1. Express the confidence interval(34.7%,50.3%)in the form ofp^margin of error._________ % _________%Write your answers as percent, without the percent symbol, to 1 decimal place.2. In a convenience sample conducted by a marketing agency, 393 of 985 people residing in the U.S. who are age 15-19 years confessed to bringing their cell phone with them on every trip to the bathroom. Check the criteria for calculating a 99% confidence interval.a)p= _____________Round to 3 decimal places, if needed.Check requirements:b) Are the observations independent? Check this by usingn=0.05N._________=0.05NWhat does this tell us the required population size is?Round to 1 decimal place, if needed.N= _____________c)Is the sample size large enough? Check this by usingnp^=10andn(1-p^) =10.Round to the nearest whole number.np=___________n(1-p) =_____________This means that the sampling distribution ofp^isa). Approximately Normal because the sample sizen=30.b). Approximately Normal becausenp^=10andn(1-p^) =10.c). Not Normal becausenp^andn(1-p^)are not both greater or equal to 10.d). Approximately Normal regardless of sample size.e). Approximately Normal becausenp^<10andn(1-p^) <10.f). Unknown shape because not enough information is given in the problem.3. At a small college, there are a total of 1000 students who are taking math. The Dean of Science randomly samples 52 of those students and 24 of them were planning on taking another math course. Check the criteria for calculating a 95% confidence interval of the proportion of students at this college who are planning on taking another math class.a)p=__________Round to 4 decimal places, if needed.Check requirements:b. Are the observations independent? Check this by usingn=0.05N.___________=0.05NWhat does this tell us about the required population size?Round to 1 decimal place, if needed.N=______________Is the sample size large enough? Check this by usingnp^=10andn(1-p^)=10.Round to the nearest whole number.np=___________n(1-p) =______________This means that the sampling distribution ofp^isa). Unknown shape because not enough information is given in the problem.b). Approximately Normal regardless of sample size.c). Not Normal becausenp^andn(1-p^)are not both greater or equal to 10.d). Approximately Normal becausenp^<10andn(1-p^) <10.e). Approximately Normal becausenp^=10andn(1-p^) =10.f). Approximately Normal because the sample sizen=30.4. The results of a poll were that 159 of 331 Americans decided not to go to college because they could not afford it.(a) Calculate a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it and interpret the interval in con.lower bound: ____________ (please round to 3 decimal places)upper bound: _____________ please round to 3 decimal places)Interpret the confidence interval in con:a). We can be 90% confident that our confidence interval contains the sample proportion of Americans who choose not to go to college because they cannot afford itb). We can be 90% confident that our confidence interval contains the proportion of Americans who choose not to go to college because they cannot afford it.c). 90% of Americans choose not to go to college because they cannot afford itSuppose we wanted the margin of error for the 90% confidence level to be about 1.5%. How large of a survey would you recommend?Use these z*90% 1.6595% 1.9698% 2.3399% 2.58A survey should include at least__________ people.MathStatistics and Probability MATH 1040
