UCLA conducted a survey of more than 263,000 college freshmen from 385 colleges in fall 2005. The results of students' expected majors by gender were reported in The Chronicle of Higher Education (2/2/2006). Suppose a survey of 5,000 graduating females and 5,000 graduating males was done as a follow-up last year to determine what their actual majors were. The results for females are shown in the table below. The second column in the table does not add to 100% because of rounding. Conduct a goodness-of-fit test to determine if the actual college majors of graduating females fit the distribution of their expected majors. (Use a significance level of 0.05.) Major Women - Expected Major Women - Actual Major Art & Humanities 14.0% 670 Biological Sciences 8.4% 410 Business 13.1% 685 Education 13.0% 650 Engineering 2.6% 145 Physical Sciences 2.6% 125 Professional 18.9% 975 Social Sciences 13.0% 605 Technical 0.4% 15 Other 5.8% 300 Undecided 8.0% 420 Part (a) State the null hypothesis. The actual college majors of graduating females and their expected majors are independent events. The distributions of the actual college majors of graduating females and their expected majors are the same.     The actual college majors of graduating females and their expected majors are dependent events. The actual college majors of graduating females fit the distribution of their expected majors. The actual college majors of graduating females do not fit the distribution of their expected majors. Part (b) State the alternative hypothesis. The actual college majors of graduating females and their expected majors are independent events. The actual college majors of graduating females and their expected majors are dependent events.     The actual college majors of graduating females do not fit the distribution of their expected majors. The distributions of the actual college majors of graduating females and their expected majors are not the same. The actual college majors of graduating females fit the distribution of their expected majors. Part (c) What are the degrees of freedom? (Enter an exact number as an integer, fraction, or decimal.)

In 1993 approximately 62.1 million Americans suffered injuries, as reported by the National Center for Health Statistics in Vital and Health Statistics. More males (33.4 million) were injured than females (28.7 million). Those statistics do not tell us whether males and females tend to be injured in similar circumstances. One set of categories commonly used for accident circumstances. One set of categories commonly used for accident circumstance is "while at work," "home", "motor vehicle", and "other". A random sample of accident reports gave the data in contingency table below. Male Female While at work 19 24 27 Home 14 Motor Vehicle 26 Other At the 5% significance level, do the data provide sufficient evidence to conclude that an association exists between accident circumstances and sex? Type in Canvas the grand total. 35

Suppose an internet marketing company wants to determine the current percentage of customers who click on ads on their smartphones. How many customers should the company survey in order to be 90% confident that the estimated proportion is within 2 percentage points of the true population proportion of customers who click on ads on their smartphones?