STATISTICAL ANALYSIS

Statistical analysis

Statistical analysis

Question #1: Calculations for Wait times

Unbiased point estimate for customer wait times per visit

Table 1

Statistics

Wait time

N

Valid

50

Missing

0

Mean

22.9000

The point estimator for customer wait times per visit is “22.9”.

Sample standard deviation of customer wait times per visit

Table 2

Statistics

Wait time

N

Valid

50

Missing

0

Std. Deviation

13.60110

The standard deviation for customer wait time per visit is “13.6”.

95% confidence interval for the true mean

Table 3

Descriptives

Statistic

Std. Error

Wait time

Mean

22.9000

1.92349

95% Confidence Interval for Mean

Lower Bound

19.0346

Upper Bound

26.7654

5% Trimmed Mean

22.9000

Median

21.0000

Variance

184.990

Std. Deviation

13.60110

Minimum

1.00

Maximum

46.00

Range

45.00

Interquartile Range

25.00

Skewness

.097

.337

Kurtosis

-1.332

.662

The estimated confidence interval is 19.03 (upper bound) and 26.76 (upper bound).

Assumptions made from part c

The assumption made from part c is that the predicted waiting time for customer lies between 19.03 and 26.76 but if the waiting time is increased, the customer may not visit or become default.

Conclusion drawn from part c

The confidence interval level shows that the waiting time of customer per visit will fall between 19.03 and 26.76.

Precision in estimation and change in confidence interval by increasing sample size

Table 4

Descriptives

Statistic

Std. Error

waittime

Mean

22.9000

1.35322

95% Confidence Interval for Mean

Lower Bound

20.2149

Upper Bound

25.5851

5% Trimmed Mean

22.9000

Median

21.0000

Variance

183.121

Std. Deviation

13.53223

Minimum

1.00

Maximum

46.00

Range

45.00

Interquartile Range

25.00

Skewness

.095

.241

Kurtosis

-1.326

.478

Question #2: Calculations for Improvement in table management

Null and Alternative hypotheses

H0: The improvement in table management is insignificant to reduced wait times, increased customer satisfaction, and dinner service table turnover.

H1: The improvement in table management is significant to reduced wait times, increased customer satisfaction, and dinner service table turnover.

The critical value

The critical value calculated is 1.976. It is calculated through excel. The tabulated value is 1.644. However, the formula for calculation t-value is:

The value of the test statistic

The test statistics measures all the F value, t values, and z values of the test. Following are techniques used for test statistics;

The population standard deviation for the sample is 8 and standard deviation is 11.

Variance of population= 8 squared =56

Variance of sample= 11 squared = 113

Thus f value= 113/ 56

F value calculated = 2.017

F value tabulated = 1.000

Conclusion and interpretation of the hypothesis test

The value of f calculated > f tabulated, so reject H0 and accept HI. The value of t calculated > t tabulated, so reject H0 and accept HI. It shows that there is significant relationship between customer satisfaction and reduced wait times, increased customer satisfaction, and dinner service table turnover.

Question # 3: Calculations of the satisfaction data

Exclusion of independent variables from the correlation matrix

Table 5

The above correlation matrix shows that out of five independent variables, there are two independent variables that must be removed from the model to make more significant results. These two independent variables are; vegetarian and price per cover. These two independent variables are suggested to be removed because these two variables share negative correlation with the customer satisfaction that shows a weak and negative relationship

Significant contribution of five explanatory variables to the regression model

Table 6

The multiple regression model shows that the overall explanatory power of the model is 98.6% and R square is the coefficient of determination that shows the explained variation. This model explains 97.2% explained variation and remaining is unexplained variation.

The null hypothesis is;

H0: There is an insignificant relationship between dependent variable and independent ...