1. A researcher is testing the claim that adults consume an average of at least 1.85 cups of coffee per day. A sample of 35 adults shows a sample mean of 1.70 cups per day with a sample standard deviation of 0.4 cups per day. Test the claim at a 5% level of significance. What is your conclusion? 2. A government Bureau claims that more than 50% of US, tax returns were filed electronically last year. A random sample of 150 tax returns for last year contained 86 that were filed electronically. Test the Bureau's claim at a 5% level of significance. What is your conclusion? Report the p-value for this test. 3. A major automobile company claims that its New electric powered car has an average range of more that 10o miles. A random sample of 50 new electric cars was selected to test the claim. Assume that the population test. standard deviation is 12 miles. A 5% level of significance will be used for the A) What would be the consequences of making a Type ll error in this problem Compute the Probability of making a Type ll error if the true population mean is 105 miles. C) What is the maximum probability of making a Type I error in this problem? Please Note: A hypothesis test answer must contain: a Null and an Alternate Hypothesis, a computed value of the test statístic, a critical value of the test statistic, a Decision, and a Conclusion.
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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