Note in 31 and 33 there are some tedious calculations that I did for you. You can see the output once you knit this file.

9.2

21.

  1. This is incorrect because the interval we get is not synonamous with the confidence that we have in the event that our parameter will be within the confidence interval. What the statement is actually saying is the probability, which is not what finding the point estimate means. This statement is implying that the population mean varies rather than the interval.

  2. This is correct because it is noting that the confidence interval percent is a measure of how sure we can be an event is going to happen. An interval has been provided for the population mean.

  3. This is flawed because it is talking about the number of people who worked those hours, not actually the confidence interval at all of how many people worked those hours. Again this is a proportion which is not what we are looking for. This statement is implying things about the indivdual and not the mean.

  4. This is incorrect because it talks about adults in Idaho where teh data actually concerend adult Americans.

23.

We are 90% confident that the mean service time at the taco bell drive throughs is between 161.5 adn 164.7 seconds.

25.

One way to help increse the percision of the interval would be to increase the number of the sample size, n, then your lenght of the interval will decrease. Another way to help improve precision would be to decrease the percent of the confidence interval becasue this will then also decreases the lenght of the confidence interval and as a result make the interval more narrow and precise.

27.

  1. Since the data is skewed right, you need a larger sample size in order to make the distribtion normal again because that is one of the caveats to making the equations work and using the t table.

  2. This satisfies the requirements for constructing a confidence interval because the sample size is greater than or equal to 30 which is one of the other caveats for t tables. The sample size is also less than or equal to 5% of the population.

  3. The 90% confidence interval is (0.1647, 0.1693) We are 90% confident that the mean BAC found in fatal car crashes where teh driver had a positive BAC is between 0.1647 and 0.1693 g/dL.

  4. It is possible that the mean of all BAC drivers invlolved in fatal accidents who have a positive BAC is less than the legal intoxication level because it could be that the confidence interval did not capture the true mean, however it is not likley becasue 0.08 is not within the boundries of the counfidence interval.

29. The confidence interval for 95% is (317.63,394.57). We are 95% confident that the mean licks it takes to reach the center of the lollipop is between 317.63 adn 394.57 licks.

31.

  1. The point esstimate is 4.893. This is the sample mean (the sum of all the values given divided by the number of values)

  2. The 95% CI for the mean pH of rainwater in Tucker country, West virginia is (4.690, 5.096). We are 95% percent confident that the mean of pH rainwater in Tucker County, West Virgina is between 4.690 and 5.096.

data <- c(4.58,5.72,5.19,4.75,5.05,5.02,4.8,4.74,4.77,4.76,4.77,4.56)
mean(data)
## [1] 4.8925
sd(data)
## [1] 0.3194064

  1. The 99% CI for the mean pH of rainwater in Tucker country, West virginia is (4.607, 5.179). We are 99% percent confident that the mean of pH rainwater in Tucker County, West Virgina is between 4.607 and 5.179. .

  2. As the level of confidence increases, the interval will also increase. This is because the mean of error value increases. The is due to the fact that the more confident you can be in your data, comes with the price of the broadening of the interval boundries. This is becasue the larger the expected proportion of intervals that will contain the parameter, the larger the margin of error.

33.

  1. skip

  2. skip

data2 <- c(3148,2057,1758,663,1071,2637,3345,773,743,1370)
mean(data2)
## [1] 1756.5
sd(data2)
## [1] 1007.454

  1. The 95% CI is (1035.8, 2477.2). We are 95% confident that the mean repair cost for low impact collision mini and micro motor vehicles is between $1035.8 and $2477.2.

  2. The 95% CI would probably be more narrow because now you are dealing with only Mini cooper low impact colliision, whereas before it was dealing with a vareity of styles/types of motor vehicles so the variability would have been wider.

9.3

5.

Chi square for 0.05 is 30.144. Chi square for 0.95 is 10.117

7. Chi square for 0.01 is 40.289. Chi square for 0.99 is 9.542

9.

  1. The 90% CI is (7.94, 23.66).

  2. The 90% CI is (8.59, 20.63). Increasing teh sample size effectivley narrows the confience interval.

  3. The 98% CI is (6.61, 31.36). Increasing the confidence level will broaden the confidence interval.

11.

The 95% CI is (0.226, 0.542). We are 95% confident that the population standard deviation of the pH rainwater in Tucker County, West Virginia, is between 0.226 and 0.542.

13.

The 90% CI is (734.8, 1657.5). We are 90% confident that the population standard deviation of the money it cost to repair a low impact collision of mini and micro vehicles is within $734.8 and $1657.5