Question 1 (15 pts) Small bacinceses are often mentionvel ly jpolicymakess as playing a hey fole in providitig gooel atd atable jobs for workers in the United States. This problem asios you to aishlyae whether they influence wueloers" career prospects early on in thesr warkins careers. Buppose that 15% of all baviacises in the Vuited Stafes ate Staall besincmes. The temainias 850 are either Mediun or Large businesses Stuppose that the share of Medinm besisesses ar WeE and the share of Large businesaes is 55%. Morewer, supviose that workets are either Farly in their career of Late in their career, 55% of worloer are Farly Career worlares aad the remaining 45% are Late Caperr worlerm. You have a job working as a reseatsh atiahst at the Dnited States Cetwas Bureat stmilyigg denographic patterns of workers and dyratmios of businesus. You and your colleagoes cotatuct a sarvey and find that if a worker is Late Carecr, they have an 75% probahility of working at a Large basimess. a) ( 3pts ) Find, yout boss asks yot to wse your survey results as well as your knowledge of statistios on businesees and wodkers to fill wut the following ftolability takle. Sle has been woeking at the Census Bureau a long time, so she knows a few of these statistirs and already pot yout startod. b) (4 pts) Your boss asks you the following: If a worker works at a Senall besibes,, what is the prolability they are as Early Careve warker? c) ( 4 pts) If a worker works at a Staall tasines, what is the prohability they are a Late Carer worker? d) ( 4 pts) Do you think Early Career wotiors are more bloriy to woti at Small betainears or Large businnsoes? Explain. You are interested in beconing a corporate lawyer and you want to get a sense of the salary level in this profession. Your older sister is a corporate lawyer, so you ask 10 of her friends who also work in corporate law their salaries in the last year. In sum, the ten friends made a lot of money: you added together their 10 salaries and found the amount $2,000,000 ! Now you want to use this information to estimate the average salary in corporate law (the average salary in the population of corporate lawyers). Suppose that you know that the variance of salaries in corporate law is $250,000 dollars squared. You decide that you want to be "90\% confident" about any estimate you get. a. (5 pts) What is the z/2 value for a 90% confidence level? How do you know? b. (5 pts) What is the margin of error ME for your estimate? c. (5 pts) What is the upper confidence limit (UCL) and the lower confidence limit (LCL)? d. (5 pts) What is the 90% confidence interval? e. (5pts) Provide an accurate interpretation of this confidence interval. You have an internship at the Gillette World Shaving Headquarters in Boston. The company is developing a new line of razors and management asks you to oonduct market research on men's shaving habits, You conduct a survey where a sample of men report the number of times that they shave in one week. Suppose you know that the number of times per week men shave in the population is normally distributed with a variance of 2. You hypothesize that in the population, men shave at least on average 4 times per week. Now, suppose that you randomly select 121 men and find they shave 3.6 times per week on average. a. (5 pts) Complete a hypothesis test at a 1 percent significance level. Is this a one-sided or two-sided hypothesis test? Clearly specify the following: i. The null and alternative hypotheses. ii. The critical values for the test. iii. Any values that will cause you to reject your null hypothesis. iv. Your actual test statistic. v. The conclusion you draw from your results. b. (5 pts) What is the p-value? c. (5 pts) Briefly (three sentences or less) report a summary of your findings to management, Do you still support your original claim that men shave (on average) at least 4 times per week? For your senior thesis, you are testing whether more years of schooling leads to higher income. You gather some data and produce the following regression output. Y^=25989.29+1133.409X sb1=52.83532,R2=0.1737,n=2191 a). (5 pts) Which is the dependent variable Y and which is the independent variable X. b). ( 5 pts) Interpret the R2 value. c). (5pts) Interpret the estimate b0 of the coefticient 0. d). (5 pts) Conduct a two-sided hypothesis test for the population slope coefficient 1. e). (5 pts) According to your results is years of schooling correlated to higher income? If yes, what is the sign of the correlation
