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 (Update, Virginia Department of Transportation, Winter 2000). One of the experts claims that driving conditions are dangerous if the variance of speeds exceeds 80 (mph)2. On a heavily traveled highway, a random sample of 52 cars revealed a mean and a variance of speeds of 58.5 mph and 85.4(mph)2, respectively. (You may find it useful to reference the appropriate table: chi-square table or F table) a. Select the competing hypotheses to test if the variance of speeds exceeds 80 (mph)2. multiple choice 1 H0: σ2 ≤ 80; HA: σ2 > 80 H0: σ2 ≥ 80; HA: σ2 < 80 H0: σ2 = 80; HA: σ2 ≠ 80 b-1. Find the p-value. multiple choice 2 p-value 0.10 0.05 p-value < 0.10 0.025 p-value < 0.05 0.01 p-value < 0.025 p-value < 0.01 b-2. At the 10% significance level, can you conclude that driving conditions are dangerous on this highway? multiple choice 3 Do not reject H0; we cannot conclude the variance of the speeds is greater than 80 mpg2. Reject H0; we can conclude the variance of the speeds is greater than 80 mpg2. Do not reject H0; we can conclude the variance of the speeds is greater than 80 mpg2. Reject H0; we cannot conclude the variance of the speeds is greater than 80 mpg2
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 (Update, Virginia Department of Transportation, Winter 2000). One of the experts claims that driving conditions are dangerous if the variance of speeds exceeds 80 (mph)2. On a heavily traveled highway, a random sample of 52 cars revealed a mean and a variance of speeds of 58.5 mph and 85.4(mph)2, respectively. (You may find it useful to reference the appropriate table: chi-square table or F table) a. Select the competing hypotheses to test if the variance of speeds exceeds 80 (mph)2. multiple choice 1 H0: σ2 ≤ 80; HA: σ2 > 80 H0: σ2 ≥ 80; HA: σ2 < 80 H0: σ2 = 80; HA: σ2 ≠ 80 b-1. Find the p-value. multiple choice 2 p-value 0.10 0.05 p-value < 0.10 0.025 p-value < 0.05 0.01 p-value < 0.025 p-value < 0.01 b-2. At the 10% significance level, can you conclude that driving conditions are dangerous on this highway? multiple choice 3 Do not reject H0; we cannot conclude the variance of the speeds is greater than 80 mpg2. Reject H0; we can conclude the variance of the speeds is greater than 80 mpg2. Do not reject H0; we can conclude the variance of the speeds is greater than 80 mpg2. Reject H0; we cannot conclude the variance of the speeds is greater than 80 mpg2
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 (Update, Virginia Department of Transportation, Winter 2000). One of the experts claims that driving conditions are dangerous if the variance of speeds exceeds 80 (mph)2. On a heavily traveled highway, a random sample of 52 cars revealed a mean and a variance of speeds of 58.5 mph and 85.4(mph)2, respectively. (You may find it useful to reference the appropriate table: chi-square table or F table) a. Select the competing hypotheses to test if the variance of speeds exceeds 80 (mph)2. multiple choice 1 H0: σ2 ≤ 80; HA: σ2 > 80 H0: σ2 ≥ 80; HA: σ2 < 80 H0: σ2 = 80; HA: σ2 ≠ 80 b-1. Find the p-value. multiple choice 2 p-value 0.10 0.05 p-value < 0.10 0.025 p-value < 0.05 0.01 p-value < 0.025 p-value < 0.01 b-2. At the 10% significance level, can you conclude that driving conditions are dangerous on this highway? multiple choice 3 Do not reject H0; we cannot conclude the variance of the speeds is greater than 80 mpg2. Reject H0; we can conclude the variance of the speeds is greater than 80 mpg2. Do not reject H0; we can conclude the variance of the speeds is greater than 80 mpg2. Reject H0; we cannot conclude the variance of the speeds is greater than 80 mpg2
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 (Update, Virginia Department of Transportation, Winter 2000). One of the experts claims that driving conditions are dangerous if the variance of speeds exceeds 80 (mph)2. On a heavily traveled highway, a random sample of 52 cars revealed a mean and a variance of speeds of 58.5 mph and 85.4(mph)2, respectively. (You may find it useful to reference the appropriate table: chi-square table or F table)
a. Select the competing hypotheses to test if the variance of speeds exceeds 80 (mph)2.
multiple choice 1
H0: σ2 ≤ 80; HA: σ2 > 80
H0: σ2 ≥ 80; HA: σ2 < 80
H0: σ2 = 80; HA: σ2 ≠ 80
b-1. Find the p-value.
multiple choice 2
p-value
0.10
0.05
p-value < 0.10
0.025
p-value < 0.05
0.01
p-value < 0.025
p-value < 0.01
b-2. At the 10% significance level, can you conclude that driving conditions are dangerous on this highway?
multiple choice 3
Do not reject H0; we cannot conclude the variance of the speeds is greater than 80 mpg2.
Reject H0; we can conclude the variance of the speeds is greater than 80 mpg2.
Do not reject H0; we can conclude the variance of the speeds is greater than 80 mpg2.
Reject H0; we cannot conclude the variance of the speeds is greater than 80 mpg2
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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