The dataset (provided below this question) lists the ages of customers at 5 different coffee stores in a major metropolitan city. At the 1% significance level, is there evidence of a difference in the population mean ages between the customers at the five stores. Note: Please only provide the t stat, p-value and the appropraite lower, upper, or two tailed test critical value. Ages of customers in 5 different coffee stores STORE A STORE B STORE C STORE D STORE E 30 33 18 27 34 29 27 32 28 25 21 19 35 27 20 20 40 36 36 45 33 28 15 27 28 29 42 35 29 43 33 34 33 18 35 32 14 23 16 45 8 37 29 18 14 41 23 35 30 28 18 37 40 41 35 21 29 26 38 56 37 41 43 29 33 41 29 23 36 41 39 20 47 29 28 26 25 27 28 32 44 38 40 32 20 14 27 48 42 37 33 38 37 29 31 27 42 41 32 8 35 35 17 26 29 8 23 51 16 13 26 42 36 29 47 20 33 37 38 28 28 16 30 35 47 40 44 42 34 32 22 30 16 26 24 31 35 32 35 23 30 10 22 26 18 26 29
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.
Q: The dataset (provided below this question) lists the ages of customers at 5 different coffee stores in a major metropolitan city. At the 1% significance level, is there evidence of a difference in the population mean ages between the customers at the five stores.
Note: Please only provide the t stat, p-value and the appropraite lower, upper, or two tailed test critical value.
| Ages of customers in 5 different coffee stores | ||||
| STORE A | STORE B | STORE C | STORE D | STORE E |
| 30 | 33 | 18 | 27 | 34 |
| 29 | 27 | 32 | 28 | 25 |
| 21 | 19 | 35 | 27 | 20 |
| 20 | 40 | 36 | 36 | 45 |
| 33 | 28 | 15 | 27 | 28 |
| 29 | 42 | 35 | 29 | 43 |
| 33 | 34 | 33 | 18 | 35 |
| 32 | 14 | 23 | 16 | 45 |
| 8 | 37 | 29 | 18 | 14 |
| 41 | 23 | 35 | 30 | 28 |
| 18 | 37 | 40 | 41 | 35 |
| 21 | 29 | 26 | 38 | 56 |
| 37 | 41 | 43 | 29 | 33 |
| 41 | 29 | 23 | 36 | 41 |
| 39 | 20 | 47 | 29 | 28 |
| 26 | 25 | 27 | 28 | 32 |
| 44 | 38 | 40 | 32 | 20 |
| 14 | 27 | 48 | 42 | 37 |
| 33 | 38 | 37 | 29 | |
| 31 | 27 | 42 | 41 | |
| 32 | 8 | 35 | 35 | |
| 17 | 26 | 29 | 8 | |
| 23 | 51 | 16 | 13 | |
| 26 | 42 | 36 | 29 | |
| 47 | 20 | 33 | 37 | |
| 38 | 28 | 28 | 16 | |
| 30 | 35 | 47 | 40 | |
| 44 | 42 | 34 | 32 | |
| 22 | 30 | 16 | 26 | |
| 24 | 31 | 35 | 32 | |
| 35 | 23 | 30 | 10 | |
| 22 | 26 | 18 | ||
| 26 | 29 |
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