A national organization has been working with utilities throughout the nation to find sites for large wind machines that generate electricity. Wind speeds must average more than 13 miles per hour (mph) for a site to be acceptable. Recently, the organization conducted wind speed tests at a particular site. To determine whether the site meets the organization's requirements, consider the test, Ho: μ =13 Ha: μ >13 where μ is the true mean wind speed at the site and a=.05 Suppose the observed significance level ( p-value) of the test is calculated to be p=0.4413 Interpret this result. Since the p-value greatly exceeds α = .05, there is strong evidence to reject the null hypothesis. Since the p-value exceeds α = .05, there is insufficient evidence to reject the null hypothesis. We are 55.87% confident that μ = 13. The probability of rejecting the null hypothesis is 0.4413.
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.
A national organization has been working with utilities throughout the nation to find sites for large wind machines that generate electricity. Wind speeds must average more than 13 miles per hour (mph) for a site to be acceptable. Recently, the organization conducted wind speed tests at a particular site. To determine whether the site meets the organization's requirements, consider the test, Ho: μ =13 Ha: μ >13 where μ is the true mean wind speed at the site and a=.05 Suppose the observed significance level ( p-value) of the test is calculated to be p=0.4413 Interpret this result.
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Since the p-value greatly exceeds α = .05, there is strong evidence to reject the null hypothesis.
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Since the p-value exceeds α = .05, there is insufficient evidence to reject the null hypothesis.
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We are 55.87% confident that μ = 13.
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The probability of rejecting the null hypothesis is 0.4413.
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