1. Identify whether each of the following is a matched pairs or a two sample t-test. Justify your decision. a. Does reading on a light-emitting e-reader at bedtime increase how long it takes to fall asleep? A sample of 12 adults slept in the lab on two different nights. In random order,subjects read for 30 minutes in a print book one night and with a light-emitting e-readerthe other night. How long (in minutes) it took subjects to reach a deep sleep stage was recorded. The researchers compared the difference in the amount of time it took theperson to reach deep sleep. b. A diet has been developed for raising cows. Two random samples of size 9 are independently selected, and one is given the standard diet while the other is given the new diet. After 18 weeks, the weight gain was measured for each cow.
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.
1. Identify whether each of the following is a matched pairs or a two sample t-test. Justify your decision.
a. Does reading on a light-emitting e-reader at bedtime increase how long it takes to fall asleep? A sample of 12 adults slept in the lab on two different nights. In random order,subjects read for 30 minutes in a print book one night and with a light-emitting e-readerthe other night. How long (in minutes) it took subjects to reach a deep sleep stage was
recorded. The researchers compared the difference in the amount of time it took theperson to reach deep sleep.
b. A diet has been developed for raising cows. Two random samples of size 9 are independently selected, and one is given the standard diet while the other is given the new diet. After 18 weeks, the weight gain was measured for each cow.
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