
State the null and alternative hypothesis.
Find the degrees of freedom for the
Find the critical value of chi-square from Appendix E or from Excel’s
Calculate the chi-square test statistics at 0.10 level of significance and interpret the p-value.
Check whether the conclusion is sensitive to the level of significance chosen, identify the cells that contribute to the chi-square test statistic and check for the small expected frequencies.
Calculate the p-value using Excel’s function if necessary.
Perform a two-tailed, two-sample z test for

Answer to Problem 21CE
The null hypothesis is:
And the alternative hypothesis is:
The degrees of freedom for the contingency table is 1.
The critical-value using EXCEL is 2.706.
There is no enough evidence to conclude that grade and order handed in are independent.
The p-value for the hypothesis test is 0.382.
The conclusion is not sensitive to the level of significance chosen.
The cells (1, 1) and (1, 2) contribute the most to the chi-square test statistic.
There is no expected frequencies that are too small.
It is verified that
Explanation of Solution
Calculation:
The table summarizes the grade and order of papers handed in.
The claim is to test whether the data provide sufficient evidence to conclude that the grade and order handed in are independent. If the claim is rejected, then the grade and order handed in are not independent.
The test hypotheses are given below:
Null hypothesis:
Alternative hypothesis:
The degrees of freedom can be obtained as follows:
Substitute 2 for r and 2 for c.
Thus, the degrees of freedom for the contingency table is 1.
Procedure for critical-value using EXCEL:
Step-by-step software procedure to obtain critical-value using EXCEL software is as follows:
- Open an EXCEL file.
- In cell A1, enter the formula “=CHISQ.INV.RT(0.10,1)”
- Output using EXCEL software is given below:
Thus, the critical-value using EXCEL is 2.706.
Test statistic:
Software procedure:
Step by step procedure to obtain the chi-square test statistics and p-value using the MINITAB software:
- Choose Stat > Tables >Cross Tabulation and Chi-Square.
- Choose Row data (categorical variables).
- In Rows, choose Grade.
- In Columns, choose Order handed in.
- In Frequencies, choose Count.
- In Display, select Counts.
- In chi-square, select Chi-square test, Expected cell counts and Each cell’s contribution to chi-square.
- Click OK.
Output using the MINITAB software is given below:
Thus, the test statistic is 0.764 and the p-value for the hypothesis test is 0.382.
Rejection rule:
If the p-value is less than or equal to the significance level, then reject the null hypothesis
Conclusion:
Here, the p-value is greater than the level of significance.
That is,
Therefore, the null hypothesis is not rejected.
Thus, the data provide sufficient evidence to conclude that the grade and order handed in are independent.
Take
Here, the p-value is greater than the level of significance.
That is,
Therefore, the null hypothesis is not rejected.
Thus, the data provide sufficient evidence to conclude that the grade and order handed in are independent.
Thus, the conclusion is same for both the significance levels.
Hence, the conclusion is not sensitive to the level of significance chosen.
The cells (1, 1) and (1, 2) contribute most to the chi-square test statistic.
Since all
Two-tailed, two-sample z test:
The test hypotheses are given below:
Null hypothesis:
Alternative hypothesis:
The proportion of students who finish an exam first and get “B or better” on the exam is denoted as
Where
The proportion of students who finish later and get “B or better” on the exam is denoted as
Where
The pooled proportion is denoted as
Test statistic:
The z-test statistics can be obtained as follows:
Thus, the z-test statistic is 0.87.
The square of the z-test statistic is,
Thus the square of the z-test statistic is same as the chi-square statistics.
Procedure for p-value using EXCEL:
Step-by-step software procedure to obtain p-value using EXCEL software is as follows:
- Open an EXCEL file.
- In cell A1, enter the formula “=2*(1-NORM.S.DIST(0.8740,1))”
- Output using EXCEL software is given below:
Thus, the p-value using EXCEL is 0.382, which is also same as the p-value obtained in chi-square test.
Thus, it is verified that
Want to see more full solutions like this?
Chapter 15 Solutions
Applied Statistics 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


