Datatrident University Bus 520 Business Analytics And Decisi

Datatrident Universitybus520 Business Analytics And Decision Makingm

Generate a 95% confidence interval for the following two variables by hand: Annual Amount Spent on Organic Food and Age. Average Annual Amount Spent on Organic Food (ð‘¥ Ì…) Average Age (ð‘¥ Ì…) t-value from the t-table (t) t-value from the t-table (t) standard deviation for this variable (s) standard deviation for this variable (s) number of observations (n) number of observations (n) Margin of Error ERROR:#DIV/0! Margin of Error ERROR:#DIV/0! Upper Limit of Confidence Interval ERROR:#DIV/0! Upper Limit of Confidence Interval ERROR:#DIV/0! Lower Limit of Confidence Interval ERROR:#DIV/0! Lower Limit of Confidence Interval ERROR:#DIV/0!

Generate a 95% confidence interval for the following two variables using the Excel formula =CONFIDENCE.T(): Annual Income and Number of People in the Household. Remember, this formula will just give you the margin of error. You will still need to add it to the mean and subtract it from the mean to get the upper and lower limits of the confidence interval. margin of error from the =CONFIDENCE.T() formula Average Annual Income Upper Limit of Confidence Interval 0 Lower Limit of Confidence Interval 0 margin of error from the =CONFIDENCE.T() formula Average Number of People Upper Limit of Confidence Interval 0 Lower Limit of Confidence Interval 0

Interpret the confidence intervals for Average Annual Income.Interpret the confidence intervals for Average Number of People.

The client insists the average income of his organic food customers is $150,000. Conduct a hypothesis test at the 0.10 level to test his statement. What is your decision? Step 1: State the Null and Alternate Hypotheses Null Hypothesis Alternate Hypothesis Step 2: Determine Alpha (Stated in Question) 0.10 Step 3: Determine Which Test Statistic Will Be Used Step 4: Formulate a Decision Rule Step 5: Make a Decision Hint: This will be a 2-tail t-test.

Paper For Above instruction

Business analytics plays a crucial role in decision-making processes by providing valuable insights derived from data analysis. The assignment at hand involves calculating confidence intervals and conducting hypothesis testing for various variables related to consumer behavior among organic food buyers. The focus is on understanding the precision of sample estimates, interpreting confidence intervals, and evaluating claims through statistical testing.

In this analysis, the primary goal is to generate confidence intervals for variables such as the annual amount spent on organic food, age, annual income, and the number of people in a household. The confidence interval offers a range within which the true population parameter is likely to fall, with a specified level of confidence, here 95%. Hands-on calculations and Excel formulas contribute to understanding the principles of statistical inference efficiently.

Calculating Hand-Drawn Confidence Intervals

The first step entails manually computing confidence intervals for two variables: the annual amount spent on organic food and age. These calculations require the sample means, standard deviations, and the sample size. The t-value corresponding to a 95% confidence level can be retrieved from the t-distribution table, depending on degrees of freedom (n-1). The formula for the margin of error (ME) is given by:

ME = t * (s / √n)

The upper and lower bounds of the confidence interval are then computed as:

Lower limit = sample mean - ME

Upper limit = sample mean + ME

These computations require precise input data, such as the mean, standard deviation, and the number of observations. Unfortunately, in this scenario, specific numerical data are missing (indicated by #DIV/0!), but the process remains standard, emphasizing the importance of understanding the formulas and table lookups in statistical inference.

Using Excel for Confidence Interval Estimation

The second part involves using the Excel function =CONFIDENCE.T() to determine the margin of error for the variables of annual income and household size. This function requires the significance level (α), the standard deviation, and the sample size as inputs. Once the margin of error is obtained, the upper and lower bounds of the confidence interval are calculated by adding and subtracting this margin from the sample mean, respectively.

This approach highlights the efficiency of software tools in statistical analysis, reducing manual calculations and minimizing errors.

Interpreting Confidence Intervals

The interpretation of the computed confidence intervals provides insights into the data's underlying population. For average annual income, a confidence interval of, say, $X to $Y, suggests that with 95% confidence, the true average income of the population of organic food consumers lies within this range. Such interpretations help marketers and policymakers tailor their strategies based on income levels, consumer demographics, and spending behaviors.

Similarly, for the average number of people in a household, the confidence interval offers an estimate of household size among customers, guiding targeted marketing efforts and resource allocation.

Hypothesis Testing of Income Claim

The client believes that the average income of his organic food customers is $150,000. To validate this claim statistically, a hypothesis test at the 0.10 significance level is performed. The null hypothesis (H0) states that the true mean income is $150,000, whereas the alternative hypothesis (H1) suggests it differs from this value.

The test statistic employed is a t-test, calculated by:

t = (sample mean - hypothesized mean) / (s / √n)

The decision rule involves comparing the computed t-value with critical t-values at the 0.10 significance level for a two-tailed test, derived from the t-distribution table.

If the absolute value of the calculated t exceeds the critical t, reject H0; otherwise, fail to reject H0. Based on the results, conclusions can be drawn about the validity of the client’s assertion.

Conclusion

This statistical analysis enables data-driven decision-making by quantifying the uncertainty around sample estimates and testing assertions about the population parameters. Mastery of confidence interval computations and hypothesis tests is essential for effective business analytics, informing strategic decisions and ensuring accurate interpretations of consumer data.

References

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