Statistic Essay Example

  • Category:
    Mathematics
  • Document type:
    Assignment
  • Level:
    High School
  • Page:
    3
  • Words:
    2151

11STATISTICS

Statistics

Introduction

This paper focuses on the hypothesis testing for purposes of providing sufficient statistical assistance in order to help Michael Jenkins in making decisions regarding location, promotion, and last but not the least pricing strategy. The client’s dream of an upscale restaurant that would feature drinks, deserts and finest entrees in a strategic atmosphere would require many hypothetical testing methods. This hypotheses method in this essay will include; samples t-tests, ANOVA, paired sample t-test, independents sample t-test, and Chi-test to make his business a success.

From the information given, it is clear that he needs additional and fundamental information on whether a good market exists for the services he intends to render. Furthermore, critical information needs to be provided, for instance, the best promotion strategy of the restaurant in his town upon opening. The design of his restaurant, the best location and the market price for the upscale entree are some of the many choices to be factored in. The company has promised that upon collection of reliable and valid information to patronizing the restaurant it create an accurate break analysis and compare it with the expected numbers of patrons.

As a matter of fact, the research company had made several estimates of demand by employing a forecasting model. For instance, a 4% heads of household at the 12 post code locality claimed they were “very likely” to patronize it and if the same persons spent average of $200 a month in restaurants and would be willing $18 on average for an à la carte entrée. This model predicted an excellent performing restaurant in terms of its operation. The company had also obtained a demographic data on each and every post code within the metropolitan area. These were categorized into groups of four according to their similarities as summarized on appendix 1.

The available demographic information shown suggests that either a locality within post codes 3,4, and 5 or among 6,7,8 and 9.The unfortunate scenario of these sets of post codes is that they are not close to each other and a comprehensive analysis shall be taken to assist Michael in this and other critical decisions.

This report basically focuses on addressing ten identified questions and to conduct hypothesis and then statistically analyze this for sole purpose of assisting Michael in making informed and valid business decision that is based on verified evidence and finally to determine whether “Divine Elegance“ would be a success.

Data Screening

The very first step is data collection. Once this is collected and before it is analyzed is it of fundamental importance to view and screen this data. Based on the screening process, I believe that the data of 60 are logically inconsistent. The 60 data relating to the evening meal price, entrée customer is likely to pay 999 dollars. In reality this has a low possibility. In this regard, these data shall not be included in the data analysis. Consequently, I accept the null hypothesis. This then makes me to conclude that the price on average for the evening meal entrée is not significantly different from the 18 dollars.

Ho: μ=18

H1: μ≠ 18

One-sample statistics

What would you expect an average evening meal entree |340 |$18.8353 |$9.82784 |$.53299 |

Probable Patron of the new restaurant? | Mean | N | Std. Deviation |

Yes | $30.2364 | 110 | $8.81817 |

No | $13.3826 | 230 | $3.69724 |

Total | $18.8353 | 340 | $9.82784 |

From the above it is evident that the majority of respondents who are likely patrons to Michaels restaurant are ready to pay $21-$30 with the largest group are ready to pay between $31 -$40 for their entrees.

H1: μ ≠ $18 Therefore, the nulls hypothesis rejected. The mean of the sample is not $18.

In layman’s words, the results are significant statistically and conclusions obtained from the test data in order to make inferences concerning the general population. In this particular case, we tested on whether potential patrons are ready to pay the $18.00 for an entrée as it was used as an assumed price for an entrée in the preliminary analysis. First, in the group of potential patrons tested it was found out that the average or mean price they were prepared to pay for an entrée was a sum of $30.23. It was also worth noting that over the larger sampled population the mean price people were ready to pay $18.83. This amount is slightly higher than the allowed price but it was also noted that the average for those unlikely to be patrons was over 13 dollars. Therefore, from this we are able to determine that patrons are mostly likely prepared to pay slightly more than the 18 dollars used in the forecasting. They are on average prepared to pay 30.23 dollars for an individual entrée.

Variable 1

Variable 2

18.83529

Variance

96.58636

0

Observations

Pooled Variance

48.29318

Hypothesized Average

Differencev

0

1.567188

P(T<=t) 1-tail

0.058769

t Criticle 1-tail

1.647104

P(T<=t) 2-tail

0.117537

t Criticals 2-tail

1.963469

The next item to analyze would be the dollars spend per month in the restaurants for the meals |400 |$150.0525 |$92.70629 |$4.63531. From the analyses it is probable for patrons on mean spend between 200 and 300 dollars for foods per month. The test is significant statistically and thus the result indicates Michael forecasting at 200 dollars as to be correct with his market target.

It is stated on the question that assumptions have already been made that areas B and C are considered to be the most likely localities for r Michael’s restaurant. Subsequent, assumptions shall be made with this in considerations. The assumptions were based on demographic research and previous market conducted by a research agency. With this in mind the question would be, is it area b or c? It is clear that areas B and C have been the great focus in this survey as evidenced by their large sizes

H0: Areas B and C shall provide good locations for Michael to open the restaurant.

H0: b = (is equal to) c

H1: One area (B or C) will offer a better location for Michael to open the restaurant.

