Chi-Square Goodness of Fit and Independence (50 points) For this homework assignment, you will use hand calculations and JMP software to work through the problems in order to develop an understanding...

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Chi-Square Goodness of Fit and Independence (50 points) For this homework assignment, you will use hand calculations and JMP software to work through the problems in order to develop an understanding of inferential statistics using Nominal data. The inferential statistics we will be using in this class with nominal data are Chi-Square Goodness of Fit and Chi-Square Measures of Independence. Please work through the following problems on your own. Feel free to consult other students if you need help, but please, complete the homework assignment on your own. Avoid plagiarism or duplicate copies of other students, per the University of Florida academic code. For hand calculations, please show all steps of the calculation for credit. This can be submitted as a scanned copy of a hand-written sheet, or through online on word or an excel document. If the answer is written with no calculations – you will receive no credit for that question. For all problems that you are to use JMP, a screenshot or picture of each output must be included for full credit. Without this proof, no credit will be given. For all examples, we will assume an alpha of 0.05. 1. You and a friend are planning to use a coin in order to decide who gets to go on a free vacation. The winner of a coin toss will win the trip. However, prior to the coin toss, you want to check to make sure the coin is fair. You therefore wish to use a Chi-Square Goodness of Fit test, along with a randomly flipping the coin 20 times, in order to make sure it does not significantly vary from the expected distribution. For this example, the expected frequency of a heads is 0.5, and the expected frequency of a tails is 0.5. Please calculate the Chi-Square by hand for the following data in the table below, keeping in mind that there are 20 samples, so adjust your expected frequency as necessary (10 points): Heads 12 Tails 8 Total 20 a. Fill in the information in the following table to help you calculate a Goodness-of-Fit Chi-Square (4 Points):