Statistics 101: Practice Problems for Final ExamThis sheet contains practice problems for the final exam. It is longer than theactual final so that you have extra problems. Other material in the text and from lectures may appear on the final exam.Questions 1 – 19 refer to a random sample of 500 heads of households. The data are sampled from the households collected in the March 2000 Current Population Survey. For this problem, we’ll assume that the data are a simple random sampleof 500 households from the entire U.S. population.People who own their homes have to pay taxes on their property. Below is a histogram that shows property taxes for all 500 households in the sample.Property tax for all households0 1000 3000 5000 7000 90001. True or False: More than 45% of these households have property taxes greaterthan the mean.2. Choose the value that you think is closest to the standard deviation of theseproperty taxes: 10, 100, 1000, 10000.3. True or False: If we remove all the houses that have property taxes equal tozero, the average of the remaining taxes would be larger than $1,050.4. True or False: A normal curve can be used to determine the percentage of houses paying above $500 with very good accuracy.5. Estimate the percentage of households that pay more than $2000 in property taxes. _____Below is a box plot of property tax by marital status. The marital status 1 is for a married householder; 5 is for a divorced householder; and, 7 is for a single householder. There are 219 married people, 84 divorced people, and 108 single people. The other people in the sample who have other marital statuses are not displayed in this graph.Oneway Analysis of property tax By marital status: 1 = married, 5 = divorced, 7 = singleproperty tax01000200030004000500060007000800090001 5 7marital status6. Order the three groups by median property tax, going from largest to smallest. _________7. True or false: The standard deviation of property taxes for these married people is closer in value to the standard deviation for these single people thanit is to the standard deviation for these divorced people.8. True or false: A larger percentage of these married people have property taxes below 500 than do these divorced people.9. Which of these three groups has the largest percentage of people not paying any property tax?10. True or False: The standard error of the sample average property tax for divorced people is larger than the standard error for the sample average property tax for married people.Below is a box plot of property taxes for male and female household heads. Men are coded with a 1, and women are coded with a 2.Oneway Analysis of property tax By sex: men = 1 and women = 2property tax01000200030004000500060007000800090001 2sexMeans and Std DeviationsLevel Number Mean Std Dev1 257 996.086 1507.102 242 754.942 1162.0511. Are the assumptions for using confidence intervals or hypothesis tests involving sample average of property taxes likely to hold? Explain your reasoning.12. Give a 95% confidence interval for the difference in average property taxes for male and female household heads. 13. Based on the interval, do you think there is overwhelming evidence that the average property tax amounts differ?14. Check all of the following that are true:___ There is a 95% chance that the population difference in average property taxes is between the two values you determined in 14.___ If we pick two households at random so that one is headed by a male and theother by a female, the difference in their property taxes will fall within the upper and lower limits 95% of the time.___ If we took another random sample of 500, then another, then another, and soon, we’d expect 95% of the formed confidence intervals to contain the populationdifference in average property taxes.15. Test the null hypothesis that there is no difference in average property taxes between male and female household heads. State your null and alternative hypotheses, the test statistic, the p-value, and your conclusions. Consider a p-value near 0.05 to be small.16. Check all of the following that are true.____ The probability that the null hypothesis is true equals the p-value from the previous part.____ It may be the case that the results are due to chance, and our conclusion from the hypothesis test is wrong._____ The chance of getting a value of the test statistic as or more extreme than what was observed, assuming the null hypothesis is true, equals the p-value. Below are scatter plots of property tax, household income, number people in the household, and age of the household head.Scatterplot Matrix02000400060008000050000100000150000200000250000300000135720406080property tax0 2000 5000 8000household income0 100000 250000number people in house1 2 3 4 5 6 7 8age of hh2030 50 70 90Questions 17 – 19 refer to the plot above.17. Order income, number of people, and age of household head in terms of correlation with property tax, going from largest to smallest.18. The value of the correlation between household income and age of household head is closest to which of the following values: -.5, -.25, 0, .25, .5.19. If you fit a regression between property tax (outcome) and income (predictor), which of the following statements would be true. You can choose more than one.___ The slope of the line would be positive.___ The intercept of the line would be greater than 1000.20. Does taking additional vitamin C help prevent thecommon cold? Nobel Laureate Linus Pauling (1901 - 1994) performed arandomized experiment to address this question and reported hisresults in the Proceedings of the National Academy of Sciences.Pauling randomly assigned 279 French skiers to be in one of twogroups: a group that took vitamin C supplements or a group that took aplacebo (a sugar pill). The numbers of people for each category are summarized below: Got a cold Did not get a coldVitamin C 17 122Placebo 31 109Pretend that you are the consulting statistician for Linus Pauling (alofty honor indeed!)i) Pauling seeks to know if there is evidence that the population incidence rate of colds for people who take Vitamin C is less than the population incidence rate of colds for people who take the placebo. What doyou tell him? State clearly and justify your null and alternativehypotheses, the test statistic, the p-value, and conclusions. ii) Asking people to take