Charlie wishes to investigate the effects of gummy bears which have been claimed to help increase the speed of hair growth. After a probability-based sampling plan is used, she randomly assigns half of the participants to ingest the gummies (treatment) and keeps the other half as a control group. To gauge the positive effect of the gummy, she calculates the ratio of the average speed of hair growth in treatment group (speed1) to the average speed of hair growth in the control group (speed2). Denoting this ratio by R, so R = speed1 / speed2. At the end of the study, she finds that speed1 is equal to 2 times speed2. The null hypothesis is that the speeds are the same (i.e., no effect from ingesting gummies). She then conducts a hypothesis test to see whether there is significant evidence to conclude that ingesting gummies is associated to hair growth, and obtains a p-value of 0.04. Which of the following interpretation of the p-value is correct? a) There is a 96% chance of obtaining an R value of 2 or more, given that the gummies do not work. b) There is a 4% chance of obtaining an R value of 2 or more, given that the gummies do not work. c) There is a 96% chance of obtaining an R value of 1 or more, given that the gummies do not work. d) There is a 4% chance of obtaining an R value of 1 or more, given that the gummies do not work.
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.
Charlie wishes to investigate the effects of gummy bears which have been claimed to help increase the speed of hair growth. After a probability-based sampling plan is used, she randomly assigns half of the participants to ingest the gummies (treatment) and keeps the other half as a control group.
To gauge the positive effect of the gummy, she calculates the ratio of the average speed of hair growth in treatment group (speed1) to the average speed of hair growth in the control group (speed2). Denoting this ratio by R, so R = speed1 / speed2. At the end of the study, she finds that speed1 is equal to 2 times speed2. The null hypothesis is that the speeds are the same (i.e., no effect from ingesting gummies).
She then conducts a hypothesis test to see whether there is significant evidence to conclude that ingesting gummies is associated to hair growth, and obtains a p-value of 0.04.
Which of the following interpretation of the p-value is correct?
a) There is a 96% chance of obtaining an R value of 2 or more, given that the gummies do not work.
b) There is a 4% chance of obtaining an R value of 2 or more, given that the gummies do not work.
c) There is a 96% chance of obtaining an R value of 1 or more, given that the gummies do not work.
d) There is a 4% chance of obtaining an R value of 1 or more, given that the gummies do not work.
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