Introduction 2
Descriptive statistics 2
Inferential statistics 3
Regression analysis 3
Testing means using the T-test 6
Analysis of variance (ANOVA) 7
Conclusions 8
References 8
Term paper
Introduction
In this paper we are interested with will look keenly on the areas we have covered throughout weeks. In this case we will be looking at the descriptive statistics, inferential statistics, hypothesis development and testing, selection of appropriate test statistics and finally evaluating statistical results. This paper will reflect on these course elements in analyzing and making decisions about the data. We are interested with the type of travel made by different visitors in the hotel. We will evaluate if there is any significance difference between different types of visitors in the hotel. Descriptive statistics, regression analysis, and ANOVA will be used to compare if there is any significant difference between the types of visitors in the hotel.
Descriptive statistics
Statistics is in everyday activities, it hard to go without any encounter of statistics. Without statistics we couldn’t be able to plan our budgets, pay our taxes, enjoy our self to the fullest or even evaluate our performance in the various job positions.
Descriptive statistics include qualitatively describing the features of gathering of information. Descriptive statistics aim at summarizing the sample unlike inferential statistics that aim at learning about the population. The descriptive statistics are not obtained on the ground of probability theory. Some of the measures used to describe the data are the measures of central tendency and the measures of dispersion. The measure of central tendency that we are going to look at include; mean, median and mode while the measures of dispersion that we are going to look at include; the standard deviation, minimum and maximum. These descriptive statistics will just provide simple summaries about the sample observations. In the descriptive statistics of each variable the variable were grouped into business couple, and solo the descriptive statistics of these variable per groups were obtained as follow in the table below
Descriptive Statistics: Business, Couple, Solo
Variable Mean Q1 Median Q3 IQR
Business 85.75 68.75 91.50 97.00 28.25
Couple 92.0 35.3 74.5 166.3 131.0
Solo 115.3 8.8 50.0 287.0 278.3
Inferential statistics
The inferential statistics uses the sample to draw conclusions about the population of the data. Unlike the descriptive statistics, inferential statistics uses the probability theory to make a conclusion about the entire population. In this paper, we will be interested with the t-test, analysis of variance, and the regression analysis as these are what we have covered throughout the course.
Regression analysis
The regression analysis helps use to find if the predictor variables are related to the dependent variables. In this study we decide to investigate if the variables type of business visit is related to the visitor for business, person who visited for couples, and person who were solo visitors. In this study, we are also interested in determining the relationship between the type of business and the location of the hotel.
Scatter plot
Testing means using the T-test
A t statistics is usually used to test if there is any significant difference in means between any two groups. In this study we are interested in the difference in means between the type of travel, business type visitors, and the couple visitors. In this case the null hypothesis is that there is no significant difference between the mean number of visitors in the hotel for business visit and those who are there for couple visit while the alternative hypothesis is that there is significant difference between the mean number of visitors in the hotel for business visit and those who are there for couple visit. The t-test is limited to only two groups.
Two-Sample T-Test and CI: Business, travel type
Two-sample T for Business
Travel type N Mean Std SE Mean
Business 4 85.8 16.0 8.0
Couple 4 92.0 71.7 36
Difference = mu (business) - mu (couple)
Estimate for difference: -6.3
95% CI for difference: (-123.2, 110.7)
T-Test of difference = 0 (vs not =): T-Value = -0.17 P-Value = 0.876 DF = 3
Analysis of variance (ANOVA)
The analysis of variance is used when there are more than two means to be compared. In study we see that the grade type of person that visit the hotel into three groups. These groups include; the person who are in the business visit, the person who are in the couple visit, and those who are solo visits. In this case a t-test cannot be used and hence the ANOVA is applied to compare the number of type of visitors who visit the hotel. That is, those on business visit, those on couple visit, and those of solo visit. The analysis of variance also allows us to investigate the interaction between the variables or the groups unlike the t-test the interaction cannot be investigated. For example, in the investigation if there is any difference in the number of visitor in the hotel and the type of visit made by the as well as their interaction, a two way-factor with replication is used. See results below
One-way ANOVA: number of person versus business type
Source DF SS MS F P
Business type 2 1933 967 0.09 0.014
Error 9 96032 10670
Total 11 97965
S = 103.3 R-Sq = 1.97% R-Sq(adj) = 0.00%
Individual 95% CIs For Mean Based on
Pooled StDev
Level N Mean StDev ----+---------+---------+---------+-----
Business 4 85.8 16.0 (---------------*----------------)
Couple 4 92.0 71.7 (----------------*----------------)
Solo 4 115.3 163.1 (---------------*----------------)
----+---------+---------+---------+-----
0 70 140 210
Pooled Std = 103.3
Grouping Information Using Tukey Method
Business
Type N Mean Grouping
Solo 4 115.3 A
Couple 4 92.0 B
Business 4 85.8 C
Means that do not share a letter are significantly different.
