
Concept explainers
a.
Find the possible number of different
a.

Answer to Problem 9E
The possible number of different samples of size 3 is 20.
Explanation of Solution
From the given information, the number of cases each partner actually tried in court is 3, 6, 3, 3, 0 and 1.
The possible number of different samples of size 3 is obtained by using the following formula:
Substitute 6 for the N and 3 for the n
Then,
Thus, the possible number of different samples of size 3 is 20.
b.
Give the all possible samples of size 3.
Find the
b.

Answer to Problem 9E
All possible samples of size 3 are
The mean of each sample is 4, 4, 3, 2, 2, 2, 2, 1.33, 1.33, 1.33, 4, 3, 3, 2.33, 3, 3.33, 2.33, 2.33, 2.33, 3.33 and 3.33.
Explanation of Solution
The mean is calculated by using the following formula:
Sample | Mean |
Thus, all possible samples of size 3 are
Thus, the mean of each sample is 4, 4, 3, 2, 2, 2, 1.33, 1.33, 1.33, 4, 3, 3, 2.33, 3, 3.33, 2.33, 2.33, 2.33, 3.33 and 3.33.
c.
Compare the mean of the sample means to the population mean.
c.

Answer to Problem 9E
The mean of the distribution of the sample means is equal to the population mean.
Explanation of Solution
The mean of the sample means is calculated as follows:
Population mean is calculated as follows:
The population mean is 2.67.
Comparison:
The mean of the distribution of the sample mean is 6.8 and the population mean is 6.8. The two means are exactly same.
Thus, the mean of the distribution of the sample means is equal to the population mean.
d.
Give the comparison of the dispersion in sample means with that of the population.
d.

