How would the width of a 95% confidence interval for a population mean, based on a sample of size n = 400, compare to the width of a 95% confidence interval for the same population mean based on a sample of size n = 200? Select one: a. On average, the confidence interval for n = 200 would be narrower b. On average, the confidence interval for n = 400 would be narrower c. On average, the two confidence intervals will have the same width d. It depends on the population distribution A random sample of 36 Uniform[0, 1] random variables is observed. The distribution of the sample mean of these random variables is ... Select one: a. approximately Uniform b. exactly Uniform c. approximately Normal d. impossible to tell Given a random sample from a Normal population, how would the width of the 95% confidence interval for the population mean compare to that of the 90% confidence interval for the same population mean, from the same data? Select one: a. The 95% confidence interval would be narrower than the 90% confidence interval b. The 95% confidence interval would be wider than the 90% confidence interval c. Both intervals would be the same width d. It depends on the data
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.
![How would the width of a 95% confidence interval for a population mean, based on a sample of size n =
400, compare to the width of a 95% confidence interval for the same population mean based on a sample
of size n = 200?
Select one:
a. On average, the confidence interval for n = 200 would be narrower
b. On average, the confidence interval for n = 400 would be narrower
c. On average, the two confidence intervals will have the same width
d. It depends on the population distribution
A random sample of 36 Uniform[0, 1] random variables is observed. The distribution of the sample mean of
these random variables is...
Select one:
a. approximately Uniform
b. exactly Uniform
c. approximately Normal
d. impossible to tell
Given a random sample from a Normal population, how would the width of the 95% confidence interval for
the population mean compare to that of the 90% confidence interval for the same population mean, from
the same data?
Select one:
a. The 95% confidence interval would be narrower than the 90% confidence interval
b. The 95% confidence interval would be wider than the 90% confidence interval
c. Both intervals would be the same width
d. It depends on the data
O O O](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffdd94542-6c12-40f3-8be5-b5c48236f949%2F2c9a818b-8abd-440e-9b40-b589f678ce88%2F2300ln8_processed.jpeg&w=3840&q=75)
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