Suppose the mean IQ score of people in a certain country is 100. Suppose the director of a college obtains a simple random sample of 41 students from that country and finds the mean IQ is 103.2 with a standard deviation of 13.6. Complete parts (a) through (d) below. Write a conclusion for the test. Choose the correct answer below. O A. Reject Ho- There is sufficient evidence to conclude that the mean IQ score of people in the country is greater than 100 at the a = 0.01 level of significance. B. Do not reject Ho. There is not sufficient evidence to conclude that the mean IQ score of people in the country is greater than 100 at the a = 0.01 level of significance. OC. Reject Ho. There is not sufficient evidence to conclude that the mean IQ score of people in the country is greater than 100 at the a = 0.01 level of significance. O D. Do not reject Ho. There sufficient evidence to conclude that the mean IQ score of people in the country is greater than 100 at the a = 0.01 level of significance. (b) Consider the hypotheses Ho: u = 101 versus H4: µ> 101. Explain what the director is testing. Perform the test at the a = 0.01 level of significance. Write a conclusion for the test. Explain what the director testing. Choose the correct answer below. O A. The director is testing if the sample provided sufficient evidence that the population mean IQ score is actually not greater than 101. O B. The director testing if the sample provided sufficient evidence that the population mean IQ score is actually equal to 101. c. The director is testing if the sample provided sufficient evidence that the population mean IQ score is actually greater than 101. O D. The director is testing if the sample provided sufficient evidence that the population mean IQ score is actually not equal to 101. Find the test statistic for this hypothesis test. 1.04 (Round to two decimal places as needed.) Find the P-value for this hypothesis test. I(Round to three decimal places as needed.)

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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.