# Hypothesis Testing Applied Managerial Statistics PaperUser

### Question Descriptio

Complete the following four hypotheses, using α = 0.05 for each. The week 5 spreadsheet can be used in these analyses.

• 1. Mean sales per week exceed 42.5 per salesperson
• 2. Proportion receiving online training is less than 55%
• 3 Mean calls made among those with no training is at least 145
• 4. Mean time per call is 14.7 minutes
• Using the same data set from part A, perform the hypothesis test for each speculation in order to see if there is evidence to support the manager’s belief. Use the Eight Steps of a Test of Hypothesis from Section 9.1 of your text book as a guide. You can use either the p-value or the critical values to draw conclusions. Be sure to explain your conclusion and interpret that to the claim in simple terms
• Compute 99% confidence intervals for the variables used in each hypothesis test, and interpret these intervals.
• Write a report about the results, distilling down the results in a way that would be understandable to someone who does not know statistics. Clear explanations and interpretations are critical.
• All DeVry University policies are in effect, including the plagiarism policy.
• Project Part B report is due by the end of Week 6.
• Project Part B is worth 100 total points. See grading rubric below.

The Eight Steps of Testing Hypotheses At step 1, establishing a null and an alternative hypothesis, it is important that the business researcher clearly identify what is being tested and whether the hypotheses are one-tailed or two-tailed. In the hypothesis testing process, it is always assumed that the null hypothesis is true at the beginning of the study. In other words, it is assumed that the process is in control (no problems in the process), the market share has not increased, older workers are not more loyal to a company than younger workers, and so on. This process is analogous to the U.S. trial system in which the accused is presumed innocent at the beginning of the trial. Step 2 is to select the most appropriate statistical test to use for the analysis. In selecting such a test, the business researcher needs to consider the type, number, and level of data being used in the study along with the statistic used in the analysis (mean, proportion, etc.).

In addition, business researchers should consider the assumptions underlying certain statistical tests and determine whether they can be met in the study before using such tests. At step 3, the value of alpha is set. Alpha is the probability of committing a Type I error and will be discussed later. Common values of alpha include .05, .01, .10, and .001. Step 4 is to establish the decision rule, which should be done before the study is undertaken. Using alpha and the test statistic, critical values can be determined. These critical values are used at the decision step (step 7) to determine whether the null hypothesis is rejected or not. If the p-value method (discussed later) is utilized, the value of alpha is used as a critical probability value. The process begins by assuming that the null hypothesis is true. Data are gathered and statistics computed. If the evidence is away from the null hypothesis, the business researcher begins to doubt that the null hypothesis is really true. If the evidence is far enough away from the null hypothesis that the critical value is surpassed, the business researcher will reject the null hypothesis and declare that a statistically significant result has been attained.

The first four steps in testing hypotheses should always be completed before the study is undertaken. It is not sound research to gather data first and then try to determine what to do with them. Step 5 is to gather sample data. This step might include the construction and implementation of a survey, conducting focus groups, randomly sampling items from an assembly line, or even sampling from secondary data sources (e.g., financial databases). In gathering data, the business researcher is cautioned to recall the proper techniques of random sampling (see Chapter 7, Section 7.1). Care should be taken in establishing a frame, determining the sampling technique, and constructing the measurement device. A strong effort should be made to avoid all nonsampling errors. After the data are sampled, the test statistic can be calculated (step 6). Step 7 is reaching a statistical conclusion. Using step 4 (decision rule) and the value of the test statistic (step 6), the business researcher can draw a statistical conclusion. In all hypothesis tests, the business researcher needs to conclude whether the null hypothesis is rejected or is not rejected.

