hree different brands of tires were compared for wear characteristics. For each brand of tire, ten tires were randomly selected and subjected to standard wear testing procedures. The average mileage obtained for each brand of tire and sample standard deviations( both in 1000 miles) are shown below. Brand A Brand B Brand C
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.
Three different brands of tires were compared for wear characteristics. For each brand of tire, ten tires were randomly selected and subjected to standard wear testing procedures. The average mileage obtained for each brand of tire and sample standard deviations( both in 1000 miles) are shown below.
Brand A Brand B Brand C
Sample size 10 10 10
Average mileage (X mean) 37 38 33
Sample ST. Deviation (s) 3 4 2
- State the null and alternative hypotheses to see if the mean mileage for all three brands of tires is the same.
- Find the overall sample mean(x), overall sample size(nt), and the number of treatments (k).
- Compute the sum of squares between treatments (SSTR) and then sum of squares due to error(SSE).
- Carry the analysis of variance procedure for a completely randomized design by completing an ANOVA table.
- Compute the p-value. At the 1% level of significance , can you reject the null hypotheses in part (a)? Explain. What conclusion can you draw in this context?
- Use Fisher’s LSD procedure to determine which mean(if any) is different from the others. Use Level of significance=0.05.
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