According to the AAA Foundation for Traffic Safety’s American Driving Survey, U.S. drivers spend, on average, 51 minutes behind the wheel each day. A researcher believes this is an overstatement. To investigate, a random sample of 75 drivers were selected. The study revealed that the mean time behind the wheel for the sample of 75 drivers was 46.4 minutes with a standard deviation of 18.8 minutes. Is there convincing evidence that the mean time behind the wheel for all U.S. drivers is less than 51 minutes? Use α = 0.01.

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A: Hey there! Thank you for posting the question. Since there are multiple questions posted, we will…

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Q: Two researchers conducted a study in which two groups of students were asked to answer 42 trivia…

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A:

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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.