Probability Theory Test

The probability of observing a particular value of a continous random variable ___

is 0.

Define a confidence interval.

A confidence interval is a range of values used to estimate the true value of a population parameter. The confidence level is the probability the interval actually contains the population parameter, assuming that the estimation process is repeated a large number of times.

Consider the following three events for college students: Describe the event C/A in words.

A female college student finishes her undergraduate in four years.

Alex hypothesized that students study less than the recommended two hours per credit hour each week outside of class. Alex performed a hypothesis test and told a colleague that he had evidence to indicate his hypothesis was true. which of the following is a true statement that his colleague could have said?

Alex might have made a Type 1 Error.

There were 100 random samples of the same size taken from a population which is known to have a normal distribution with some mean and a known standard deviation. A 95% confidence interval for the population mean was constructed for each of the 100 random samples. If all the conditions are satisfied, what percentage of these confidence intervals would capture the true population mean?

Approximately 95% of them.

Katy had two choices of routes to get her to work...

It takes Katy 5 minutes LONGER to get to work using ROUTE 2, on average, than ROUTE 1.

The probability of smoking and annual income question:

No, because the probability of smoking is different for people who earn over $75,000 per year, the events are not independent.

In a normal distribution, approximately 68% of the area under the normal curve is within how many standard deviation(s) of the mean?

One.

Suppose you want to know how likely it is that a student graduates with a Bachelor's degree in 4 years if they were in the top 10% of their high school graduating class. Which of the following probabilities will answer your question?

P (earn BS degree/ top 10%)

What is the symbol used for SAMPLE STANDARD DEVIATION?

S

Suppose an experiment consists of rolling a fair die ten times and recording the number of sevens obtained. If event E is defined as getting at least one 7, how would you describe the complement of E?

The complement of event E is the event that NO SEVENS ARE OBTAINED.

A college student was interested in the average amount college students spend on entertainment each week. He randomly sampled 200 students and found the following 95% confidence interval: (24,28) in dollars per week. If this student randomly sampled 100 students instead, what would happen to the margin of error (assuming everything else remained the same)?

The margin of error would increase.

Suppose x bar= 60; Ho: ux=50; ux>50, and the p-value from a one sample t-test is 0.04. what does this p-value mean?

The probability of getting a sample mean of 60 or more if the true population mean is 50 is 0.04.

Identify the requirements for a discrete probability distribution.

The sum of the probabilities must equal one. Each probability must be between zero and one inclusive.

If a Z-score is equal to zero, which of the following must be true?

The x-value must be equal to the mean of the distribution.

If a z score is equal to zero, which of the follow must be true?

The x-value must equal to the mean of the distribution.

Dora likes to explore....The t-statistic for this problem is 6.661. Based on this t-statistic, what is the conclusion?

There is sufficient evidence to indicate that the average height of all Mountain ash trees in southeast Australia is more than 250 feet.

Identify which of the following is NOT A property of the Normal probability density function or state that they all are.

These are all properties of the Normal Probability Distribution.

Which of the following is not a valid explanation of the Law of Large Numbers?

These statements are all valid.

A study about New York City public school kids and their bullying:

a one sample t-test

Whats the symbol to represent the sample variance?

s2