An independent consumer group tested radial tires from two major brands (1, 2) to determine whether there were any differences in the expected tread life. The data (in thousands of miles) are provided in (the image attached). Is mean performance different for the two brands? a. First test the variances of the tread lives of the two brands to determine which assumption about equality of variances to use. Use 90% confidence and the critical
An independent consumer group tested radial tires from two major brands (1, 2) to determine whether there were any differences in the expected tread life. The data (in thousands of miles) are provided in (the image attached). Is mean performance different for the two brands? a. First test the variances of the tread lives of the two brands to determine which assumption about equality of variances to use. Use 90% confidence and the critical
An independent consumer group tested radial tires from two major brands (1, 2) to determine whether there were any differences in the expected tread life. The data (in thousands of miles) are provided in (the image attached). Is mean performance different for the two brands? a. First test the variances of the tread lives of the two brands to determine which assumption about equality of variances to use. Use 90% confidence and the critical
Problem 6 An independent consumer group tested radial tires from two major brands (1, 2) to determine whether there were any differences in the expected tread life. The data (in thousands of miles) are provided in (the image attached). Is mean performance different for the two brands? a. First test the variances of the tread lives of the two brands to determine which assumption about equality of variances to use. Use 90% confidence and the critical value approach. b. Based on the result of part a, answer the question about the mean performance of the two brands using the p-value approach and 99% confidence. c. Is the proportion of tires that last at least 55,000 miles larger for Brand 2 tires? Use 99% confidence and the critical value approach.
Transcribed Image Text:This table displays a comparison of data between two brands, labeled as Brand 1 and Brand 2. Each row represents a data point for both brands.
| | Brand 1 | Brand 2 |
|---|---------|---------|
| 1 | 50 | 57 |
| 2 | 54 | 65 |
| 3 | 52 | 47 |
| 4 | 47 | 52 |
| 5 | 61 | 48 |
| 6 | 56 | 57 |
| 7 | 51 | 56 |
| 8 | 51 | 68 |
| 9 | 48 | 67 |
| 10| 56 | 58 |
| 11| 50 | 62 |
| 12| 60 | 56 |
| 13| 58 | 56 |
| 14| | 62 |
| 15| | 57 |
| 16| | 53 |
The table can be used to analyze and compare the performance or characteristics of the two brands across the given data points. Note that some entries for Brand 1 are missing from rows 14 to 16.
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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