H1: b ≠ (is not equal to) c

H1: b ≠ c

A cross tabulation is always used to compare the relationship between two variables that are different. In this regard we shall be comparing location b and c and “Is the respondent a likely a patron” as the variable. With this testing the hypothesis that b and c offers equally good locations for Michael to open the restaurant is possible. (See appendix 1). As to which code area would provide the best restaurant location for Michael, it is evident that area B is the most suitable for its location and the average amount of dollars spend actually differs among the patrons in the different area codes.

The people with a higher income are likely to patron his restaurant. As demonstrated with a correlation analysis the strength of relationship between variable is established.( Appendix 2). I would also do a cross tabulation to test. This would establish the relationship between the gender and whether or not one is would be possible patron. Finally, test the assumption of those questioned were spread between females and males and compare the frequencies. The results for the target group have a preference for elegant desire. In spite of the fact that overall popular prefer a simple décor I recommend elegant décor based on the outcome.

The overall surveyed samples prefer a Jazz combo station. In spite of this, the target market of probable patrons considerably prefers a string quartet. It is without doubt that I would recommend string quartet based on this. The radio station Michael would use for his advertisement, it is statistically evident from the Easy Listening Radio is the most popular overall. In addition, the news at 6 pm and Business sections of the local newspaper and editorial par would be best for him to use in that order.

There is a likelihood of patronizing the restaurant through common culminated variables by factoring in the variables common to probable patrons. In addition the mean age for a probable patron is higher with no relationship between the genders.

Live entertainment can be in form of quartet or a jazz combo and we can test by:

H0- Probable patrons have no preference between a string quartet and a jazz combo

H1- Probably patrons prefer Jazz or strings more than the other.

As for how to promote, Jazz Combo music radio channel would be ideal choice to promote the restaurant. With regard to the potential patrons, probable patrons were born between 1940 and 1949; however, there is no significant association between gender and whether or not someone is a probable patron.

H0- There is no relationship between gender and whether or not someone is a probable patron.

H1- There is a relationship between gender and whether someone is a probable patron.

I would do a cross tabulation to test the relationship between gender and whether or not someone is a possible patron. I would also test the assumption that those questioned are spread equally between male and females and compare their frequencies.

Conclusion and Recommendation

In the process of break-even analysis, there are several assumptions, which have to be made to generate the conclusion that the upscale restaurant would be an successful operation. For one thing, the demand for an upscale restaurant should be determined at the first place. Based on the hypothesis test results, I maintain that the areas with post code 3, 4 and 5 would be the best location for the restaurant. Concerning which areas are the best location for this restaurant, there are two criteria should be taken into consideration, including the number of people residing in those areas, and how much they are willing to pay for their meal. Even though this area has less population, residents have high possibility to be able to afford higher price to dine in a fine restaurant (mean = $250.7). As for the area with post code 6, 7, 8, and 9, occupants are less likely to have the capability to afford expensive meals, although there are more local residents.

For another, the price level is also essential in terms of whether the restaurant is successful. From the one sample t-test, there is sufficient evidence to support that potential patrons are willing to pay an average of $18 for an entrée. In this case, this project seems feasible.

References

Perkins, A. and Baxter, S. (2012). Foundations of Business Analysis: Fundamentals of Quantitative and Qualitative Analysis. Pearson

Appendix 1

A Cross tabulation gives us information about bivariate relationships.

Probable Patron of the new restaurant? * Please check the letter that includes the Post Code in which you live (coded by letter). Cross tabulation |

| Please check the letter that includes the Post Code in which you live (coded by letter). | Total |

| A (1 and 2) | B (3, 4, and 5) | C (6, 7, 8, and 9) | D (10, 11, and 12) | |

Probable Patron of the new restaurant? | Yes | Count | 0 | 91 | 19 | 1 | 111 |

| | % within Probable Patron of the new restaurant? | 0.0% | 82.0% | 17.1% | 0.9% | 100.0% |

| | % within Please check the letter that includes the Post Code in which you live (coded by letter). | 0.0% | 75.8% | 8.6% | 2.5% | 27.8% |

| No | Count | 20 | 29 | 201 | 39 | 289 |

| | % within Probable Patron of the new restaurant? | 6.9% | 10.0% | 69.6% | 13.5% | 100.0% |

| | % within Please check the letter that includes the Post Code in which you live (coded by letter). | 100.0% | 24.2% | 91.4% | 97.5% | 72.2% |

Total | Count | 20 | 120 | 220 | 40 | 400 |

| % within Probable Patron of the new restaurant? | 5.0% | 30.0% | 55.0% | 10.0% | 100.0% |

| % within Please check the letter that includes the Post Code in which you live (coded by letter). | 100% | 100% | 100% | 100% | 100% |

Chi-Squares Tests |

| Values | dfs | Asymp. S (2-sid) |

Pearsons Chi-Squares | 198.868a | 3 | 0.00 |

The Likelihood Ratios | 201.011 | 3 | .000 |

Linear Association | 78.406 | 1 | .000 |

No Valid Case | 400 |

a. 0 cells (0.0%) has expected counts less < 5. The minimum count is 5.55. |

p-value is <.05. Therefore it is statistically significant. There is a strong suggestion from the data that area B is likely to be a better location for Michael to start his restaurant.