Chapter 11: Goodness of Fit 560 students from UC Berkeley are surveyed about whether they are from Northern California, Southern California, Central California, or from another state or country. A researcher is interested in seeing if the proportion of students from each of the four regions are all the same for all UC Berkeley students. The table below shows the outcome of the survey. Fill in the expected frequencies. Frequencies of UCB Students' Home Towns Outcome Frequency Expected Frequency Northern 138 California Southern 111 California Central 171 California Out of State 1402 goodness of fit Suppose a random sample of 860 athletes from the college are asked what their major is. The table below shows the results of the survey. Observed Frequencies of Majors from the Sample Outcome Observed Frequency Math/Science 233 Arts & Humanities 141 Business & Economics 243 Other 243 The distribution of majors at the college is shown in the second column of the table below. Fill in the expected frequencies. (Round to the nearest whole number). Frequencies of Majors at the College Outcome Expected Percent Expected Frequency Math/Science 23 Arts & Humanities 27 Business & 29 Economics Other 21X Chapter 11: Goodness of Fit A die is rolled 120 times to see if it is fair. The table below shows the frequencies for each of the six possible outcomes. Use a level of significance of a = 0.05. a. Complete the rest of the table by filling in the expected frequencies (enter your answers in fraction form): Frequency of Dice Values Outcome Frequency | Expected Frequency 11 2 22 3 21 25 5 22 6 18 6. What is the correct statistical test to use? Select an answer v c. What are the null and alternative hypotheses? Ho: The distribution of die rolls is not uniform. The die rolls are independent. The distribution of die rolls is uniform. The die rolls are dependent. H1: O The die rolls are dependent. The distribution of die rolls is not uniform. The die rolls are independent. O The distribution of die rolls is uniform. d. The degrees of freedom = . The test-statistic for this data = (Please show your answer to three decimal places.) f. The p-value for this sample = (Please show your answer to four decimal places.) g. The p-value is Select an answer va . Based on this, we should Select an answer v i. Thus, the final conclusion is... There is sufficient evidence to conclude that the distribution of die rolls is not uniform. There is insufficient evidence to conclude that the distribution of die rolls is not uniform. There is insufficient evidence to conclude that the die rolls are dependent. There is sufficient evidence to conclude that the die rolls are dependent. O There is sufficient evidence to conclude that the distribution of die rolls is uniform