An energy company wants to choose between two regions in a state to install energy-producing wind turbines. A researcher claims that the wind speed in Region A is less than the wind speed in Region B. To test the regions, the average wind speed is calculated for 60 days in each region. The mean wind speed in Region A is 13.9 miles per hour. Assume the population standard deviation is 2.7 miles per hour. The mean wind speed in Region B is 15.2 miles per hour. Assume the population standard deviation is 3.1 miles per hour. At α=0.05, can the company support the researcher's claim? Complete parts (a) through (d) below. (a) Identify the claim and state H0 and Ha. What is the claim? A. The wind speed in Region A is the same as the wind speed in Region B. B. The wind speed in Region A is less than the wind speed in Region B. C. The wind speed in Region A is not greater than the wind speed in Region B. D. The wind speed in Region A is not less than the wind speed in Region B. Let Region A be sample 1 and let Region B be sample 2. Identify H0 and Ha. H0: μ1 greater than or equals≥ less than or equals≤ greater than> less than< not equals≠ μ2 Ha: μ1 greater than or equals≥ less than or equals≤ greater than> less than< not equals≠ (b) Find the critical value(s) and identify the rejection region. The critical value(s) is/are z0= (Round to three decimal places as needed. Use a comma to separate answers as needed.) What is the rejection region? Select the correct choice below and fill in the answer box(es) within your choice. (Round to three decimal places as needed.) A. z< or z> B. z> C. z< (c) Find the standardized test statistic z. z= (Round to two decimal places as needed.) d) Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim. ▼ H0. There is not or is enough evidence at the 5% level of significance to ▼ reject or support the researcher's claim that the wind speed in Region A is ▼ the same as less then not greater than not less than the wind speed in Region 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.
An energy company wants to choose between two regions in a state to install energy-producing wind turbines. A researcher claims that the wind speed in Region A is less than the wind speed in Region B. To test the regions, the average wind speed is calculated for
days in each region. The mean wind speed in Region A is
miles per hour. Assume the population standard deviation is
miles per hour. The mean wind speed in Region B is
miles per hour. Assume the population standard deviation is
miles per hour. At
can the company support the researcher's claim? Complete parts (a) through (d) below.
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