Answer to Problem 9E
The dispersion in the population is greater than with that of the sample mean.
Explanation of Solution
A frequency distribution for the sample means is obtained as follows:
Let
Sample mean | f | Probability |
1.33 | 3 | |
2 | 3 | |
2.33 | 4 | |
3 | 4 | |
3.33 | 3 | |
4 | 3 | |
Software procedure:
Step-by-step procedure to obtain the bar chart using MINITAB:
- Choose Graph > Bar chart.
- Under Bars represent, enter select Values from a table.
- Under One column of values select Simple.
- Click on OK.
- Under Graph variables enter probability and under categorical variable enter sample mean.
- Click OK.
Output using MINITAB software is given below:
From the bar chart it can be observed that the shape of the distribution of the sample means is normal.
Thus, the shape of the distribution of the sample means is normal.
From the given information, the number of cases by the six partners each is 3, 6, 3, 3, 0 and 1.
Number of cases | f | Probability |
0 | 1 | |
1 | 1 | |
3 | 3 | |
6 | 1 | |
Software procedure:
Step-by-step procedure to obtain the bar chart using MINITAB:
- Choose Graph > Bar chart.
- Under Bars represent, enter select Values from a table.
- Under One column of values select Simple.
- Click on OK.
- Under Graph variables enter probability and under categorical variable enter Number of cases.
- Click OK.
Output using MINITAB software is given below:
From the bar chart it can be observed that the shape of the population distribution is uniform.
Thus, the shape of the population distribution is uniform.
The population values are 3, 6, 3, 3, 0 and 1. From the part b, the mean of each sample is 4, 4, 3, 2, 2, 2, 1.33, 1.33, 1.33, 4, 3, 3, 2.33, 3, 3.33, 2.33, 2.33, 2.33, 3.33 and 3.33.
The population values are between 0 and 6. The sample mean values are between 1.33 and 4.
Thus, the dispersion in the population is greater than with that of the sample mean.
Want to see more full solutions like this?
Chapter 8 Solutions
Statistical Techniques in Business and Economics
- Pls help asaparrow_forwardSolve the following LP problem using the Extreme Point Theorem: Subject to: Maximize Z-6+4y 2+y≤8 2x + y ≤10 2,y20 Solve it using the graphical method. Guidelines for preparation for the teacher's questions: Understand the basics of Linear Programming (LP) 1. Know how to formulate an LP model. 2. Be able to identify decision variables, objective functions, and constraints. Be comfortable with graphical solutions 3. Know how to plot feasible regions and find extreme points. 4. Understand how constraints affect the solution space. Understand the Extreme Point Theorem 5. Know why solutions always occur at extreme points. 6. Be able to explain how optimization changes with different constraints. Think about real-world implications 7. Consider how removing or modifying constraints affects the solution. 8. Be prepared to explain why LP problems are used in business, economics, and operations research.arrow_forwardged the variance for group 1) Different groups of male stalk-eyed flies were raised on different diets: a high nutrient corn diet vs. a low nutrient cotton wool diet. Investigators wanted to see if diet quality influenced eye-stalk length. They obtained the following data: d Diet Sample Mean Eye-stalk Length Variance in Eye-stalk d size, n (mm) Length (mm²) Corn (group 1) 21 2.05 0.0558 Cotton (group 2) 24 1.54 0.0812 =205-1.54-05T a) Construct a 95% confidence interval for the difference in mean eye-stalk length between the two diets (e.g., use group 1 - group 2).arrow_forward
- An article in Business Week discussed the large spread between the federal funds rate and the average credit card rate. The table below is a frequency distribution of the credit card rate charged by the top 100 issuers. Credit Card Rates Credit Card Rate Frequency 18% -23% 19 17% -17.9% 16 16% -16.9% 31 15% -15.9% 26 14% -14.9% Copy Data 8 Step 1 of 2: Calculate the average credit card rate charged by the top 100 issuers based on the frequency distribution. Round your answer to two decimal places.arrow_forwardPlease could you check my answersarrow_forwardLet Y₁, Y2,, Yy be random variables from an Exponential distribution with unknown mean 0. Let Ô be the maximum likelihood estimates for 0. The probability density function of y; is given by P(Yi; 0) = 0, yi≥ 0. The maximum likelihood estimate is given as follows: Select one: = n Σ19 1 Σ19 n-1 Σ19: n² Σ1arrow_forward
- Please could you help me answer parts d and e. Thanksarrow_forwardWhen fitting the model E[Y] = Bo+B1x1,i + B2x2; to a set of n = 25 observations, the following results were obtained using the general linear model notation: and 25 219 10232 551 XTX = 219 10232 3055 133899 133899 6725688, XTY 7361 337051 (XX)-- 0.1132 -0.0044 -0.00008 -0.0044 0.0027 -0.00004 -0.00008 -0.00004 0.00000129, Construct a multiple linear regression model Yin terms of the explanatory variables 1,i, x2,i- a) What is the value of the least squares estimate of the regression coefficient for 1,+? Give your answer correct to 3 decimal places. B1 b) Given that SSR = 5550, and SST=5784. Calculate the value of the MSg correct to 2 decimal places. c) What is the F statistics for this model correct to 2 decimal places?arrow_forwardCalculate the sample mean and sample variance for the following frequency distribution of heart rates for a sample of American adults. If necessary, round to one more decimal place than the largest number of decimal places given in the data. Heart Rates in Beats per Minute Class Frequency 51-58 5 59-66 8 67-74 9 75-82 7 83-90 8arrow_forward
- can someone solvearrow_forwardQUAT6221wA1 Accessibility Mode Immersiv Q.1.2 Match the definition in column X with the correct term in column Y. Two marks will be awarded for each correct answer. (20) COLUMN X Q.1.2.1 COLUMN Y Condenses sample data into a few summary A. Statistics measures Q.1.2.2 The collection of all possible observations that exist for the random variable under study. B. Descriptive statistics Q.1.2.3 Describes a characteristic of a sample. C. Ordinal-scaled data Q.1.2.4 The actual values or outcomes are recorded on a random variable. D. Inferential statistics 0.1.2.5 Categorical data, where the categories have an implied ranking. E. Data Q.1.2.6 A set of mathematically based tools & techniques that transform raw data into F. Statistical modelling information to support effective decision- making. 45 Q Search 28 # 00 8 LO 1 f F10 Prise 11+arrow_forwardStudents - Term 1 - Def X W QUAT6221wA1.docx X C Chat - Learn with Chegg | Cheg X | + w:/r/sites/TertiaryStudents/_layouts/15/Doc.aspx?sourcedoc=%7B2759DFAB-EA5E-4526-9991-9087A973B894% QUAT6221wA1 Accessibility Mode பg Immer The following table indicates the unit prices (in Rands) and quantities of three consumer products to be held in a supermarket warehouse in Lenasia over the time period from April to July 2025. APRIL 2025 JULY 2025 PRODUCT Unit Price (po) Quantity (q0)) Unit Price (p₁) Quantity (q1) Mineral Water R23.70 403 R25.70 423 H&S Shampoo R77.00 922 R79.40 899 Toilet Paper R106.50 725 R104.70 730 The Independent Institute of Education (Pty) Ltd 2025 Q Search L W f Page 7 of 9arrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin HarcourtHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL


