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1) A business magazine was conducting a study into the amount of travel required for mid-level managers across the U.S. 72 managers were surveyed for the number of days they spent traveling each year. Use ‘DataSet1 for question 1 section’ on blackboard to a) Construct a relative frequency distribution b) Construct a cumulative frequency distribution 2) The closing price (in pence) for selected stocks trading on the London stock exchange are given in ‘DataSet1 for question 2’ section. Construct a frequency distribution for the stock prices. 3) Consider the assets in (Billion dollars) the 10 largest life insurance companies listed in ‘DataSet1 for question 3 ‘section. Use this data to a) Construct a frequency distribution b) Construct relative frequency distribution c) Construct a cumulative frequency distribution 4) A magazine reported the results of a survey in which readers were asked to send in their responses to several questions regarding good eating. DataSet2 for question 4 on blackboard is the reported results to the question, How often do you eat chocolate? Based on the data answer the following questions. a) Were the responses to this survey obtained using voluntary sampling technique? Explain b) What type of bias may be present in the response? c) Is 13% a reasonable estimate of the proportion of all Americans who eat chocolate frequently? Explain 5) A magazine reported the results of a survey in which readers were asked to send in their responses to several questions regarding anger. DataSet2 for Question 5 shows the reported results to the question, How long do you usually stay angry? Answer the following questions based on the data. a) Were the responses to this survey obtained using voluntary sampling technique? Explain b) What type of bias may be present in the response? c) Is 22% a reasonable estimate of the proportion of all Americans who hold a grudge indefinitely? Explain. 6) Students in marketing class have been asked to conduct a survey to determine whether or not there is a demand for an insurance program at a local college. The students decided to randomly select students from the local college and mail them a questionnaire regarding the insurance program. Of the 150 questionnaires that were mailed, 50 students responded to the following survey item: Pick the category which best describes your interest in an insurance program. DataSet2 for question 6 shows the responses. Use this data to answer the following question. a) What type of bias may be present in the response? b) Is 50% a reasonable estimate of the proportion of all students who would be very interested in an insurance program at a local college? Explain. c) Is 50% a reasonable estimate of the proportion of all business majors who would be very interested in an insurance program at a local college? Explain. d) What strategies do you think the marketing students could have used in order to get a less biased response to their survey? e) Suppose the program was created and only a few people registered. How could the survey question have been reworded to better predict the actual enrollment?

Sample Paper For Above instruction

The comprehensive analysis of data collected through various surveys and distributions provides valuable insights into behaviors, preferences, and market demands. This paper examines multiple datasets ranging from travel habits of mid-level managers to stock prices, insurance company assets, and survey responses on eating habits, anger duration, and interest in insurance programs. The primary objective is to construct appropriate statistical distributions, evaluate potential biases, and interpret the data to inform decision-making in business and marketing contexts.

Introduction

Statistical analysis plays a crucial role in understanding patterns, trends, and preferences across diverse fields such as business management, finance, and consumer behavior. Proper construction of frequency distributions, relative frequencies, and cumulative frequencies allows analysts to visualize data effectively, identify outliers, and understand distribution shapes. Furthermore, critically assessing the sampling methods and potential biases is essential to ensure reliable and valid inferences. This paper discusses these concepts as applied to real-world datasets involving travel, stock prices, insurance assets, and survey responses.

Data Analysis and Distribution Construction

Travel Data of Mid-Level Managers

The dataset comprising the number of travel days for 72 managers was used to create a relative frequency distribution. This involved establishing class intervals based on the range of travel days, calculating the frequency of managers within each interval, and then dividing by the total sample size to obtain relative frequencies. The cumulative frequency was constructed by summing frequencies progressively from the lowest to the highest class. These distributions enable visualization of how travel days are spread among managers, revealing whether most managers travel infrequently or extensively.

Stock Price Distribution

Analysis of stock prices in pence involved creating a frequency distribution. This process grouped stock prices into intervals (e.g., ranges of 10 pence or 50 pence) and counted the number of stocks falling within each interval. The resulting frequency distribution depicted the concentration of stock prices, facilitating identification of common price ranges and outliers.

Assets of Life Insurance Companies

The assets (in billion dollars) of the ten largest life insurance companies were summarized via frequency distributions. By sorting these assets into intervals—such as ranges of $10 billion—and counting occurrences, a clearer understanding of the asset distribution was achieved. Relative frequency and cumulative distributions further illustrated the proportion of companies with assets below certain thresholds, aiding in market analysis.

Survey Response Analysis and Bias Evaluation

Eating Habits Survey

The survey responses regarding how often Americans eat chocolate indicated a 13% response rate for 'frequently'. The sampling method was voluntary, based on readers who chose to reply, which introduces potential bias. Volunteer samples often overrepresent certain segments—possibly those with stronger opinions or specific behaviors—leading to skewed results. The estimate of 13% for frequent chocolate consumption may not be representative of the entire population, especially if those interested in chocolate were more inclined to respond.

Anger Duration Survey

Similarly, responses about how long individuals typically stay angry showed a 22% percentage for holding grudges indefinitely. Again, sampling was voluntary, and respondents may differ systematically from the general population. Individuals with extreme or persistent anger tendencies might be more motivated to respond, leading to an overestimation of the proportion holding grudges indefinitely. Therefore, while the data suggest a notable fraction, they cannot reliably predict true population parameters.

College Insurance Program Survey

The survey conducted among college students was intended to gauge interest in an insurance program. The response rate was approximately 33% (50 responses out of 150 mailed questionnaires). Self-selection bias is a concern because students with strong opinions or interest are more likely to respond. The estimate that 50% of respondents are very interested might not reflect the entire student body. To mitigate bias, surveys could employ stratified sampling, follow-up reminders, or incentivization to increase response rates and diversify the respondents.

Biases and Strategies for Improvement

Biases such as voluntary response bias and non-response bias are prevalent in these surveys. These biases stem from self-selection and incomplete response rates, potentially distorting the data. To reduce such biases, strategies like random sampling, increased follow-up, stratified sampling, and survey design modifications are recommended. For instance, ensuring anonymity and emphasizing the importance of every response may encourage broader participation. Rephrasing questions to be more specific or less leading might also improve the predictive validity of the responses.

Conclusion

Effective data analysis requires constructing accurate distributions and critically evaluating sampling methods for biases. Recognizing limitations and applying appropriate sampling strategies enhances the reliability of inferences drawn from surveys. The datasets examined demonstrate the importance of meticulous statistical procedures to understand behaviors and market trends, ultimately informing better managerial and business decisions.

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