Step 8 is determining the business implications of the statistical decision. That is, after a statistical decision is made, the business researcher or decision maker decides what business implications the study results contain. If the statistical decision is to fail to reject the null hypothesis, then typically the business decision maker is left with the status quo. However, if the statistical decision is to reject the null hypothesis, it is at this step that the business decision maker must decide if the results are substantive. In either case, there may be business decisions to be made. For example, if the hypothesistesting procedure results in a conclusion that train passengers are significantly older today than they were in the past, the manager may decide to cater to these older customers or to draw up a strategy to make ridership more appealing to younger people. 1 NOTE: This is a template to help you format Project Part B. I have put some explanations in red.

Please delete these before submitting the assignment. All text in your submission should be black. Project Part B: Hypothesis Testing By Applied Managerial Statistics Put date of submission here 1 2 Put a table of contents on this page. 2 3 1. Introduction Provide the purpose of this report and an overview of its content. NOTE FOR SECTIONS 2, 3, 4, 5: The Course Project Overview section in the MODULES section of the shell, identifies 4 claims (hypotheses) that need to be tested. Please put the results of these hypothesis tests in section 2, 3, 4, 5. Each section should consist of a table similar to what is given in Section 2. Reviewing the Worksheet problems at the end of this week’s notes in the FILES section should help you in filling out the items in the table. 2. Hypothesis Test 1: Mean Sales per Week Hypothesis statement Ex.

The mean sales per week exceeds 42.5 per sales person. Null and alternate hypotheses Ho: Ha: Type of test Right tail or left tail or two tail. Briefly explain the reason for your answer. Use z or t? Select z or t and explain your selection. Rejection region Assume alpha = .05. Where is the rejection region? Format should be something like, for example, z>2.3 Test statistic Give value of the test statistic p-value Give value of the p-value Hypothesis test result using p-value Do we reject or not reject Ho. Why? Hypothesis test result using test Do we reject or not reject Ho. Why? statistic Do the results support the claim Avoid statistical jargon, i.e. don’t just mention “null being made? hypothesis” or “alternate hypothesis”. Restate the claim. State your answer in terms that a business person would understand? Example: “Since we are rejecting Ho, we have support for Ha, which is the martian’s claim. Therefore we can support the martian’s claim their average height is more than 24 inches”. 99% Confidence Interval for the Give the 99% confidence interval for the mean of the mean variable being tested above. 3. Hypothesis Test 2: Put a meaningful header (Similar to section 2. The claim is in Course Project Overview in the Shell) 3 4 Please see the COURSE PROJECT OVERVIEW in the shell for which hypothesis to test.

Create a table similar to the one in section 2 above. 4. Hypothesis Test 3: Put a meaningful header (Similar to section 2. The claim is in Course Project Overview in the Shell) Please see the COURSE PROJECT OVERVIEW in the shell for which hypothesis to test. Create a table similar to the one in section 2 above. 5. Hypothesis Test 4: Put a meaningful header (Similar to section 2. The claim is in Course Project Overview in the Shell) Please see the COURSE PROJECT OVERVIEW in the shell for which hypothesis to test. Create a table similar to the one in section 2 above. 6. Summary 1-2 paragraph summary of your findings. 4 1 Project Part A: Descriptive Statistics By May 16, 2021 1 2 Table of Contents Introduction ……………………………………………………………………………………………………………………. 3 Description of the five variables ……………………………………………………………………………………….. 3 Discription of the five numerical measurements ………………………Error! Bookmark not defined. Measurement of each variable ………………………………………………………………………………………….. 5 Sales ………………………………………………………………………………………………………………………….. 6 Calls…………………………………………………………………………………………………………………………… 5 Pairing of Variables ………………………………………………………………………………………………………… 5 Correlation between Sales and Calls ………………………………………………………………………………. 6 Correlation between Sales and Training Type …………………………………………………………………. 6 Summary ……………………………………………………………………………………………………………………….. 7 Reference ………………………………………………………………………………………………………………………. 8 2 3 Introduction This report will analyze factors utilizing information got from the MATH534_Project_Data_SALESCALL_A Excel spreadsheet. This report will utilize graphical and mathematical procedures to sum up the discoveries, including the five-number outline that will be utilized for every variable.

