Some transportation experts claim that it is the variability of speeds, rather than the level of speeds, that is a critical factor in determining the likelihood of an accident occurring. One of the experts claims that driving conditions are dangerous if the variance of speeds exceeds 76 (mph) 2. On a heavily traveled highway, a random sample of 53 cars revealed a mean and a variance of speeds of 62.5 mph and 96.4 (mph) 2, respectively. (You may find it useful to reference the appropriate table: chi-square table or Ftable) a. Select the competing hypotheses to test if the variance of speeds exceeds 76 (mph) 2. He: 0² ≤ 76; HA: 0² > 76 He: 0² 76; HA: 0² < 76 H₂: 02 = 76; HA: 0² # 76 b-1. Find the p-value. O 0.05 s p-value < 0.10 O 0.025 s p-value < 0.05 O 0.01 s p-value < 0.025 O p-value < 0.01 O p-value 20.10 b-2. At the 10% significance level, can you conclude that driving conditions are dangerous on this highway? Reject Ho; we can conclude the variance of the speeds is greater than 76 mpg². Do not reject He; we cannot conclude the variance of the speeds is greater than 76 mpg². Reject He; we cannot conclude the variance of the speeds is greater than 76 mpg². O Do not reject Ho; we can conclude the variance of the speeds is greater than 76 mpg².

Construct a numerical example, i.e., a data set, such that a two-sample t-test will yield an insignificant test result but a pair t-test will yield a significant test result. (For the two-sample t-test, you can either assume equal variances or unequal variances, which will not affect the key idea of this question.) I need to know how this is possible and what the basics of making this data set should be.

A factor in determining the usefulness of an examination as a measure of demonstrated ability is the amount of spread that occurs in the grades. If the spread or variation of examination scores is very small, it usually means that the examination was either too hard or too easy. However, if the variance of scores is moderately large, then there is a definite difference in scores between "better," "average," and "poorer" students. A group of attorneys in a Midwest state has been given the task of making up this year's bar examination for the state. The examination has 500 total possible points, and from the history of past examinations, it is known that a standard deviation of around 60 points is desirable. Of course, too large or too small a standard deviation is not good. The attorneys want to test their examination to see how good it is. A preliminary version of the examination (with slight modifications to protect the integrity of the real examination) is given to a random sample of…

The accounting department analyzes the variance of the weekly unit costs reported by two production departments. A sample of 16 cost reports for each of the two departments shows cost variances of 2.3 and 5.4, respectively. Is this sample sufficient to conclude that the two production departments differ in terms of unit cost variance? Use  ? = 0.10. State the null and alternative hypotheses. -H0: ?12 > ?22 Ha: ?12 ≤ ?22 -H0: ?12 ≠ ?22 Ha: ?12 = ?22      -H0: ?12 ≤ ?22 Ha: ?12 > ?22 -H0: ?12 = ?22 Ha: ?12 ≠ ?22 Find the value of the test statistic. (Round your answer to two decimal places.) statistic=?? Find the p-value. (Round your answer to four decimal places. Remember: When using WebAssign technology to find p-values, use the entire test statistic (not the rounded answer from the previous question.)) p-value = ??   State your conclusion. -Reject H0. We can conclude that there is a difference between the population variances. -Do not reject H0. We cannot conclude that…