Sección: Intervalos de confianzaConstruya un intervalo de confianza del 95% para la proporción de llamadas resueltas usando aproximación normal. ¿Cuál es el intervalo?

Please note that this question consists of seven parts. Show all your work. You may use Minitab but you need to show the steps to get the answer. Just giving the answer without showing work may result in zero for the question.  A random sample of 300 students is taken. A contingency table below summarizes the data on whether a student is in Honor Roll or not, and whether a student is a Music student or not. The expected counts are provided in red within the parentheses. Music Student Honor Roll Student Total Yes No Yes 17 (16.17)  33 (33.83)  50 No 80 (80.83) 170 (169.17) 250 Total 97 203 300   Write in the context of the problem the null and alternative hypotheses to test if there is an association between “Music Student” and “Honor Roll Student”. Under the null hypothesis, how many students, who are music students and are in Honor roll, should we expect to see? Clearly show the mathematical calculation to obtain this value. Calculate the test statistic for the test of the hypotheses in part 1.  You must show the mathematical calculation to obtain the value of the test statistic. You may use Minitab to get the very final numerical value.  State the distribution of the test statistic under the null hypothesis, including the degrees of freedom.  Find the p-value for the test of the hypotheses in part 1. You must clearly write down the probability statement for the p-value. You can then use the appropriate table or Minitab to find the final numerical value of the p value.  Write the final conclusion in the context of the problem at 5% significance level. From the methods covered in this course, suggest another test that would answer the same research question (you do not need to conduct the testing procedure here).     

Please note that this question consists of eight parts. Show all your work. Just giving the answer without showing work may result in zero for the question.  There is a dataset on “crime” and “edu” which gives characteristics of 84 medium-sized U.S. counties. The overall purpose for the data set is to analyze factors that predict crime. The variable “crime” is the crime rate reported per 100,000 residents last year. The variable “edu” is the percentage of individuals in the county having at least a high-school diploma.  The researcher is interested in developing a regression model to predict the “crime” based on the “edu” using these data. Partial output of the regression analysis is provided below. Write down in the context of the problem the least squares regression line for predicting the crime rate from the education percentage. Write in the context of this problem the interpretation of the estimated slope. We want to see if there is convincing evidence that the crime rate decreases as the education percentage increases. Write the appropriate null and alternative hypotheses to test this. Use the proper notations when setting up the hypotheses.   Calculate the test statistic for the test in part 3. Show how you calculate it. Find the p value for the test. You must clearly write down the probability statement for the p-value. You can use the appropriate distribution table or Minitab for the value.  Write the final conclusion of the test in part 3 in the context of the problem. Use 5% significance level.  What is the correlation between the crime rate and the education percentage? Explain how you find it. What is the predicted crime rate for a county with 71% residents who have at least a high-school diploma? Show how you calculate it.     

Students in an introductory chemistry class participate in a mid-semester survey. They were asked whether having recitation classes better prepare them for the course. Their opinions were coded as “0” if the answer was No, “1” if the answer was Somewhat helpful, and “2” if the answer was Yes. This variable is:   

Find the following numerical values. (a)

A vending machine sells bottles of coke, diet coke, lemonade, sweet tea, and water.  (a) How many different selections are there for a purchase of 10 bottles, assuming there are more than 10 bottles of each type?Answer: selections (b) If the machine shows that there are only two bottles of coke left for sale (where there are more than 10 bottles of each of the others), how many different selections are there for a purchase of 10 bottles?Answer: selections

A coin is tossed 12 times and the results are recorded. (a) How many outcomes have exactly 4 heads?Answer: outcomes (b) How many outcomes have at most 2 heads?Answer: strings

Find the following values. (a)

Consider reordering the letters in the word SUCCESS. (a) How many different ways are there to reorder the letters in a row?Answer: ways (b) How many different ways are there to reorder the letters in a row, which both begin and end with S?Answer: ways

In a group of 00 people, how many people at least must have the same first and last initials (from the 26 letters of English alphabet), assuming each person has a first and last name?