Night Owls - A MSU psychologist reports that 38% of MSU students regularly sleep less than 8 hours each night. Cindy believes that the actual proportion of MSU students who regularly sleep less than 8 hours each night is less than the value reported by the MSU psychologist. She randomly selects 150 students and asks them, "Do you regularly sleep less than 8 hours each night?" She finds that 52 of the 150 students answered "yes" to the question. 1. Which one of the following statements about the number 38% is correct? A. It is a sample statistic. B. It is a standard error. C. It is a margin of error. D. It is a claimed parameter. 2. Choose the null and alternative hypotheses Cindy should use to test her theory. A. Ho : p = 0.38, HA:P< 0.35 B. Ho : p = 0.38, HA:p> 0.38 C. Ho : p = 0.38, HA: p# 0.38 D. Ho : p = 0.38, HA:p< 0.38 3. If you assume that the observations in the sample are independent, what is the smallest value the sample size could be to meet the conditions for this hypothesis test? A. 20 B. 52 C. 10 D. 27 E. 29 F. None of the above 4. Calculate the test statistic. 5. Calculate the p value. 6. Which of the following describes the probability represented by the p-value for this test? A. It is the probability that less than 38% of MSU students regularly sleep less than 8 hours a day if, in fact, 34.67% actually do. B. It is the probability that 38% of all MSU students regularly sleep less than 8 hours a day, assuming the null model is valid. C. It is the probability that any random sample of 150 MSU students would have 34.67% saying they regularly sleep less than 8 hours a day. D. It is the probability that a random sample of 150 MSU students would result in 34.67% or fewer who regularly sleep less than 8 hours a day, assuming the null model is valid. E. None of the above.
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.
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