
a.
Give all the possible samples of size 2.
Find the
a.

Answer to Problem 21CE
All possible samples of size 2 are
The mean of every sample is 1, 1.5, 2, 1.5, 2, 2.5, 2, 2.5 and 3.
Explanation of Solution
The mean is calculated by using the following formula:
Sample | Mean |
Thus, all possible samples of size 2 are
Thus, the mean of every sample is 1, 1.5, 2, 1.5, 2, 2.5, 2, 2.5 and 3.
b.
Compute the means of the distribution of the sample mean and the population mean.
Give the comparison of the mean of the distribution of the sample mean with the population mean.
b.

Answer to Problem 21CE
The means of the distribution of the sample mean and the population mean are 2 and 2.
The mean of the distribution of the sample means is equal to the population mean.
Explanation of Solution
Population mean is calculated as follows:
Then, the population mean is 2.
The mean of the sample means is calculated as follows:
Then, mean of the distribution of the sample mean is 2.
Thus, the means of the distribution of the sample mean and the population mean are 2 and 2.
Comparison:
The mean of the distribution of the sample mean is 2 and the population mean is 2. The two means are exactly same.
Thus, the mean of the distribution of the sample means is equal to the population mean.
c.
Give the dispersion of the population with that of the sample mean.
c.

Answer to Problem 21CE
The dispersion in the population is two times greater than that of the sample mean.
Explanation of Solution
The variance of the population is
The variance of the sample means is
Thus, the dispersion in the population is two times greater than that of the sample mean.
d.
Give the shapes of the two distributions.
d.

Answer to Problem 21CE
The shape of the population distribution is Uniform.
The shape of the distribution of the sample means is triangular.
Explanation of Solution
The frequency distribution of the population is:
Values | Frequency | Probability |
1 | 1 | |
2 | 1 | |
3 | 1 | |
Software procedure:
Step-by-step procedure to obtain the bar chart using MINITAB:
- Choose Stat > 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 Values.
- Click OK.
Output using MINITAB software is given below:
From the MINITAB output, it can be observed that the shape of the population distribution is uniform.
Thus, the shape of the population distribution is Uniform.
The frequency distribution of the sample means is:
Sample mean | Frequency | Probability |
1 | 1 | |
1.5 | 2 | |
2 | 3 | |
2.5 | 2 | |
3 | 1 | |
Software procedure:
Step-by-step procedure to obtain the bar chart using MINITAB:
- Choose Stat > 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 MINITAB output, it can be observed that the shape of the distribution of the sample means is triangular.
Thus, the shape of the distribution of the sample means is triangular.
Want to see more full solutions like this?
Chapter 8 Solutions
Statistical Techniques in Business and Economics
- QUAI6221wA1.docx X + int.com/:w:/r/sites/TertiaryStudents/_layouts/15/Doc.aspx?sourcedoc=%7B2759DFAB-EA5E-4526-9991-9087A973B894%7 26 QUAT6221wA1 Q.1.1.8 One advantage of primary data is that: (1) It is low quality (2) It is irrelevant to the purpose at hand (3) It is time-consuming to collect (4) None of the other options Accessibility Mode Immersive R Q.1.1.9 A sample of fifteen apples is selected from an orchard. We would refer to one of these apples as: (2) ھا (1) A parameter (2) A descriptive statistic (3) A statistical model A sampling unit Q.1.1.10 Categorical data, where the categories do not have implied ranking, is referred to as: (2) Search D (2) 1+ PrtSc Insert Delete F8 F10 F11 F12 Backspace 10 ENG USarrow_forwardepoint.com/:w:/r/sites/TertiaryStudents/_layouts/15/Doc.aspx?sourcedoc=%7B2759DFAB-EA5E-4526-9991-9087A 23;24; 25 R QUAT6221WA1 Accessibility Mode DE 2025 Q.1.1.4 Data obtained from outside an organisation is referred to as: (2) 45 (1) Outside data (2) External data (3) Primary data (4) Secondary data Q.1.1.5 Amongst other disadvantages, which type of data may not be problem-specific and/or may be out of date? W (2) E (1) Ordinal scaled data (2) Ratio scaled data (3) Quantitative, continuous data (4) None of the other options Search F8 F10 PrtSc Insert F11 F12 0 + /1 Backspaarrow_forward/r/sites/TertiaryStudents/_layouts/15/Doc.aspx?sourcedoc=%7B2759DFAB-EA5E-4526-9991-9087A973B894%7D&file=Qu Q.1.1.14 QUAT6221wA1 Accessibility Mode Immersive Reader You are the CFO of a company listed on the Johannesburg Stock Exchange. The annual financial statements published by your company would be viewed by yourself as: (1) External data (2) Internal data (3) Nominal data (4) Secondary data Q.1.1.15 Data relevancy refers to the fact that data selected for analysis must be: (2) Q Search (1) Checked for errors and outliers (2) Obtained online (3) Problem specific (4) Obtained using algorithms U E (2) 100% 高 W ENG A US F10 点 F11 社 F12 PrtSc 11 + Insert Delete Backspacearrow_forward
- A client of a commercial rose grower has been keeping records on the shelf-life of a rose. The client sent the following frequency distribution to the grower. Rose Shelf-Life Days of Shelf-Life Frequency fi 1-5 2 6-10 4 11-15 7 16-20 6 21-25 26-30 5 2 Step 2 of 2: Calculate the population standard deviation for the shelf-life. Round your answer to two decimal places, if necessary.arrow_forwardA market research firm used a sample of individuals to rate the purchase potential of a particular product before and after the individuals saw a new television commercial about the product. The purchase potential ratings were based on a 0 to 10 scale, with higher values indicating a higher purchase potential. The null hypothesis stated that the mean rating "after" would be less than or equal to the mean rating "before." Rejection of this hypothesis would show that the commercial improved the mean purchase potential rating. Use = .05 and the following data to test the hypothesis and comment on the value of the commercial. Purchase Rating Purchase Rating Individual After Before Individual After Before 1 6 5 5 3 5 2 6 4 6 9 8 3 7 7 7 7 5 4 4 3 8 6 6 What are the hypotheses?H0: d Ha: d Compute (to 3 decimals).Compute sd (to 1 decimal). What is the p-value?The p-value is What is your decision?arrow_forwardWhy would you use a histograph or bar graph? Which would be better and why for the data shown.arrow_forward
- Please help me with this question on statisticsarrow_forwardPlease help me with this statistics questionarrow_forwardPlease help me with the following statistics questionFor question (e), the options are:Assuming that the null hypothesis is (false/true), the probability of (other populations of 150/other samples of 150/equal to/more data/greater than) will result in (stronger evidence against the null hypothesis than the current data/stronger evidence in support of the null hypothesis than the current data/rejecting the null hypothesis/failing to reject the null hypothesis) is __.arrow_forward
- Please help me with the following question on statisticsFor question (e), the drop down options are: (From this data/The census/From this population of data), one can infer that the mean/average octane rating is (less than/equal to/greater than) __. (use one decimal in your answer).arrow_forwardHelp me on the following question on statisticsarrow_forward3. [15] The joint PDF of RVS X and Y is given by fx.x(x,y) = { x) = { c(x + { c(x+y³), 0, 0≤x≤ 1,0≤ y ≤1 otherwise where c is a constant. (a) Find the value of c. (b) Find P(0 ≤ X ≤,arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin HarcourtGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning



