ALL QUESTIONS 1. Find the specified areas for a N (0, 1) density. (a) The area below Z = 0.8 Round your answer to four decimal places. Area = (b) The area above Z = 1.3 Round your answer to four decimal places. Area = c) The area between Z = 1.73 and Z = 1.25 Round your answer to four decimal places. Area = 2. Find endpoint(s) on a N (0, 1) density with the given property. (a) The area to the right of the endpoint is about 0.05. Round your answer to two decimal places. Endpoint = (b) The area to the left of the endpoint is about 0.36. Round your answer to two decimal places. Endpoint = 3. Find the specified areas for a normal density. (a) The area above 7 on a N (5, 1.4 ) distribution Round your answer to three decimal places. Area = (b) The area below 15 on a N (20, 3.1) distribution Round your answer to three decimal places. Area = (c) The area between 87 and 100 on a N (100, 5.9) distribution Round your answer to three decimal places. Area = 4. Find endpoint(s) on the given normal density curve with the given property. (a) The area to the right of the endpoint on a N (25,7) curve is about 0.25. Round your answer to one decimal place. Endpoint = (b) The area to the left of the endpoint on a N (500,73) curve is about 0.02. Round your answer to one decimal place. Endpoint = (c) The symmetric middle area on a N (10,2) curve is about 0.95. Round your answers to one decimal place. Enter your answers in increasing order. The endpoints are __________________ and _________________________ 5. Boys Heights Heights of ten year old boys (5th graders) follow an approximate normal distribution with mean inches and standard deviation inches (a) According to this normal distribution, what proportion of 10 year old boys are between 4ft 3.5in and 5ft 0.5 in tall (between 51.5 inches and 60.5 inches)? Round your answer to four decimal places. Proportion = (c) A parent says his 10 -year-old son is in the 97th percentile in height. How tall is this boy? Round your answer to two decimal places. Height = 6. The distribution of sample proportions of US adults with a college degree for random samples of size is n =500 is N (0.325, 0.021) . How often will such samples have a proportion, that is more than 350 ? Round your answer to one decimal place. _________________% of samples of 500 US adults will contain more than 35.0%s with at least a bachelor's degree. 6. Find the area in the right tail more extreme than Z =3.07 in a standard normal distribution. Round your answer to three decimal places. Area = 7. The following is a set of hypotheses, some information from one or more samples, and a standard error from a randomization distribution. Z= 8. Z= The following is a set of hypotheses, some information from one or more samples, and a standard error from a randomization distribution. 9. Find the -value based on a standard normal distribution for each of the following standardized test statistics. (a) Z = -1.07 for a left tail test for a mean Round your answer to three decimal places. p-value = (b) Z = 4.03 for a right tail test for a proportion Round your answer to four decimal places. p-value = (c) Z = -1.63 for a two-tailed test for a difference in means Round your answer to four decimal places. p-value = 10. MORE BENEFITS OF EATING ORGANIC Using specific data, we find a significant difference in the proportion of fruit flies surviving after 13 days between those eating organic potatoes and those eating conventional (not organic) potatoes. This exercise asks you to conduct a hypothesis test using additional data. In this case, we are testing where and represent the proportion of fruit flies alive at the end of the given time frame of those eating organic food and those eating conventional food, respectively. Use 5% a significance level. Effect of Organic Soybeans After 5 Days After 5 days, the proportion of fruit flies eating organic soybeans still alive is 0.92 , while the proportion still alive eating conventional soybeans is 0.84 . The standard error for the difference in proportions is 0.022. What is the value of the test statistic? Round your answer to two decimal places. Z= p-value = What is the conclusion? Reject H_O or Do not Reject H_O ? Is there evidence of a difference? Yes or No 11. MORE BENEFITS OF EATING ORGANIC Using specific data, we find a significant difference in the proportion of fruit flies surviving after 13 days between those eating organic potatoes and those eating conventional (not organic) potatoes. This exercise asks you to conduct a hypothesis test using additional data. In this case, we are testing where and represent the proportion of fruit flies alive at the end of the given time frame of those eating organic food and those eating conventional food, respectively. Use 5% a significance level. Effect of Organic Potatoes After 11 Days After 11 days, the proportion of fruit flies eating organic potatoes still alive is 0.68, while the proportion still alive eating conventional potatoes is 0.65 . The standard error for the difference in proportions is 0.03. What is the value of the test statistic? Round your answer to two decimal places. Z= p-value = What is the conclusion? Reject H_O or Do not Reject H_O ? Is there evidence of a difference? Yes or No 12.How Do You Get Your News? A study by the Pew Research Center 1 reports that in 2010, for the first time, more adults aged 18 to 29 got their news from the Internet than from television. In a random sample of adults of all ages in the US, 66% said television was one of their main sources of news. Does this provide evidence that more than 65% of all adults in the US use television as one of their main sources for news? A randomization distribution for this test shows SE = 0.013 . What is the test statistic? Round your answer to two decimal places. Z= p-value = 13 Find the Z* values based on a standard normal distribution for each of the following. . (a) An %80 confidence interval for a proportion. Round your answer to three decimal places. = (b) An 84% confidence interval for a slope. Round your answer to three decimal places. = (c) A 92% confidence interval for a standard deviation. Round your answer to three decimal places. = 13. Find the indicated confidence interval. Assume the standard error comes from a bootstrap distribution that is approximately normally distributed. Round your answers to three decimal places. The 90% confidence interval is _____________ to __________________ 14. A survey of 1000 air travelers1 found that 60% prefer a window seat. The sample size is large enough to use the normal distribution, and a bootstrap distribution shows that the standard error is SE 0.015. Use a normal distribution to find a 95% confidence interval for the proportion of air travelers who prefer a window seat. Round your answers to three decimal places. The 95% confidence interval is _____________ to __________________ 15. Hospital admissions for asthma in children younger than 15 years was studied 1 in Scotland both before and after comprehensive smoke-free legislation was passed in March 2006. Monthly records were kept of the annualized percent change in asthma admissions, both before and after the legislation was passed. For the sample studied, before the legislation, admissions for asthma were increasing at a mean rate of 5.2 per year. The standard error for this estimate is 0.7 per year. After the legislation, admissions were decreasing at a mean rate of 18.2% per year, with a standard error for this mean of 1.79% . In both cases, the sample size is large enough to use a normal distribution. Find a 90% confidence interval for the mean annual percent rate of change in childhood asthma hospital admissions in Scotland before the smoke-free legislation. Round your answers to one decimal place. (a) The 90% confidence interval is _____________ to __________________ (b) Find a 90% confidence interval for the same quantity after the legislation. Round your answers to one decimal place. The 90% confidence interval is _____________ to __________________ 16. Suppose 40% of students at a large university take Intro Stats. Randomly sample 55 students from this university and count the number who have taken Intro Stats. Does this process describe a binomial random variable? YES or NO If it is binomial, give values for n and p. If it is not binomial, enter NA in both entry fields. n= p= 17. Calculate the requested quantity. 4! = 18. Calculate the requested quantity. 10! = 19. Calculate the requested quantity. = 20. Calculate the requested quantity. = P(X =2) = P(X =4) = 21. Calculate the mean and standard deviation of a binomial random variable with n = 7 and p = 0.3. Enter the exact answer for the mean, and round your answer for the standard deviation to three decimal places. = = 22. Boys or Girls? Worldwide, the proportion of babies who are girls is about 0.49. A couple hopes to have 3 children and we assume that the sex of each child is independent of the others. Let the random variable represent the number of boys in the three children, so X might be 0,1, 2, or 3 . Give the probability function for each value of X x p(x) 0 1 2 3 23. In the 2010 US Census, we learn that 65% of all housing units are owner-occupied while the rest are rented. Use this information to find the following probabilities. (a) If we take a random sample of 18 housing units, find the probability that exactly 12 of them are owner-occupied. Round your answer to four decimal places. P(X =12) = (b) If we take a random sample of 18 housing units, find the probability that 16 or more of them are owner-occupied Round your answer to four decimal place =