The postal service sorts mail as Priority Mail Express, Priority Mail, First-Class Mail, or Standard Mail. Over a period of 3 weeks, 18 of each type were mailed from the Network Distribution Center in Atlanta, Georgia, to Des Moines, Iowa. The total delivery time in days was recorded. Minitab was used to perform the ANOVA. The results follow: Source DF SS MS F P Factor 3 2.91 0.97 3.73 0.015 Error 68 17.36 0.26 Total 71 20.27 Level N Mean StDev Priority Mail Express 18 2.917 0.427 Priority Mail 18 2.941 0.741 First-Class Mail 18 3.402 0.440 Standard Mail 18 3.215 0.311 Using the ANOVA results, compare the average delivery times of the four different types of mail. Identify the null hypothesis and the alternate hypothesis. Null hypothesis: H0: μ1 ≠ μ2 ≠ μ3 ≠ μ4 H0: μ1 = μ2 = μ3 = μ4 a b Alternate hypothesis: H1: At least one mean is different. H1: All means are equal. What is the decision rule? Use the 0.05 significance level. (Round your answer to 2 decimal places.) Use the 0.05 significance level to test if this evidence suggests a difference in the means for the different types of mail.
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
The postal service sorts mail as Priority Mail Express, Priority Mail, First-Class Mail, or Standard Mail. Over a period of 3 weeks, 18 of each type were mailed from the Network Distribution Center in Atlanta, Georgia, to Des Moines, Iowa. The total delivery time in days was recorded. Minitab was used to perform the ANOVA. The results follow:
| Source | DF | SS | MS | F | P | |
| Factor | 3 | 2.91 | 0.97 | 3.73 | 0.015 | |
| Error | 68 | 17.36 | 0.26 | |||
| Total | 71 | 20.27 | ||||
| Level | N | Mean | StDev |
| Priority Mail Express | 18 | 2.917 | 0.427 |
| Priority Mail | 18 | 2.941 | 0.741 |
| First-Class Mail | 18 | 3.402 | 0.440 |
| Standard Mail | 18 | 3.215 | 0.311 |
Using the ANOVA results, compare the average delivery times of the four different types of mail.
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Identify the null hypothesis and the alternate hypothesis.
Null hypothesis:
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H0: μ1 ≠ μ2 ≠ μ3 ≠ μ4
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H0: μ1 = μ2 = μ3 = μ4
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a
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b
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Alternate hypothesis:
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H1: At least one mean is different.
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H1: All means are equal.
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What is the decision rule? Use the 0.05 significance level. (Round your answer to 2 decimal places.)
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Use the 0.05 significance level to test if this evidence suggests a difference in the means for the different types of mail.
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