c) What conclusion do you draw from the hypothesis test in point b about the possible difference in the mean amount of antibody after oral administration of the vaccines? d) The researchers also created a 95% confidence interval for the difference between the averages. Will the confidence interval contain the value 0? Justify your answer without calculating the confidence interval. e) Let us now assume that there is in fact a difference in the efficacy of the vaccines. Is this in line with your conclusion in point c? If not, what kind of error occurred?
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 team of researchers working on the development of vaccines conducted a study on two vaccines. Thirty individuals participated in the study and were randomly assigned to two groups and one group received vaccine 1 and the other group vaccine 2. The researchers then measured the amount of antibody in the individuals' blood after ingestion, entered R and calculated some fish sizes that can be seen here below.
x̄1 = 494,54, s1 =52,39, x̄2 = 467,93, s2 = 45,20, d = 26,61, sd = 68,69.
Blood levels of antibodies can be expected to follow
c) What conclusion do you draw from the hypothesis test in point b about the possible difference in the
d) The researchers also created a 95% confidence interval for the difference between the averages. Will the confidence interval contain the value 0? Justify your answer without calculating the confidence interval.
e) Let us now assume that there is in fact a difference in the efficacy of the vaccines. Is this in line with your conclusion in point c? If not, what kind of error occurred?
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