We considered the differences between the temperature readings in January 1 of 1968 and 2008 at 51 locations in the continental US in Exercise 5.19. The mean and standard deviation of the reported differences are 1.1 degrees and 4.9 degrees respectively. (a) Calculate a 90% confidence interval for the average difference between the temperature measurements between 1968 and 2008. lower bound: degrees(please round to two decimal places) upper bound: degrees(please round to two decimal places) (b) Interpret this interval in context. There is a 90% chance that the difference in temperatures in a city from year to year will be between the lower bound and upper bound O We are 90% confident that the true mean difference in temperatures is contained between the lower bound and upper bound O We are 90% confident that 90% of the time the differences in temperatures from year to year will be between the lower bound and upper bound O We are 90% confident that the mean difference in these sample temperatures is contained between the lower bound and upper bound (c) Does the confidence interval provide convincing evidence that the temperature was higher in 2008 than in 1968 in the continental US? Explain. No, because the confidence interval contains 0 O No, because the confidence interval is not very wide O Yes, because the confidence interval contains mostly positive numbers Yes, because the confidence interval contains negative numbers
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
We considered the differences between the temperature readings in January 1 of 1968 and 2008 at 51 locations in the continental US in Exercise 5.19. The mean and standard deviation of the reported differences are 1.1 degrees and 4.9 degrees respectively.
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