From past records it is known that the average life of a battery used in a digital clock is 305 days. The lives of the batteries are normally distributed. The battery was recently modified to last longer. A sample of 40 modifed batteries was tested. It was discovered that the mean life was 311 days, and the sample standard deviation was 22 days. At the 0.01 level of sigificance, did the modofication increase the mean life of the battery? (a) State the null and alternative hypotheses for this test. (b) Compute the value of the Test Statistic? (c) State the critical region for this test. (d) State the conclusion for the test. Give reasons for your answer.
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.
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