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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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- Suppose we randomly sample 50 diabetics from among Irvine residents for a research study, and then for each diabetic we sample one non-diabetic Irvine resident with the same sex, age (within 5 years), and race. Among these participants there are 21 pairs for which the diabetic reports low SES and the non-diabetic reports high SES, 9 pairs for which both report low SES, 2 pairs for which both report high SES, and 18 pairs for which the diabetic reports high SES and the non-diabetic reports low SES. Test the null hypothesis that there is no association between SES and diabetes in Irvine.In Jolie’s new Thai restaurant, she observes the age of her customers and notes down which of the groups they belong to – ’18 years old and below’ or ‘above 18 years old’, and whether they spent more than $30 on a single meal - ‘big spender’ or ‘non-big spender’. Given that rate (big spender | above 18 years old) > rate (big spender | 18 years old and below), what conclusion can be made? a) Being a big spender and being above 18 years old are negatively associated.b) Being a big spender and being above 18 years old are positively associated.c) Being above 18 years old is positively associated with visiting her restaurant.d) Being above 18 years old causes one to become a big spender.A sample of 250 high school students were asked, “If you had $1000 to contribute to one kind of charitableorganization, which type of organization would you choose? Here is a two-way table that displays data ongender and response to this question. Which of the following conclusions seems to be supported by the data?(a) Most of the females who chose a health organization would have chosen an environmental organizationas their second choice, had they been asked.(b) There is no association between gender and choice of organization.(c) The proportion of males who said they would contribute to an environmental organization is higher thanthe proportion of females who said they would contribute such an organization.(d) None of the students surveyed said they would contribute to religious organizations.(e) The marginal relative frequencies of organization are 140, 110.
- A large national union wants to know the attitudes of each membership toward a proposed collective bargaining agreement, a random sample of 450 members taken in 4 unions yields the following. At 0.05 level of significance, is there a relationship bet the attitudes of the union members and the local union to which they belong? Attitudes of Membership In Favor Opposed Uncertain Local No.1 18 30 12 Local No.2 71 89 20 Local No.3 51 27 12 Local No.4 59 42 19Wolak, Mitchell, and Finkelhor (2002) used a survey of 1,501 adolescents to examine online relationships. The results showed that 14% reported close online friendships during the past year, 7% reported face-to-face meetings with online friends, and 2% reported romantic online relationships. Is this an example of a research design?If researchers reported that, for a correlated-groups design, t(20) = 3.57, p<.05, you can conclude that
- at a factory the emplyess were surveted and classified according to their level of education and if they smoked. educational level smoking habit Not hs graduate hs graduate college graduate smoke 6 14 19 dont smoke 18 7 25 if an emolyee is selected at random find these prob. a) the emplyoee smokes given that he or she graduated from college b) given that the employee did not graduate hs, he or she is a smokerConsider the following information about travelers onvacation (based partly on a recent Travelocity poll):40% check work email, 30% use a cell phone to stayconnected to work, 25% bring a laptop with them, 23%both check work email and use a cell phone to stayconnected, and 51% neither check work email nor usea cell phone to stay connected nor bring a laptop. Inaddition, 88 out of every 100 who bring a laptop alsocheck work email, and 70 out of every 100 who use acell phone to stay connected also bring a laptop.a. What is the probability that a randomly selectedtraveler who checks work email also uses a cellphone to stay connected?b. What is the probability that someone who brings alaptop on vacation also uses a cell phone to stayconnected?c. If the randomly selected traveler checked work emailand brought a laptop, what is the probability that he/she uses a cell phone to stay connected?Suppose that 60% of all students who have to buy a text for a particular course want a new copy, whereas the others want a used copy. Consider randomly selecting 15 purchasers, is a result of 12 a significantly high value for people who want a used copy of the book?
- Psychologist Bernie Silverman of Michigan State University tested the effect of astrological compatibility on marriages. In studying 2,978 marriage records and 478 corresponding divorce records in Michigan, Dr. Silverman found couples whose marriges were made in horoscope heaven united and split up just as frequently as those who were not astrologically compatible. He concluded that astrological compatibility did not have an effect on marriage success. Identify the population.A market research organization claims that, among500 shoppers interviewed, 308 regularly buy Product X,266 regularly buy Product Y, 103 regularly buy both, and59 buy neither on a regular basis. Using a Venn diagramand filling in the number of shoppers associated with thevarious regions, check whether the results of this studyshould be questioned.Students who are home-schooled often attend their local schools to participate in various types of activities such as sports or musical ensembles. According to the government, 82% of home-schoolers receive their education entirely at home, while 12% attend school up to 9 hours per week and 6% spend from 9 to 25 hours per week at school. A survey of 85 students who are home-schooled revealed the following information about where they receive their education. Entirely at home Up to 9 hours 9 to 25 hours 50 25 10 At α=0.05, is there suffificient evidence to conclude that the proportions differ from those stated by the government?