Tukey 95% Simultaneous Confidence Intervals
All Pairwise Comparisons among Levels of business type
Individual confidence level = 97.91%
Business type = business subtracted from:
Business
Type Lower Center Upper ---------+---------+---------+---------+
Couple -197.8 6.3 210.3 (----------------*----------------)
Solo -174.5 29.5 233.5 (----------------*----------------)
---------+---------+---------+---------+
-120 0 120 240
Business type = couple subtracted from:
Business
Type Lower Center Upper ---------+---------+---------+---------+
Solo -180.8 23.3 227.3 (----------------*----------------)
---------+---------+---------+---------+
-120 0 120 240
Conclusions
In this analysis it clear that there is a significant difference between the different types of business the visitors had in the hotel. It’s also clear that the data provided show that there is a significant linear relationship between the visitor who had a couple visit in the hotel and those who had a solo visit in the hotel.
References
Tunner. D. E and Youssef-Morgar C.M (2013) statistics for managers. San Diego CA Bridge
point Education.
Kutner, M. H., C. J. Nachtsheim, J. Neter, andW. Li (2005). Applied Linear Statistical Models
(5th ed.). New York: McGraw-Hill/Irwin.
Brue Stanley. & Randy Grant. “The Evolution Of Economic Thought” Thomson Corporation,
2007. 61-83.print
APPENDIX
Question one
Q1 - How competitive is Janes Treasure with Jane Hotels in other cities?
b) From the above analysis we can see that jane treasure is better that Viking jane, but bonnie jane hotel is better than jane treasure.
c)
Bonnie jane is excellent since the values are very close to 5 points
Viking jane is skewed towards the point 4. This means that the Viking jane hotel is very good
Q2 - Determining target traveller types?
- The total sample is 1172 and the total population is 9500. The proportion represented is =11729500
=0.1234
Percentage is 12.34$
(b) The probability of solo travellers is 461/1172
=0.3933
The probability of couple travellers is 368/1172
=0.32
The probability of the business travellers 343/1172
=0.2927
The probability of the business travel at location aspect is 97/644
=0.151
The probability of the solo traveler at the aspect of the location is 354/644
=0.55
The probability of the couple traveller at the aspect of the location is 193/644
=0.30
d)
The probability of the business travel at location aspect is 14/140
=0.1
The probability of the solo traveler at the aspect of the location is 63/140
=0.45
The probability of the couple traveller at the aspect of the location is 14/140
=0.1
Q3 - Do higher prices produce higher ratings?
- The scatter plot of the prices verse the rating
(b)From the scatter plot, we can observe that as the price increased the overall rating increases. An increase of price by one unit lead to a decrease by 0.029304 unit, in the increase in rating on the hotel. The intercept has a value of -0.79054, this implies that when the prices are zero the rating of the hotels are negative
c) I do not have any concern about fitting the data in a regression analysis.
(d) Yes the price of $160 will generate a rating of approximately 4. That is
=160×0.029304-0.79054
≅4
Based on the scatter plot it is appropriate to make a regression line fit of the data
Q4 - Calculating time based on time of year
(b)
The 97.5% confidence level
C
- The probability that it exceed upper bound is
=0.05
- The probability that it below the lower bound
=0.0986122
=0.05
iii)
When the price is set to be $160, then the rating is 4
