Suppose that a scientist seeks to compare the ability of a new hand sanitizer to eliminate Pseudomonas aeruginosa bacteria against the hand sanitizer currently in use. Assume that the mean number of bacteria remaining on a hand after using sanitizer is approximately normally distributed; however, the population standard deviation is unknown. The scientist selects a simple random sample of 5656 students. Each subject uses the new hand sanitizer on one randomly‑chosen hand and the sanitizer currently in use on the other. The number of Pseudomonas aeruginosa bacteria remaining on each hand after using the sanitizers is determined, and the difference in the number of bacteria on the hand treated with the new sanitizer and the number of bacteria on the hand treated with the current sanitizer is determined. Choose the procedure for estimating the mean difference. a. two‑sample tt‑hypothesis test for independent means b. one‑sample tt‑confidence interval for independent means c. matched‑pairs tt‑hypothesis test for dependent means d. matched‑pairs tt‑confidence interval for dependent means e. two‑sample tt‑confidence interval for independent means
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 that a scientist seeks to compare the ability of a new hand sanitizer to eliminate Pseudomonas aeruginosa bacteria against the hand sanitizer currently in use. Assume that the mean number of bacteria remaining on a hand after using sanitizer is approximately
The scientist selects a simple random sample of 5656 students. Each subject uses the new hand sanitizer on one randomly‑chosen hand and the sanitizer currently in use on the other. The number of Pseudomonas aeruginosa bacteria remaining on each hand after using the sanitizers is determined, and the difference in the number of bacteria on the hand treated with the new sanitizer and the number of bacteria on the hand treated with the current sanitizer is determined.
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