Suppose you know the population average wage in the manufacturing industry in California is $24.66 per hour. You take a survey 30 people that work in manufacturing in Utah to answer the following research question. Research Question: Is the population average manufacturing wage in Utah less than $24.66 per hour, the population average manufacturing wage in the California? You know the population standard deviation for manufacturing wages in Utah is $2.35 per hour. Suppose you are using a significance level of 0.01 or 1% (α = 0.01). What is the probability that you will correctly reject the null hypothesis if the true average manufacturing wage in Utah is $24 per hour? (In other words, what is the power of the test if the true average wage in Utah is $24 per hour?)
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.
Suppose you know the population average wage in the manufacturing industry in California is $24.66 per hour. You take a survey 30 people that work in manufacturing in Utah to answer the following research question.
Research Question: Is the population average manufacturing wage in Utah less than $24.66 per hour, the population average manufacturing wage in the California?
You know the population standard deviation for manufacturing wages in Utah is $2.35 per hour.
Suppose you are using a significance level of 0.01 or 1% (α = 0.01).
What is the probability that you will correctly reject the null hypothesis if the true average manufacturing wage in Utah is $24 per hour? (In other words, what is the power of the test if the true average wage in Utah is $24 per hour?)
Round your answer to three decimal places.
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