Education influences attitude and lifestyle. Differences in education are a big factor in the "generationgap." Is the younger generation really better educated? Large surveys of people age 65 and older weretaken in m = 32 U.S. cities. The sample mean for these cities showed that x₁ = 15.2% of the older adultshad attended college. Large surveys of young adults (age 25-34) were taken in m2 = 33 U.S. cities. Thesample mean for these cities showed that x₂ = 18.7% of the young adults had attended college. Fromprevious studies, it is known that o 1 = 6.6% and σ 2 = 5.8%.(a) Does this information indicate that the population mean percentage of young adults who attendedcollege is higher? Use x = 0.05.(1) What is the level of significance?State the null and alternate hypotheses.Ho: μμ2; H₁ H1> μL ₂μη; Η: μι < μ 2Ho: μμ₂; H₁: μl ₁ = μl ₂Ho: μη = μη Η: με #μεH₂: μl 1 =(ii) What sampling distribution will you use? What assumptions are you making?The Student's t. We assume that both population distributions are approximately normal with knownstandard deviations. The Student's t. We assume that both population distributions are approximatelynormal with unknown standard deviations. The standard normal. We assume that both populationdistributions are approximately normal with known standard deviations. The standard normal. Weassume that both population distributions are approximately normal with unknown standard deviations.What is the value of the sample test statistic? Compute the corresponding zor t value as appropriate.(Test the difference μμ2. Round your answer to two decimal places.)1(iii) Find (or estimate) the P-value. (Round your answer to four decimal places.) -3-2-10lower limitupper limit1-3(b) Find a 90% confidence interval forμι-μ 2.(Round your answers to two decimal places.)-2-10 1-3-2-101-3-2-101(iv) Based on your answers in parts (i)-(iii), will you reject or fail to reject the null hypothesis? Are the datastatistically significant at level < ?At the x = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statisticallysignificant. At the x = 0.05 level, we reject the null hypothesis and conclude the data are notstatistically significant.At the x = 0.05 level, we reject the null hypothesis and conclude the dataare statistically significant. At the x = 0.05 level, we fail to reject the null hypothesis and conclude thedata are statistically significant.(v) Interpret your conclusion in the context of the application.Fail to reject the null hypothesis, there is insufficient evidence that the mean percentage of young adultswho attend college is higher. Reject the null hypothesis, there is insufficient evidence that the meanpercentage of young adults who attend college is higher. Reject the null hypothesis, there issufficient evidence that the mean percentage of young adults who attend college is higher. Fail toreject the null hypothesis, there is sufficient evidence that the mean percentage of young adults whoattend college is higher.LExplain the meaning of the confidence interval in the context of the problem.Because the interval contains only positive numbers, this indicates that at the 90% confidence level, thepopulation mean percentage of young adults who attend college is lower than that of older adults.Because the interval contains both positive and negative numbers, this indicates that at the 90%confidence level, we can not say that the population mean percentage of young adults who attend collegeis higher than that of older adults. We can not make any conclusions using this confidence interval.Because the interval contains only negative numbers, this indicates that at the 90% confidence level,the population mean percentage of young adults who attend college is higher than that of older adults.

The sample size (number of cities) where people aged 65 and over took part in survey n1=32The…

Education influences attitude and lifestyle. Differences in education are a big factor in the "generation gap." Is the younger generation really better educated? Large surveys of people age 65 and older were taken in m = 32 U.S. cities. The sample mean for these cities showed that x = 15.2% of the older adults had attended college. Large surveys of young adults (age 25-34) were taken in = 33 U.S. cities. The sample mean for these cities showed that x = 18.7% of the young adults had attended college. From previous studies, it is known that o1 = 6.6% and σ 2 = 5.8%. (a) Does this information indicate that the population mean percentage of young adults who attended college is higher? Use x = 0.05. (1) What is the level of significance? State the null and alternate hypotheses. Ημι=με Ημιμα μη; Η; μι < με Ημ.<μäΗ:μι = με H: μ . = μ 2 Mi; με 1 # μ Hb: 441 = (ii) What sampling distribution will you use? What assumptions are you making? The Student's t. We assume that both population distributions are approximately normal with known standard deviations. The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. The standard normal. We assume that both population distributions are approximately normal with known standard deviations. The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. What is the value of the sample test statistic? Compute the corresponding zor t value as appropriate. (Test the difference μμ2. Round your answer to two decimal places.) (iii) Find (or estimate) the P-value. (Round your answer to four decimal places.)

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P