Example Chi-Square Test for a Multinomial Experiment

One use of a chi-square distribution is with hypothesis tests for multinomial experiments. To see how this hypothesis test works, we will investigate the following two examples.   Both examples work through the same set of steps: Form the null and alternative hypothesesCalculate the test statisticFind the critical valueMake a decision on whether to reject or fail to reject our null hypothesis.   Example 1: A Fair Coin For our first example, we want to look at a coin.   A fair coin has an equal probability of 1/2 of coming up heads or tails. We toss a coin 1000 times and record the results of a total of 580 heads and 420 tails. We want to test the hypothesis at a 95% level of confidence that the coin we flipped is fair. More formally, the null hypothesis H0 is that the coin is fair. Since we are comparing observed frequencies of results from a coin toss to the expected frequencies from an idealized fair coin, a chi-square test should be used. Compute the Chi-Square Statistic We begin by computing the chi-square statistic for this scenario. There are two events, heads and tails. Heads has an observed frequency of f1 580 with expected frequency of e1 50% x 1000 500. Tails have an observed frequency of f2 420 with an expected frequency of e1 500. We now use the formula for the chi-square statistic and see that χ2 (f1 - e1 )2/e1 (f2 - e2 )2/e2 802/500 (-80)2/500 25.6. Find the Critical Value Next, we need to find the critical value for the proper chi-square distribution. Since there are two outcomes for the coin there are two categories to consider. The number of degrees of freedom is one less than the number of categories: 2 - 1 1. We use the chi-square distribution for this number of degrees of freedom and see that χ20.953.841. Reject or Fail to Reject? Finally, we compare the calculated chi-square statistic with the critical value from the table. Since 25.6 3.841, we reject the null hypothesis that this is a fair coin. Example 2: A Fair Die A fair die has an equal probability of 1/6 of rolling a one, two, three, four, five or six. We roll a die 600 times and note that we roll a one 106 times, a two 90 times, a three 98 times, a four 102 times, a five 100 times and a six 104 times. We want to test the hypothesis at a 95% level of confidence that we have a fair die. Compute the Chi-Square Statistic There are six events, each with expected frequency of 1/6 x 600 100. The observed frequencies are f1 106, f2 90, f3 98, f4 102, f5 100, f6 104, We now use the formula for the chi-square statistic and see that χ2 (f1 - e1 )2/e1 (f2 - e2 )2/e2 (f3 - e3 )2/e3(f4 - e4 )2/e4(f5 - e5 )2/e5(f6 - e6 )2/e6 1.6. Find the Critical Value Next, we need to find the critical value for the proper chi-square distribution. Since there are six categories of outcomes for the die, the number of degrees of freedom is one less than this: 6 - 1 5. We use the chi-square distribution for five degrees of freedom and see that χ20.9511.071. Reject or Fail to Reject? Finally, we compare the calculated chi-square statistic with the critical value from the table. Since the calculated chi-square statistic is 1.6 is less than our critical value of 11.071, we fail to reject the null hypothesis.

