1. A tire company claims that its top selling brand averages at least 50,000 miles before it needs to be replaced. Past studies have shown the standard deviation is 8,000 miles. A survey of 28 owners of the tire design is conducted and the mean lifespan is 46,500 with a standard deviation of 9,800 miles. Using a 95% level of confidence, are the sample findings consistent with the company’s claim? a. What statistical test will you use to test this data ? b. State the null and alternative hypothesis . i. H0: ii. Ha: c. What are the confidence intervals ? d. What is the value of the test statistic ? e. What is the p-value ? f. Circle/highlight the correct decision about the null hypothesis . Reject H0 Fail to Reject H0 g. What are your conclusions ?
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.
1. A tire company claims that its top selling brand averages at least 50,000 miles before it needs to be replaced. Past studies have shown the standard deviation is 8,000 miles. A survey of 28 owners of the tire design is conducted and the mean lifespan is 46,500 with a standard deviation of 9,800 miles. Using a 95% level of confidence, are the sample findings consistent with the company’s claim?
a. What statistical test will you use to test this data ?
b. State the null and alternative hypothesis .
i. H0:
ii. Ha:
c. What are the confidence intervals ?
d. What is the value of the test statistic ?
e. What is the p-value ?
f. Circle/highlight the correct decision about the null hypothesis .
Reject H0 Fail to Reject H0
g. What are your conclusions ?
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