A manufacturer advertises that the average life of batteries produced by his firm is at least 12 months. The consumer board disagrees, and claims that the average life of the batteries is less than 12 months. The consumer board test a random sample of 9 batteries and find that the mean life is 10.6 months with a standard deviation of 2. Test the consumer board's claim. The rejection region at a 1% significance level (rounded off to three decimals) is: A. {T | T < 3.355} B. {Z | Z < -1.645} C. {T |T < - 2.896} D. {Z | Z < 1.645}
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.
A manufacturer advertises that the average life of batteries produced by his firm is at least 12 months. The consumer board disagrees, and claims that the average life of the batteries is less than 12 months. The consumer board test a random sample of 9 batteries and find that the mean life is 10.6 months with a standard deviation of 2. Test the consumer board's claim. The rejection region at a 1% significance level (rounded off to three decimals) is:
- A. {T | T < 3.355}
- B. {Z | Z < -1.645}
- C. {T |T < - 2.896}
- D. {Z | Z < 1.645}
A firm specializing in the preparation of income tax returns, claims the mean refund for customers who received refunds last year was different to R150. For a random sample of 12 customers who received refunds last year, the mean amount was found to be R125, with a standard deviation of R43. The test statistic (rounded off to two decimals) is:
- A. T<-2.20
- B. T=2.20
- C. Z=-2.01
- D. T=-2.01
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