The Sorrow Of War And Full Metal Jacket Essay - 1287 Words

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Marketing Strategy and Plan Business Technological Plan

Question: Describe about the Marketing Strategy and Plan for Business Technological Plan. Answer: Introduction Technology is the combination of scientific knowledge and some scientific techniques which applied for the purpose of making the life of the common people easy and convenient. One can consider twenty-first century as the era of technology as the technological development is at its pick right now. There is technology everywhere as we have become heavily dependent on them (Norman Verganti, 2014). Emerging technologies refers to those technologies which are unorthodox from the scientific point of view and at the same time they can transform the life of common people heavily. There is s great significance of emerging technologies in todays life (Vashist et al., 201). The main purpose of the report is to develop marketing plan and strategies for a new emerging technology. Standing at the time of environmental resource shortage, it is very essential to develop something which can be beneficial for both the environment and for the common people. Thus, the Next-Generation Batteries are considered as the emerging technology for this report. The first part of the report gives a brief introduction of the report. After that, a description of the product as well as the unique selling propositions is discussed. The next parts involve various stages of the development of the marketing plans and strategies of the product. These parts include the description of target customers, pricing and positioning policies, promotional techniques, financial plans and others. Lastly, based on the total report, a conclusion has been drawn. Description and Unique Selling Proposition (USP) Energy is the most important resource in the world. People all over the globe heavily depend on the source of energies for their various needs. Two of the most important source of energies is the solar energy and the wind power energy. A large number of people all over the world are using these two energies for their daily purposes. However, the fact is that there is a high uncertainty exists in the supply of solar and wind powers. On the other hand, renewable powers are not reliable to the common people as they cannot afford the price of the products. These are the main reasons why emerging technologies are gaining popularities. Among them, the Next-Generation Batteries are on e of the most important emerging technologies in the globe. There is huge difference between the existing carbon batteries and the Next-Generation Batteries. They existing lead-acid batteries consist of heavy metals, carbons, caustic chemicals and many other ingredients which have an adverse effect on the environment as well as on the humans and animals. However, the main ingredients of Next-Generation Batteries are sodium, aluminum and zinc which do not have an adverse effect toward the environment and the ecosystem. There is some Unique Selling Propositions (USP) of Next-Generation Batteries. First of all, they come in all sizes. That is they can be used for the house purposes as well as for the industrial purposes. The Next-Generation Batteries have the capacity to provide power to a whole small village. One of the greatest USPs of this kind of batteries is the affordable price. The price of Next-Generation Batteries is comparatively lower than the conventional batteries. On the other hand, Next-Generation Batteries are emission free batte ries which use less energy so that they can be used for lone times (www.weforum.org 2016). Target Customers Customers are one of the most important aspects of a marketing plan as the product is developed for them. The first aspect of developing a marketing plan is to set the target customers (Ratliff Gallego, 2013). In the case of Next-Generation Batteries, there are certain divisions in the target customers. As per the description, Next-Generation Batteries are available in different sizes for different uses. Firstly, the target customers will be divided in two age groups; they are 7years-25 years and 25 years above (Wedel Kamakura, 2012). The first age group consists of school and college goers who need to use calculators, laptops and other educational props which need batteries. The second age group consists of professionals and businessmen who need batteries for different uses. On the other hand, the Next-Generation Batteries will be available for the industrial purposes. Now-a-days businesses have become more environments friendly. Thus, the Next-Generation Batteries will be popular among the business for its environment friendly features. The Next-Generation Batteries will be available for lighting up the remote villages where there is no connection of electricity. These are the potential customers of the Next-Generation Batteries. It is believed that the unique features of the product will make in popular among the users. Pricing and Positioning Strategies Pricing and positioning strategies set the direction of a product as they are very much crucial for the success of a product. In case of the Next-Generation Batteries, high penetration pricing policy has been recommended. In the high penetration strategy, initially the price of the product is kept low to gain popularity (Spann, Fischer Tellis, 2014). This strategy is perfectly applicable for the Next-Generation Batteries as it is brand new product in the market. Though the price of this kind of batteries are lower than the conventional batteries, the much lower price at the time of introduction will help in switching the customers from other products to this product (Kireyev, Kumar Ofek, 2014). Positioning strategy refers to the techniques to present the new technology to the