A carpet manufacturer is studying the differences between two of its major outlet stores. The company is interested in the time it takes for customers to receive carpeting that has been ordered from the plant. Data concerning a sample of delivery times for the most popular type of carpet are summarized as follows: Acme Store Betty’s Store x̄ 43.7 days 34.3 days s 3.1 days 2.4 days n 31 orders 41 orders Assuming equal variances, determine at the 5% level of significance, if there is enough evidence from the sample data to conclude that Acmes’ store must wait on average significantly longer for the carpet to be delivered than Betty’s store? Then calculate and interpret a (1-α)% CI for µA - µB. Does the interval estimate for µAcme - µBetty’s support the decision? Explain. Recall that we only use the p-value decision rule for 2 sample t-tests
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 carpet manufacturer is studying the differences between two of its major outlet stores. The company is interested in the time it takes for customers to receive carpeting that has been ordered from the plant. Data concerning a sample of delivery times for the most popular type of carpet are summarized as follows:
Acme Store Betty’s Store
x̄ 43.7 days 34.3 days
s 3.1 days 2.4 days
n 31 orders 41 orders
Assuming equal variances, determine at the 5% level of significance, if there is enough evidence from the sample data to conclude that Acmes’ store must wait on average significantly longer for the carpet to be delivered than Betty’s store? Then calculate and interpret a (1-α)% CI for µA - µB. Does the
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