1) Show all work for each part, including z score, notation and individual values as shown in class. Round all probability answers to 4 decimal places and all other values to 2 decimal places. The average weight of a newborn baby born in the U.S. is normally distributed. The population mean weight is 7.5 pounds with a population standard deviation of 1.1 pounds. a) Find the probability that a newborn baby is between 6.7 pounds and 8 pounds. b) In a sample of 21 babies find the probability that the sample mean is greater than 7.7 pounds. c) Find the minimum weight for a newborn baby to be in the top 1% of the population. 2) A company wanted to find the average time it takes an employee to commute to work. It sampled 45 employees and found the average commuting time to be 27 minutes with a population standard deviation of 6 minutes. Using a 99% confidence level: Show all work. Assume a normal distribution. Show all necessary work to support your analysis. Round all answers to 2 decimal places. a) Find the Margin of Error at 99%. b) Find a 99% confidence interval. c) Write an interpretation for the interval. 3) In a random sample of 12 chemical engineers, the monthly income data for the sample is displayed. Assume the monthly incomes are normally distributed. Show all necessary work. x=6883,s 187,n=12,df 11= = a) Find the Margin of Error at 95%., show all values used. b) Find a 95% confidence interval. c) Write an interpretation for the interval. 4) In a survey of 1380 U.S. adults, 1104 (which is 80%) favor increasing federal funding for research on wind, solar, and hydrogen technology. Assume a normal distribution. a) Find the Margin of Error at 95%, round to 4 decimal places. b) Find a 95% confidence interval, round to 4 decimal places. c) Write an interpretation for the interval. Problems 5, 6, 7 are normally distributed. 5) The National Transportation Safety Board publishes statistics on the number of automobile crashes that people in various age groups have. A researcher claims the population proportion of young drivers, ages 18 – 24, having accidents is greater than 12%. Her study examined 1000 young drivers ages 18 – 24 and found that 134 had an accident this year. Test at ? = .05. a) State H0 and Ha b) Find the critical value, show work c) Find the appropriate test statistic, show work d) Do a P - value test e) Make a decision to reject or fail to reject the null hypothesis and interpret the results. 6a) State H0 and Ha b) Find the critical value, show work c) Find the appropriate test statistic, show work d) Do a P - value test e) Make a decision to reject or fail to reject the null hypothesis and interpret the results. A dietitian wishes to see if a person’s cholesterol level will lower if the diet is supplemented by a certain mineral. Six subjects were pretested, and then they took the mineral supplement for a 6 – week period. The results are shown in the table. Can it be concluded that the cholesterol has been lowered at ? = .05? 15 points Subject 1 2 3 4 5 6 Before 210 235 208 190 172 244 After 190 200 210 188 173 228 undefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefined 7a) State H0 and Ha b) Find the critical value, show work c) Find the appropriate test statistic, show work d) Do a rejection region test e) Make a decision to reject or fail to reject the null hypothesis and interpret the results. A high school counselor wants to test if there is a difference in the population means between male and female students on the math section of the ACT test. The results are displayed below. Test at ?? = .05? Assume the population variances are equal. Show all work, 15 pts. ?1= Males ?2=Females 20.86 20.43 7.98 6.2 14 14 undefinedundefinedundefinedundefinedundefined Mean Standard Deviation Observations 8) The following table is data from a study in which 788 people in a representative sample of college age students were asked how they perceive their money management skills. Do a ?2 test for independence and test at the ? = .05 level. Show all work as done in class. 15 points Perception of Money Management Skills 73 146 54 103 58 84 c) Find the appropriate test statistic, ?? d) Do a P Value test. e) Make a decision to reject or fail to reject the null hypothesis and interpret f) Show mathematically how to find E2,4. Excellent Good 104 17 8 348 Average Not Very Good Poor Total undefinedundefinedundefinedundefinedundefinedundefined Age Group Age 18 - 20 Age 21 - 22 Age 23 - 24 Totals 85 10 3 36 7 0 undefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefined 185 333 225 34 255 185 11 788 undefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefined a) State H0 and Ha b) State df, ?, ?02 , 2 9) A drug company tested three formulations of a pain relief medicine for migraine headache sufferers. For the experiment 27 volunteers were selected and were randomly assigned to one of three drug formulations. The subjects were instructed to take the drug during their next migraine headache episode and to report their pain on a scale of 1 to 10 (10 being most pain). Use ANOVA at ? = .05 to test for difference among the means. Show all work as done in class. 15 points Groups Drug A Drug B Drug C n Mean Variance 8 3.63 0.84 undefinedundefinedundefinedundefinedundefinedundefinedundefined 9 5.78 2.19 10 5.8 0.62 Grand Mean: ??? = 5.15 a) State the null and alternate hypotheses b) Identify d.f.N, d.f.D (use the value on table 7 closest to your value), and Fo c) Find MSB, MSW d) Find F e) Make decision and interpret results undefinedundefinedundefined 10) The following table and graph show the percent of people across the world living in extreme poverty since 1980. Let x = 0 represent the year 1980. (Source: World Bank) 1981 1984 1987 1990 1993 1996 1999 2002 2005 2008 2011 2014 2017 2020 Year % living in extreme 42.3 39.3 35.2 35.5 34.1 29.6 28.8 25.8 20.8 18.1 13.8 10.1 9.8 9.4 poverty x=1 x=4 x=7 x= x= x= x= x= x= x=28 x=31 x=34 x=37 x=40 10 13 16 19 22 25 Percent of world living in extreme poverty 50 45 40 35 30 25 20 15 10 5 0 y = -0.908x + 43.799 R2 = 0.9793 undefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefinedundefined 0 5 10 15 20 25 30 35 40 45 year since 1981 ****Do all work on next page. % living in extreme poverty a) Interpret slope b) Find r2and interpret c) Find r and interpret d) Find a 95% prediction interval for percent of world living in extreme poverty in 2022 (use x = 42) and interpret your answer for an error value of E = 3.8.