customers. There is no need for competitors analysis as the Next-Generation Batteries are brand new products and no other companies produce this kind of product. Hence, there is strong need to make the customers know about the products. The tagline for the Next-Generation Batteries will be Power for the World. The advertisement of this product will be come with this tagline. The USPs of the product needs to be stated clearly as it will create mass awareness about the Next-Generation Batteries (Solomon, 2014). Distribution Plan Distribution plan refers to the process of distributing the product among the customers. There are certain factors in this process that needs to be taken care in a good manner (Bai Xu, 2015). As the adopted price policy is high penetration, it is recommended that there should be fewer intermediaries between the producers and the customer. Next-Generation Batteries are a brand new technology in the market. Though it is an excellent product, it is not possible to ascertain the demand of the product. Hence, it is recommended that the company should produce a minimum unit of products to test the market demand. After that, production will be done accordingly. Various types of Next-Generation Batteries will be delivered to different shops and dealers for the purpose of selling. Customers can buy the Next-Generation Batteries from those shops directly. On the other hand, the company is planning to give dealership of the Next-Generation Batteries to the interested dealers. They will buy the product on the behalf of the company. In case of the large Next-Generation Batteries, there will be support for the installation of the batteries in plants and other places. There will be a system of after sales services for the large batteries (Raut, 2013). Offers Offer is an important tool for marketing plan. Attractive offers always help to attract more customers toward the product (Jolibert et al., 2012). In the case of the Next-Generation Batteries, there is a great significance of offers in formulating the marketing plans and strategies. As per the report, the Next-Generation Batteries are an emerging technology which has never used before. Hence, it is natural that people will be hesitated to buy the products and use them as there is a high chance of making loss. This is the part where attractive offers play a special role. Some special deals and offers have been developed. There will be a discount of 20% on the price of all batteries in the first six months of launching. Guarantee period will be offered with each type of Next-Generation Batteries. In case of any inconveniences in the guarantee period, the product will be replaces with another new one. In case of the big Next-Generation Batteries, the post installation services for six m onths will be provided in free of cost. Again, in case of the big batteries, live online support will be provided by the technological expert of the company for 24*7. These are the attractive offers and services offered by the company (Christopher, Payne Ballantyne, 2013). Marketing Materials Marketing material refers to various printed pieces that will help to market the business. There are various kind of marketing materials are available to promote the new product (Crocker, 2016). In case of the Next-Generation Batteries, the following marketing materials are suggested: A well-designed website: This is the era of internet. In this era, people like to search for everything in the Google. Thus, it is much needed to develop a well designed website which will contain all necessary information about the Next-Generation Batteries (Gibbs Gretzel, 2015). Business Cards: A well-designed business card is another excellent way to promote the business of Next-Generation Batteries. A potential customer may not be interested to by the products until he/she is handed a business card. Eye-Catching Catalogues: Catalogues are something which contained the printed images and descriptions of prices about the products. In case of Next-Generation Batteries, a catalogue is recommended to develop so that customers can see and choose the variety of Next-Generation Batteries. Professional Letterhead and Custom Envelop: It is recommended to create a letterhead and customized envelop for which will include the logo, name, address, tagline and a picture of the company. This will create a good impression to the customers. Marketing and Promotional Strategies Marketing and promotional strategies are the strategies which helps a business to reach to its target customers. There are various kinds of promotional strategies. However, all of the promotional strategies are not applicable in all situations (Kotler et al., 2015). In case of the Next-Generation Batteries, the adopted promotional strategies are discussed below: Television Ads: One of the best promotional tactics is giving the advertisement in various popular TV channels. Almost every people watches TV now-a-days. This strategy will help to promoter the Next-Generation Batteries in potential customers (Bellman et al., 2014). Internet Ads: Twenty-first century is the century of internet. Every people all over the world is using internet on daily basis. Hence, an advertisement in the internet will make a large portion of people aware of the Next-Generation Batteries. Newspapers: There are many remote places where there is no electricity for television and internet. Newspaper is the ideal medium for promotion in that kind of places. Newspaper reaches every corner of a country and an advertisement of the Next-Generation Batteries in the newspapers will let people know about the emerging technology. Public Relation: The organization should organize various kinds of public relation events stating the features of the Next-Generation Batteries. This events will help people know about the product and will also develop the