Independent random samples from two regions in the same area gave the following chemical measurements (ppm). Assume the population distributions of the chemical are mound-shaped and symmetric for these two regions. Region I: *1; n=12 438 1013 1127 737 491 840 306 402 1155 1075 500 340 Region II: X2; n2=16 778 464 563 610 827 894 476 394 824 387 816 767 479 710 389 826 Let #1 be the population mean for 1 and 42 be the population mean for *2. Find a 90% confidence interval for H1-42. Question 5 options: -119.75 to 248.25
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.
The question is in the attached picture
Given Information:
Sample size () = 12
Sample size () = 16
Sample mean is obtained using the formula:
Sample mean of first sample is:
Sample mean of second sample is:
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