Chapter 20 1. You are testing Ho:µ = 100 against Ha:µ < 100 based on an SRS of 16 observations from a Normal population. The data give ī = 98 and s = 4. The value of the t-statistic is: a) -8 b) -2 c) -0.5 2. You are testing Ho: µ = 100 against Ha:µ > 100 based on an SRS of 9 observations from a Normal population. The t statistic is t=2.10. The P-value for the statistic a) falls between 0.05 and 0.10 b) falls between 0.01 and 0.05 c) is less than 0.01 3. You have an SRS of four observations from a Normally distributed population. What critical value would you use to obtain an 80% confidence interval for the mean µ of the population? a) 1.533 b) 1.638 c) 2.353 4. You are testing Ho: µ = 0 against Ha:H # 0 based on an SRS of four observations from a Normal population. What values of the t statistic are statistically significant at the a=0.005 level? a) t> 7.453 b) t< -7.453 or t> 7.453 c) t< -5.598 or t> 5.598 5. Which of these settings does not allow use of a matched pairs t procedure? a) You interview both the instructor and one of the students in each of 20 introductory statistics classes and ask each how many hours per week homework assignment require. b) You interview a sample of 15 instructors and another sample of 15 students and ask each how many hours per week homework assignments require. c) You interview 40 students in the introductory statistics course at the beginning of the semester and again at the end of the semester and ask how many hours per week homework assignments require.
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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