Suppose that the population of scores on the subsection of the personality test has a standard deviation of 25 and that you perform your hypothesis test using the 0.01 level of significance. Based on this information, answer the questions below. Carry your intermediate computations to at least four decimal places, and round your responses as indicated. (If necessary, consult a list of formulas.) H : µ is What are the null and alternative hypotheses that you should use for the test? H :H is What is the probability that you commit a Type I error? Round your response to at least two decimal places. Assuming that the actual value of u is 135, what is the power of the test? Round your response to at least two decimal places. The probability of committing a Type II error in the second test is greater Suppose that you decide test using the same population, the same null and alternative hypotheses, and the same level significance, but for this second test you choose a random sample of size 125 instead of a random sample of size 100. Assuming that the actual value of p is 135, how does the probability that you commit a Type II error in this second test compare to the probability that you commit a Type II error in the original test? perform statistical The probability of committing a Type II error in the second test is less O The probabilities of committing a Type II error are equal
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.
One personality test available on the World Wide Web has a subsection designed to assess the "honesty" of the test-taker. After taking the test and seeing your score for this subsection, you're interested in the
among the general population on this subsection. The website reports that
is
, but you believe that
is less than
. To do a statistical test, you choose a random sample of
people and have them take the personality test.
Suppose that the population of scores on the subsection of the personality test has a standard deviation of
and that you perform your hypothesis test using the
level of significance.
Based on this information, answer the questions below.
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