Q2. A large company buys thousands of light bulbs every year. The company is currently considering three brands of light bulbs to choose from. Before the company decides which light bulbs to buy, it wants to investigate if the mean lifetimes of the three types of light bulbs are the same. The company's research department randomly selected a few bulbs of each type and tested them. The following table lists the number of hours (in thousands) that each of the bulbs in each brand lasted before being burned out. Brand I 20 24 Brand II 22 23 Brand III 23 24 18 21 20 25 *indicates a value obtained from the 4th and 5th digits of your ID. At 5% significance level, test the null hypothesis that the mean lifetime of bulbs for each of three brands is the same. Also Construct ANOVA table mentioning all necessary columns for this example,
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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