The report will give a clarification of the five-number summary and its components. This report will also analyze the relationship between three of ten pairings of these variables. Description of the five variables A variable is any characteristics, number, or quantity that can be measured or counted. A variable may also be called a data item (“Statistical Language – What are Variables?”, 2021). In this report, we center around the five variables in the Excel spreadsheet table allocated for this initial portion of the course project. The spreadsheet has five variables: sales; calls; time; years, and type. An explanation of each variable is explained as follows: • SALES represents the number of sales made this week. • CALLS represents the number of sales calls made this week. • TIME represents the average time per call this week. • YEARS represents years of experience in the call center. • TYPE represents the type of training the employee received.

Of these, this report will discuss the data for sales and calls. 3 4 Description of the numerical measurements The five numerical measurements that will be utilized for this report are: Minimum; Q1; Median; Q3; Maximum. A description for these terms is seen below: 1. Minimum refers to the minimum or least value in the data set. 2. Q1 (Quartile 1) is the middle number between the smallest number and the median of the data set. 3. Median is the middle number in a data set. 4. Q3 (Quartile 3) is the median of the upper half of the data. 5. Maximum refers to the maximum or highest value in the data set. Measurement of each variable Both types of data show that the least number of sales which is 34 while the highest number is 57. The range, which is the distinction between the greatest and least measurements, is 23. In this specific case, it very well may be seen that there is a large range between the least and 4 5 greatest qualities, which could mean there is in reality a worth or value that can altogether influence the results of the measurement, or that the values were not determined effectively. The scattering is large.

Calls The five-number summary table and corresponding chart for the number of calls made this week are enclosed below: This chart shows that were at least 117 calls and a maximum of 197 calls during the week. The range among least and most extreme qualities is 80, which may uncover a large scattering of data. The median of the calls would be 158 calls each day and the mean is 158.44. Pairings of Variables Correlation between Sales and Calls 5 6 The graph above shows the quantity of calls each week as they identify with sales. There is a positive relationship between the quantity of calls made and the quantity of sales the trendline shows. The most elevated number of sales (excluding the outliers) is 77 with 57 sales. The conclusion that can be gotten from this graph is that the quantity of sales usually rises with the quantity of calls made. Correlation between Sales and Training Type This graph shows the correlation between the number of call operators’ number of sales this week and the types of training they had. The names of the types of training were replaced 6 7 with numbers as appeared at the lower part of the graph. The trendline shows a positive relationship between sales and types of training received.

The most widely recognized training for operators is online and the least common fell on group training. The operators who received online training showed the most elevated number of sales, showing that there is a positive correlation between online training and the quantity of sales. Summary To summarize this report, the data studied showed that operators who make a higher measure of calls produce a higher number of sales. Investing higher measures of time on a call decreases the chances of making a sale.

In conclusion, operators who received online training produced the greatest number of sales. 7 8 References Statistical Language – What are Variables?. (2021). Retrieved from https://www.abs.gov.au/websitedbs/D3310114.nsf/home/statistical+language++what+are+variables#:~:text=A%20variable%20is%20any%20characteristics,type%20ar e%20examples%20of%20variables. 8 1 Project Part A: Descriptive Statistics By May 16, 2021 1 2 Table of Contents Introduction ……………………………………………………………………………………………………………………. 3 Description of the five variables ……………………………………………………………………………………….. 3 Discription of the five numerical measurements ………………………Error! Bookmark not defined. Measurement of each variable ………………………………………………………………………………………….. 5 Sales ………………………………………………………………………………………………………………………….. 6 Calls…………………………………………………………………………………………………………………………… 5 Pairing of Variables ………………………………………………………………………………………………………… 5 Correlation between Sales and Calls ………………………………………………………………………………. 6 Correlation between Sales and Training Type …………………………………………………………………. 6 Summary ……………………………………………………………………………………………………………………….. 7 Reference ………………………………………………………………………………………………………………………. 8 2 3 Introduction This report will analyze factors utilizing information got from the MATH534_Project_Data_SALESCALL_A Excel spreadsheet. This report will utilize graphical and mathematical procedures to sum up the discoveries, including the five-number outline that will be utilized for every variable.

