.8 12.0 13.1 13.5 13.7 14.1 14.2 14.7 15.0 15.1 15.5 15.8 16.0 17.5 18.2 20.2 21.1 21.5 22.2 22.4 23.1 24.5 25.7 28.5 34.6 38.5 43.0 55.6 71.3 77.8arrow_forward
- Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGALGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
- Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt





