State the Null and Alternative hypothesis of the following statement. 1. In a court trial, a suspect is presumed innocent unless proven guilty. 2. The average score of students from section A in statistics is 82 %. It is believed that this is higher than the average score of section B students in the same test. 3. The manufacturer of a patent medicine claimed that it was at least 90% effective in relieving pain for a period of 8 hours. A researcher would like to test if the manufacturer's claim is true. 4. A measuring instrument had just been readjusted. The quality control department head, wanting to know if the instrument is really in good condition, got a sample of 50 measurements of the same object. He would only classify the instrument as in good condition if the variability of measurements produced by the machine is a t most 0.5 units. 5. A woman learned about a new slimming program that involved dancing. She invited her friends to join her and they danced together for an hour a day. Of those she had invited, she randomly selected 10 and asked them to give their weights before and after two months of adapting the said program. She wanted to determine if the program was effective by comparing their weights before and after they joined.
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.
Answer Problem #2 only.
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