## Introduction

Quality of service in any business is an essential aspect that can determine the success of the company. The A1 Hotel is concerned with its service, as it is a luxury hotel. However, any company should strive to provide its customers with a high level of services. The evaluation of the service quality can ensure that people are getting the results they have played her.

## Managerial Report

The proportion of the clients that answered “Poor” to room quality is 48/200 or 24%. The proportion of those who answered “Poor” to food quality is 51/200 or 25.5%. Finally, 57/200 or 28.5% answered “Poor” to service quality. 90 of 200, or 45%, were “dissatisfied” with the service. To estimate the proportion of “dissatisfied” (*p*), it is used in the sample proportion (`p) which is 0.45. The sampling distribution of `p is approx. normal with the mean

*μ _{`p}=p*

and squared deviation

standard deviation is

The confidence interval for *p* is

For Confidence Level 0.92 z=1.75, here

, and

(“Table of z-values for Confidence Intervals”, n.d.). Therefore, the 92% confidence interval for the proportion of all recent clients that were “dissatisfied” is [0.415,0.485].

The margin of error here equals 0.035. The lower (or left) endpoint of the confidence interval is approx. 0.415. The upper (or right) endpoint of the confidence interval is approx. 0.485. The results mean that in case of performing a very large number of independent experiments with a similar confidence interval construction, in 92% of the experiments the confidence interval [0.415,0.485] will contain the estimated parameter the proportion of “dissatisfied” clients and in the remaining 8% of the experiments, the confidence interval will not contain that estimated parameter.

The analysis determined that 48 from 200 or 24% of clients answered “Poor” to room quality. The estimation of *p*, in this case, is 0.24. Z-value for Confidence Level 0.92 z=1.75. The 92% confidence interval for the proportion of all recent clients who answered “Poor” to room quality is [0.187,0.293].

The margin of error is equal

The lower (or left) endpoint of the confidence interval is approx.

**0.24 – 0.053 = 0.187**

The upper (or right) endpoint of the confidence interval is approx.

**0.24 + 0.053 = 0.293**

The results mean that in case of performing a very large number of independent experiments with a similar confidence interval construction, in 92% of the experiments the confidence interval [0.187,0.293] will contain the estimated parameter the proportion of clients who answered “Poor” to room quality. In the remaining 8% of the experiments, the confidence interval will not contain that estimated parameter.

51 from 200 or 25.5% of all recent clients answered “Poor” to food quality. The estimation of *p*, in this case, is 0.255. Z-value for Confidence Level 0.92 z=1.75. The 92% confidence interval for the proportion of all recent clients who answered “Poor” to food quality is [0.201,0.309].

The margin of error is equal to

The lower (or left) endpoint of the confidence interval is approx.

**0.255 – 0.054 = 0.201**

The upper (or right) endpoint of the confidence interval is approx.

**0.255 + 0.054 = 0.309**

The results mean that in case of performing a very large number of independent experiments with a similar confidence interval construction, in 92% of the experiments the confidence interval [0.201,0.309] will contain the estimated parameter the proportion of clients who answered “Poor” to food quality. In the remaining 8% of the experiments, the confidence interval will not contain that estimated parameter.

57 from 200 or 28.5% of all recent clients answered “Poor” to service quality. The estimation of *p*, in this case, is 0.285. Z-value for Confidence Level 0.92 z=1.75. The 92% confidence interval for the proportion of all recent clients who answered “Poor” to service quality is [0.229,0.341].

The margin of error is equal

The lower (or left) endpoint of the confidence interval is approx.

**0.285 – 0.056 = 0.229**

The upper (or right) endpoint of the confidence interval is approx.

**0.285 + 0.056 = 0.341**

The results mean that in case of performing a very large number of independent experiments with a similar confidence interval construction, in 92% of the experiments the confidence interval [0.229,0.341] will contain the estimated parameter the proportion of clients who answered “Poor” to service quality. In the remaining 8% of the experiments, the confidence interval will not contain that estimated parameter.

It is essential to define the P-value. According to Miller and Miller (2014), corresponding to an observed value of a test statistic, the P-value is the lowest level of significance at which the null hypothesis could have been. It involves determining the probability. The result is “unlikely” if the P-value is less than or equal to α. In case the P-value is more than α, it is considered to be a “likely” result. As for the null hypothesis, in cases where P-value is less than (or equal to) α, then the null hypothesis is rejected while if it is greater than α, the null hypothesis is not rejected (Hypothesis testing (P-value approach), n.d.).

Traditionally, 40% of customers have been dissatisfied. In the presented A1 Hotels data 45% of clients are “dissatisfied.” The next four steps involved in using the P-value approach to conducting any hypothesis test. Step one involves statements of the null hypothesis and the alternate hypothesis. Initial hypothesis: “the level of dissatisfaction is 40%” is the Null Hypothesis:

*H _{0}*:p=

*p*=0.4

_{0}The relevant Alternative Hypothesis is “the proportion of all recent clients is more dissatisfied than the traditional level of dissatisfaction 40%”.

*H _{1}*:p>0.4

It is the right-tailed test for *H _{0}*.

In step two, it is essential to state the size of the sample: *n=200*. In the presented A1 Hotels data, 45% of clients are “dissatisfied.” Thus, the sample proportion *p _{1}* = 0.45.

The standard error for the sample

or 3.5%. The test statistic

Step three involves using the known distribution of the test statistic to calculate the P-value. In Z- a probability of 0.9236 of Z being less than 1.43. Therefore, the P-value is 0.0778 (a probability of 1-0.9236 = 0.0778 Z more than 1.43) (How to use the Z table, n.d.). In step four, the significance level, α, the probability of making a Type I error to be small is 0.08. Compare the P-value to α.

**0.0778 < 0.08**

It means that the Null Hypothesis ** H_{0}** must be rejected in favor of the Alternative Hypothesis

**.**

*H*_{1}The analysis shows that the level of unsatisfied clients is higher than usual. Additionally, the observation of a data sample showed that the observed relative frequency is higher than the hypothetical probability. The testing of the hypothesis has demonstrated that the number of unsatisfied clients in other trials is likely to be higher than the traditional level. Most of the clients have indicated dissatisfaction with the service quality (28,5%), thus paying more attention to this aspect is recommended. The study can be improved by examining the proportion of the clients that were dissatisfied in all three categories and those who were unsatisfied with one of the options in each three of the data set.

## Conclusion

Overall, the analysis helps to determine the aspects of the A1 hotel that can be improved. The presented data has indicated that the quality of service should be given the highest priority, as most visitors were dissatisfied with it. Conducting the analysis has helped determine the aspects that have to be worked on to ensure that the clients receive the service they have paid for.

## References

Agresti, A., & Caffo, B. (2000). Simple and effective confidence intervals for proportions and differences of proportions result from adding two successes and two failures. *The American Statistician, 54*(4), 280-288.

How to use the Z table. (n.d.). Retrieved from https://www.dummies.com/education/math/statistics/how-to-use-the-z- table/

Hypothesis testing (P-value approach). (n.d.). Retrieved from https://onlinecourses.science.psu.edu/statprogram/reviews/statistical- concepts/hypothesis-testing/p-value-approach

Miller, I., & Miller, M. (2014). *John E. Freund’s mathematical statistics with applications* (8th ed.). Essex, England: Pearson Education Limited.