In His Management Information System

In His Management Information Syst

In his management information systems textbook, Professor David Kroenke raises an interesting point: “If 98% of our market has Internet access, do we have a responsibility to provide non-Internet materials to that other 2%? Suppose that 98% of the customers in your market do have Internet access, and you select a random sample of 500 customers. What is the probability that the sample has a. Greater than 99% of the customers with internet access? b. Between 97% and 99% of the customers with Internet access? c. Fewer than 97% of the customers with Internet access?

One operation of a mill is to cut pieces of steel into parts that are used in the frame for front seats in an automobile. The steel is cut with a diamond saw, and the resulting parts must be cut to be within +/- 0.005 inch of the length specified by the automobile company. The measurement reported from a sample of 100 steel parts (stored in Steel) is the difference, in inches, between the actual length of the steel part, as measured by a laser measurement device, and the specified length of the steel part. For example, the first observation, -0.002 represents a steel part that is 0.002 inch shorter than the specified length. a. Construct a 95% confidence interval estimate for the population mean difference between the actual length of the steel part and the specified length of the steel part. b. What assumption must you make about the population distribution in order to construct the confidence interval estimate in (a)? c. Do you think that the assumption needed in order to construct the confidence interval estimate in (a) is valid? Explain.

Another operation of a steel mill is to cut pieces of steel into parts that are used in the frame for front seats in an automobile. The steel is cut with a diamond saw and requires the resulting parts to be within +/- 0.005 inch of the length specified. The file Steel contains a sample of 100 steel parts. The measurement reported is the difference, in inches, between the actual length and the specified length. For example, a value of -0.002 represents a steel part that is 0.002 inch shorter than the specified length. a. At the 0.05 level of significance, is there evidence that the mean difference is not equal to 0.0 inches? b. Construct a 95% confidence interval estimate of the population mean. Interpret this interval. c. Compare the conclusions reached in (a) and (b). d. Because n = 100, do you have to be concerned about the normality assumption needed for the t test and t interval?

Although many people think they can put a meal on the table in a short period of time, an article reported that they end up spending about 40 minutes doing so. A study is conducted to test the validity of this statement. A sample of 25 people records the time to prepare and cook dinner in minutes, with results in (Dinner): 44.0, 51.9, 49.7, 40.0, 55.5, 33.0, 43.4, 41.3, 45.2, 40.7, 41.1, 49.1, 30.9, 45.2, 55.3, 52.1, 55.1, 38.8, 43.1, 39.2, 58.6, 49.8, 43.2, 47.9, 46.6. a. Is there evidence that the population time to prepare and cook dinner is different from 40 minutes? Use the p-value approach and a level of significance of 0.05. b. What assumption about the population distribution is needed in order to conduct the t test in (a)? c. Make a list of the ways to evaluate the assumption noted in (b). d. Evaluate the assumption and determine whether the t test in (a) is valid.

Paper For Above instruction

The increasing ubiquity of the internet in modern society presents both opportunities and responsibilities for businesses. Professor David Kroenke, in his management information systems textbook, poses a philosophical question about the obligation of firms to cater to customers lacking internet access, despite the global trend towards digitalization. This dilemma underscores the importance of understanding statistical probabilities and how they apply in real-world business contexts, such as market research and decision-making. The problem explores the probability of certain proportions in a sample, specifically assessing the likelihood that a randomly selected customer base with 98% internet access will have varying levels—greater than 99%, between 97% and 99%, or fewer than 97%—based on a sample of 500 customers. This application involves the binomial distribution approximation to the normal distribution due to sufficiently large sample sizes, permitting calculation of probabilities for these proportions to guide strategic decisions regarding inclusive service provision.

In the manufacturing sector, statistical inference plays a critical role in quality control, especially in metal cutting processes. One case involves measuring the difference between actual steel part lengths and their specified sizes, with the goal of maintaining tight tolerances within +/- 0.005 inch. A sample of 100 steel parts' measurement differences is analyzed to estimate the population mean difference. Constructing a 95% confidence interval for this mean involves assuming that the population of differences is approximately normally distributed, which is justified either by the central limit theorem for sample sizes of 100 or by verifying the data's normality. The validity of these assumptions directly affects confidence in the interval estimate and further informs quality assurance processes in manufacturing.

Further, hypothesis testing is applied to determine whether the mean difference significantly deviates from zero at a 5% significance level. The t-test evaluates the null hypothesis that the mean difference is zero against an alternative hypothesis. Concluding significant deviation indicates that the process may require adjustments to meet specifications consistently. The resulting confidence interval offers an estimated range within which the true mean difference lies, aiding decision makers in quality control. Comparing the results from hypothesis testing and interval estimation provides a comprehensive understanding of the process stability and accuracy.

In another context, a study investigates whether the average time to prepare and cook dinner differs from 40 minutes. A sample of 25 individuals records their cooking durations, and statistical analysis using t-tests assesses this claim. This case demonstrates the importance of normality assumptions underlying the t-test, especially with small samples. Validity of the test depends on whether the data roughly follow a normal distribution, which can be evaluated through graphical methods such as histograms or QQ plots, or numerical tests like the Shapiro-Wilk test. Ensuring the assumptions are satisfied is vital for reliable inference, emphasizing the necessity of appropriate data examination before applying parametric tests.

Overall, these examples highlight the practical application of statistical analysis in business decision-making, quality assurance, and operations management. Understanding how to construct confidence intervals, perform hypothesis tests, and evaluate assumptions ensures that managers and analysts make informed, accurate decisions. It also illustrates the importance of normality, sample size, and the approximation of binomial distributions to the normal distribution in real-world scenarios, underscoring the integration of statistical theory and practice in business environments. Employing sound methods allows organizations to optimize processes, allocate resources effectively, and serve their markets inclusively and efficiently.

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