(a)Are the data two independent samples or a simple paired sample? (b)At the 5% significance level, do the data provide sufficient evidence to conclude that, on average, the two measurement methods give different results? (c)What is the P-value of the hypothesis test in part (b)?
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.
6.Eleven tires were each measured for treadwear by two methods, one based on weight and the other on groove wear. The following are the data, in thousands of miles.
(a)Are the data two independent samples or a simple paired sample?
(b)At the 5% significance level, do the data provide sufficient evidence to conclude that, on average, the two measurement methods give different results?
(c)What is the P-value of the hypothesis test in part (b)?
(d)Obtain a confidence interval for the mean difference in measurement by the weight and groove methods corresponding to the hypothesis test in part (b)
(e)Interpret the confidence interval obtained in part (d). Does this interval support the conclusion of the hypothesis test in part (b)? Justify your answer
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