You are interested in the probability of the outcome when rolling a six-sided die. Answer the following questions using p to denote the probability of this outcome.

(a) You suspect that for this die the outcome does not occur with the same probability as with a fair die. Formulate the null and alternative hypotheses based on which you may make a statistical inference regarding your suspicion.

(b) You suspect that for this die the outcome occurs with greater probability than with a fair die. Formulate the null and alternative hypotheses based on which you may make a statistical inference regarding your suspicion.

(c) You suspect that for this die the outcome occurs with lesser probability than with a fair die. Formulate the null and alternative hypotheses based on which you may make a statistical inference regarding your suspicion.

(d) You believe that for this die the outcome occurs with the same probability as with a fair die.

How might you collect evidence in support of your belief?

Which is easier: to collect evidence in favor of balancedness or to collect evidence against balancedness?

QUESTION 12 . 1 POINT Which of the following is not a characteristic of the chi-square distribution? Select all correct answers. Select all that apply: The mean of the chi-square distribution is located to the left of the peak. The chi-square curve is nonsymmetrical. The x' curve approaches, but never touches, the positive horizontal axis. As the degrees of freedom increases, the chi-square curves look more and more like a normal curve. FEEDBIn which of the following situations should the chi-square test for goodness-of-fit be used? Select the correct answer below: An online research company puts out a survey asking people two questions. First, it asks whether they buy groceries online. Second, it asks whether they own a car or not. The data are collected and recorded in a contingency table. The company wants to determine if there is a relationship between buying groceries online and car ownership. O A researcher is trying to determine if the amount of time children spend watching television has the same distribution for boys and for girls. She surveys a random sample of families and records the distribution of time spent watching television for each gender. She wants to determine if the distributions are the same. O A professor is trying to decide if her students randomly guessed on a certain multiple choice question or if they had some idea of the correct answer. She records the number of students who answered with each answer choice and compares this distribution with a uniform distribution, which is what she would expect if everyone L had guessed.1. (10 points) A dean of a business school wanted to know whether the graduates of her school used a statistical inference technique during their rst year of employment after graduation. She surveyed 314 graduates and asked about the use of statistical techniques. After tallying the responses, she found that 204 used statistical inference within one year of graduation. Estimate with 90% condence the proportion of all business school graduates who use their statistical education within a year of graduation