The report will give a clarification of the five-number summary and its components. This report will also analyze the relationship between three of ten pairings of these variables. Description of the five variables A variable is any characteristics, number, or quantity that can be measured or counted. A variable may also be called a data item (“Statistical Language – What are Variables?”, 2021). In this report, we center around the five variables in the Excel spreadsheet table allocated for this initial portion of the course project. The spreadsheet has five variables: sales; calls; time; years, and type. An explanation of each variable is explained as follows: • SALES represents the number of sales made this week. • CALLS represents the number of sales calls made this week. • TIME represents the average time per call this week.

• YEARS represents years of experience in the call center. • TYPE represents the type of training the employee received. Of these, this report will discuss the data for sales and calls. 3 4 Description of the numerical measurements The five numerical measurements that will be utilized for this report are: Minimum; Q1; Median; Q3; Maximum. A description for these terms is seen below: 1. Minimum refers to the minimum or least value in the data set. 2. Q1 (Quartile 1) is the middle number between the smallest number and the median of the data set. 3. Median is the middle number in a data set. 4. Q3 (Quartile 3) is the median of the upper half of the data. 5. Maximum refers to the maximum or highest value in the data set.

Measurement of each variable Both types of data show that the least number of sales which is 34 while the highest number is 57. The range, which is the distinction between the greatest and least measurements, is 23. In this specific case, it very well may be seen that there is a large range between the least and 4 5 greatest qualities, which could mean there is in reality a worth or value that can altogether influence the results of the measurement, or that the values were not determined effectively. The scattering is large. Calls The five-number summary table and corresponding chart for the number of calls made this week are enclosed below: This chart shows that were at least 117 calls and a maximum of 197 calls during the week. The range among least and most extreme qualities is 80, which may uncover a large scattering of data.

The median of the calls would be 158 calls each day and the mean is 158.44. Pairings of Variables Correlation between Sales and Calls 5 6 The graph above shows the quantity of calls each week as they identify with sales. There is a positive relationship between the quantity of calls made and the quantity of sales the trendline shows. The most elevated number of sales (excluding the outliers) is 77 with 57 sales. The conclusion that can be gotten from this graph is that the quantity of sales usually rises with the quantity of calls made. Correlation between Sales and Training Type This graph shows the correlation between the number of call operators’ number of sales this week and the types of training they had. The names of the types of training were replaced 6 7 with numbers as appeared at the lower part of the graph.

The trendline shows a positive relationship between sales and types of training received. The most widely recognized training for operators is online and the least common fell on group training. The operators who received online training showed the most elevated number of sales, showing that there is a positive correlation between online training and the quantity of sales. Summary To summarize this report, the data studied showed that operators who make a higher measure of calls produce a higher number of sales. Investing higher measures of time on a call decreases the chances of making a sale. In conclusion, operators who received online training produced the greatest number of sales.

7 8 References Statistical Language – What are Variables?. (2021). Retrieved from https://www.abs.gov.au/websitedbs/D3310114.nsf/home/statistical+language++what+are+variables#:~:text=A%20variable%20is%20any%20characteristics,type%20ar e%20examples%20of%20variables. 8 Hypothesis Testing for µ and for p Note: Enter values in the green cells only. Hypothesis Test for µ Information Provided by the Problem Level of Significance Mean under H0 n Sample Mean StDev Use t or z? (decimal) NOTE: If sample standard deviation is known, use t. If population standard deviation is known, use z. Critical Values Right-Tailed (>) Left-Tailed (

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