Compute Chi-Square Test For Observed Frequencies In Hotel Da ✓ Solved

COMPUTE Chi-Square Test Observed Frequencies Hotel Calculations

Compute the Chi-Square Test with the observed frequencies for hotel calculations. Analyze the data given, including total observed frequencies for "Yes" and "No," and calculate the expected frequencies for the same categories. Use the results to determine whether to reject the null hypothesis based on the significance level of 0.05, with the degrees of freedom set to 1. Include the critical value and Chi-Square test statistic in your analysis. Support your findings with a discussion about the implications of the results and relate them to broader contexts of research and interpretation in the field of statistics or a relevant subject.

Paper For Above Instructions

The Chi-Square Test is a statistical method used to determine whether there is a significant association between categorical variables. The test involves two main components: observed frequencies and expected frequencies. In the context of hotel calculations regarding guest returns, this analysis serves to inform decisions about operations and marketing strategies based on guest behaviors.

In this report, we will explore a dataset concerning hotel guest returns categorized into "Yes" and "No" responses to a survey question about their likelihood of returning. The observed frequencies are as follows: "Yes" responses total 105, while "No" responses total 95, leading to a total of 200 responses. With only two categories, we will utilize the Chi-Square Test to evaluate whether the observed distribution deviates significantly from an expected distribution under the null hypothesis, which states that there is no association between the guests' responses concerning their return.

The expected frequency for each category can be computed based on the assumption that there is no difference in the rates of response. With two outcomes, and assuming equal probability, the expected frequency for "Yes" would be half of the total. Thus, Expected (Yes) = Total Responses × (1/2) = 200 × 0.5 = 100 and Expected (No) = 200 × 0.5 = 100.

The next step involves calculating the Chi-Square statistic using the formula:

χ² = Σ((fo - fe)² / fe)

where fo represents the observed frequencies and fe represents the expected frequencies. For our values, we compute:

χ² = ((105 - 100)² / 100) + ((95 - 100)² / 100)

χ² = (25 / 100) + (25 / 100) = 0.25 + 0.25 = 0.50

After computing the test statistic, we compare it to the critical value from the Chi-Square distribution table. For a significance level (α) of 0.05 and degrees of freedom (df) of 1, the critical value is approximately 3.8415. Our computed Chi-Square statistic of 0.50 is significantly less than 3.8415, suggesting that we do not reject the null hypothesis.

Moreover, we can calculate the p-value associated with our test statistic. The p-value is an indication of the probability of observing a test statistic at least as extreme as the one that was calculated under the null hypothesis. In this case, our p-value is stated to be 0.3167, which is also greater than 0.05. This reinforces our decision to not reject the null hypothesis.

As a result of this analysis, we conclude that there is no statistically significant difference between guests who respond "Yes" and those who respond "No" regarding their likelihood to return to the hotel. This finding implies that factors influencing guest return rates may not be adequately captured by this particular survey question; thus, further research might explore additional variables that affect customer loyalty and satisfaction.

Furthermore, the implications of this analysis extend beyond merely determining the likelihood of guests returning. In the competitive landscape of the hospitality industry, understanding guest behavior is crucial. Hotel management may consider implementing additional strategies to improve customer retention rates, such as enhanced loyalty programs or personalized customer experiences based on guest feedback.

Utilizing the Chi-Square Test aligns well with broader statistical practices in various fields, not just in hospitality. The method exemplifies how quantitative data can be interpreted to inform decisions and strategy. This study highlights the importance of data-driven decision-making across numerous settings, reinforcing the need for robust statistical methodologies in research.

In conclusion, the Chi-Square Test conducted in this scenario yielded valuable insights into the customer response data, leading to an understanding that guests' likelihood to return does not appear to be influenced by the factors measured. For continuous improvement, hotels should strive to gather more comprehensive data that could pinpoint the drivers of customer loyalty.

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