A coffee manufacturer is interested in whether the mean daily consumption of regular coffee drinkers is less than that of decaffeinated coffee drinkers. Assume the population standard deviation for those drinking regular coffee is 1.39 cups per day and 1.55 cups per day for those drinking decaffeinated coffee. A random sample of 45 regular coffee drinkers showed a mean of 4.59 cups per day. A sample of 39 decaffeinated coffee drinkers showed a mean of 5.19 cups per day. Use the 0.050 significance level. State the decision rule (the decision rule is to reject H0: z<?) (round to 2 decimal places) Compute the value of the test statistic What is the p-value?
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 coffee manufacturer is interested in whether the mean daily consumption of regular coffee drinkers is less than that of decaffeinated coffee drinkers. Assume the population standard deviation for those drinking regular coffee is 1.39 cups per day and 1.55 cups per day for those drinking decaffeinated coffee. A random sample of 45 regular coffee drinkers showed a mean of 4.59 cups per day. A sample of 39 decaffeinated coffee drinkers showed a mean of 5.19 cups per day. Use the 0.050 significance level.
- State the decision rule (the decision rule is to reject H0: z<?) (round to 2 decimal places)
- Compute the value of the test statistic
- What is the p-value?
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