According to a polling organization, 22% of adults in a large region consider themselves to be liberal. A survey asked 200 respondents to disclose their political philosophy: Conservative, Liberal, Moderate. Treat the results of the survey as a random sample of adults in this region. Do the survey results suggest the proportion higher than that reported by the polling organization? Use an a = 0.05 level of significance. E Click the icon to view the survey results. Because npo (1- Po) = 34.3 > 10; the sample size is less than 5% of the population size, and the sample is given to be random, requirements for testing the hypothesis are satisfied. (Round to one decimal place as needed.) Identify the null and alternative hypotheses for this test. Let p represent the population proportion of adults in this region who consider themselves to be liberal. Ho: P = 0.22 versus H,: P > 0.22 (Type integers or decimals. Do not round.) Find the test statistic, zo, for this hypothesis test. Zo = ] (Round to two decimal places as needed.)
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.
here is the survey result table
Moderate
Moderate
Liberal
Conservative
Liberal
Conservative
Moderate
Moderate
Moderate
Liberal
Moderate
Moderate
Moderate
Moderate
Conservative
Moderate
Moderate
Conservative
Moderate
Moderate
Liberal
Liberal
Liberal
Conservative
Liberal
Conservative
Liberal
Moderate
Liberal
Moderate
Liberal
Liberal
Conservative
Moderate
Liberal
Moderate
Liberal
Liberal
Conservative
Conservative
Moderate
Liberal
Moderate
Liberal
Liberal
Conservative
Moderate
Moderate
Conservative
Moderate
Moderate
Moderate
Conservative
Moderate
Moderate
Moderate
Moderate
Liberal
Liberal
Liberal
Moderate
Conservative
Moderate
Liberal
Moderate
Moderate
Conservative
Moderate
Conservative
Liberal
Moderate
Liberal
Moderate
Moderate
Liberal
Moderate
Moderate
Liberal
Moderate
Conservative
Moderate
Conservative
Moderate
Moderate
Moderate
Conservative
Liberal
Conservative
Moderate
Moderate
Conservative
Moderate
Conservative
Conservative
Conservative
Moderate
Conservative
Liberal
Liberal
Liberal
Liberal
Liberal
Liberal
Liberal
Moderate
Liberal
Liberal
Conservative
Moderate
Moderate
Conservative
Moderate
Liberal
Conservative
Conservative
Conservative
Liberal
Liberal
Moderate
Conservative
Conservative
Moderate
Moderate
Liberal
Conservative
Moderate
Conservative
Moderate
Moderate
Moderate
Conservative
Moderate
Conservative
Conservative
Moderate
Moderate
Conservative
Moderate
Conservative
Liberal
Conservative
Moderate
Moderate
Moderate
Liberal
Liberal
Liberal
Conservative
Moderate
Conservative
Moderate
Moderate
Liberal
Conservative
Liberal
Conservative
Moderate
Moderate
Moderate
Liberal
Moderate
Moderate
Moderate
Moderate
Conservative
Moderate
Moderate
Conservative
Moderate
Moderate
Liberal
Liberal
Liberal
Conservative
Liberal
Conservative
Liberal
Moderate
Liberal
Moderate
Liberal
Liberal
Conservative
Moderate
Liberal
Moderate
Liberal
Liberal
Conservative
Conservative
Moderate
Liberal
Moderate
Liberal
Liberal
Conservative
Moderate
Moderate
Conservative
Moderate
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