Errors. An auto parts company advertises that its specialoil additive will make the engine “run smoother, cleaner, longer, with fewer repairs.” An independent laboratory de-cides to test part of this claim. It arranges to use a taxicab company’s fleet of cars. The cars are randomly dividedinto two groups. The company’s mechanics will use theadditive in one group of cars but not in the other. At theend of a year the laboratory will compare the percentageof cars in each group that required engine repairs.a) What kind of a study is this?b) Will they do a one-tailed or a two-tailed test?c) Explain in this context what a Type I error would be.d) Explain in this context what a Type II error would be.e) Which type of error would the additive manufacturerconsider more serious? f) If the cabs with the additive do indeed run signifi-cantly better, can the company conclude it is an effect of the additive? Can they generalize this result andrecommend the additive for all cars? Explain.
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.
oil additive will make the engine “run smoother, cleaner,
cides to test part of this claim. It arranges to use a taxicab
into two groups. The company’s mechanics will use the
additive in one group of cars but not in the other. At the
end of a year the laboratory will compare the percentage
of cars in each group that required engine repairs.
a) What kind of a study is this?
b) Will they do a one-tailed or a two-tailed test?
c) Explain in this context what a Type I error would be.
d) Explain in this context what a Type II error would be.
e) Which type of error would the additive manufacturer
consider more serious?
cantly better, can the company conclude it is an effect
recommend the additive for all cars? Explain.
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