relationship between the customers and the company. Press Release: Various Press releases will be published on a regular basis. These will include the description of the verities of the Next-Generation Batteries. A lot of people will come to know about the product through these press releases. Joint Ventures and Partnerships There is a huge cost involved in the process of presenting a new emerging technology in the market. First of all, it is a process of continuous learning which requires research and the research cost is generally very high. Thus, it is suggested that the company should make a partnership or make a joint venture with other technological companies so that the research process can be carried on smoothly (Killing, 2012). In this perspective, it is recommended to tie up with electronic companies and automotive companies. These two types of companies are recommended because they have operations which include various types of batteries. On the other hand, the joint venture will help to raise funds for the further research and development of the Next-Generation Batteries. Thus, it is recommended to make a partnership or joint venture for the betterment of the research (Lorange, 2013). Financial Projection Financial projection refers to the forecast or estimation of the revenues and the expense of an organization. On the other hand, the financial projection also includes the long term financial plans of an organization (Jesus Silva, 2012). In case of the Next-Generation Batteries, it is not possible to find out the historical financial data of the product as it is brand new product. Again, it is not possible to know the revenues. However, the revenues can be estimated. There are various cost involved in the process of development and marketing of the Next-Generation Batteries. The expenses are the development expense, promotional expense, marketing expense and others. The projected expenses are shown below: Expenses Cost ($) Development Expense 2,00,000 Promotional Expense 1,00,000 Advertising Expense 75,000 Legal Expense 50,000 Distribution Expense 50,000 Others 25,000 Total 5,00,000 The above table shows the projected expenses of the development of the Next-Generation Batteries and the marketing cost. As per the above table, the expense which includes the most amount of money is the development cost of the Next-Generation Batteries. As this is a new product in the market, it needs a lot of promotion and advertisements. This is why there is a large expense projected in promotional and advertisement activities. There are other expenses like the legal and distribution expenses. It is predicted that the new technology that is the Next-Generation Batteries will generate revenue of more than $ 5, 00,000. However, the exact amount cannot be predicted. The long term financial plan of the company is to gain the top market share in terms of the revenue from Next-Generation Batteries. The expenses will be shared by the partner companies as a joint venture is proposed. On the other hand, the necessary funds will be provided by the main as well as by the partner companies (G artner, Frid Alexander, 2012). Conclusion Technology is an important aspect in todays life. It is almost difficult to survive without the help of technology. Standing at this point, emerging technologies are covering the world gradually. One of those emerging technologies is the Next-Generation Batteries. Next-Generation Batteries helps to reduce the use of natural resources. As per the report, the marketing plan and strategies of Next-Generation Batteries has been recommended. While preparing the report, it has been seen that there are certain important aspects exist which need to be considered while developing the marketing plan and strategies. One needs to identify the unique selling propositions of the product which they want to market. After that the ascertainment of potential or target customers is important. It helps to predict the customer base of the product. The next very important aspect is the setting up of pricing policy and positioning strategy. This is a very sensitive place where the effective decision is needed. Pricing should be in such a way that the customers are attracted to buy the product. After that, the product needs to be presented in such a way that the unique selling propositions are highlighted clearly. On the other hand, the advertising and promotional strategy should be effective so that the people become aware of the product. It is very important to make the financial projection along with the marketing plan as this will decide the direction of the product. Hence, it is concluded that, to make an effective marketing plan d strategy, it is necessary to consider and include all the marketing aspe cts. References Bai, X., Xu, L. (2015, March). Production and distribution plan for fresh produce under random fuzzy environment. InFuture Information Engineering and Manufacturing Science: Proceedings of the 2014 International Conference on Future Information Engineering and Manufacturing Science (FIEMS 2014), June 26-27, 2014, Beijing, China(Vol. 2, p. 139). CRC Press. 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Engelwood Cliffs, NJ: prentice Hall. Spann, M., Fischer, M., Tellis, G. J. (2014). Skimming or penetration? strategic dynamic pricing for new products.Marketing Science,34(2), 235-249. These next-generation batteries could end energy poverty. (2016).World Economic Forum. Retrieved 19 October 2016, from https://www.weforum.org/agenda/2016/06/next-generation-batteries Vashist, S. K., Luppa, P. B., Yeo, L. Y., Ozcan, A., Luong, J. H. (2015). Emerging technologies for next-generation point-of-care testing.Trends in biotechnology,33(11), 692-705 Wedel, M., Kamakura, W. A. (2012).Market segmentation: Conceptual and methodological foundations(Vol. 8). Springer Science Business Media.