A purchasing manager for a large university is investigating which brand of LCD projector to purchase to equip "smart" classrooms. Of major concern is the longevity of the light bulbs used in the projectors. The purchasing manager has narrowed down the choice of projector to two brands, Infocus and Proxima, and wishes to determine if there is any difference between the two brands in the mean lifetime of the bulbs used. The purchasing manager obtained twelve projectors of each brand for testing over the last several academic terms. The number of hours the bulbs lasted on each of the twelve machines is given in the table. Lifetimes of light bulbs (hours) Infocus 886, 611, 553, 798, 873, 960, 831, 930, 935, 921, 811, 934 Proxima 625, 794, 1000, 1030, 919, 858, 683, 887, 706, 633, 757, 938 Assume that the two populations of lifetimes are normally distributed and that the population variances are equal. Can we conclude, at the 0.05 level of significance, that there is a difference in the mean lifetime of the light bulbs in the two brands? Perform a two-tailed test. The null hypothesis: H0: The alternative hypothesis: H1: The type of test statistic: (Choose one)ZtChi squareF The value of the test statistic:(Round to at least three decimal places.) The p-value:(Round to at least three decimal places.) Can we conclude that there is a difference in the mean lifetimes of the light bulbs in the two brands? Yes No
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.
A purchasing manager for a large university is investigating which brand of LCD projector to purchase to equip "smart" classrooms. Of major concern is the longevity of the light bulbs used in the projectors. The purchasing manager has narrowed down the choice of projector to two brands, Infocus and Proxima, and wishes to determine if there is any difference between the two brands in the mean lifetime of the bulbs used.
The purchasing manager obtained twelve projectors of each brand for testing over the last several academic terms. The number of hours the bulbs lasted on each of the twelve machines is given in the table.
| Lifetimes of light bulbs (hours) | ||
|---|---|---|
| Infocus |
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| Proxima |
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Assume that the two populations of lifetimes are
level of significance, that there is a difference in the mean lifetime of the light bulbs in the two brands?
Perform a two-tailed test.
| The null hypothesis: |
H0:
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| The alternative hypothesis: |
H1:
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| The type of test statistic: | (Choose one)ZtChi squareF | |||
| The value of the test statistic: (Round to at least three decimal places.) |
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| The p-value: (Round to at least three decimal places.) |
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| Can we conclude that there is a difference in the mean lifetimes of the light bulbs in the two brands? |
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