Statistics Final

What are the two requirements for a discrete probability distribution?

(E) P(X)=1 0<=P(x)<=1

In February 2008, the Gallup organization surveyed 1,034 adults between 30 and 64 years of age and found that 535 were worried that they will outlive their money after they retire. Does the sample evidence suggest that a majority of 30 to 64 year olds in the United States are worried they will outlive their money? Use the a=0.1 level of significance

(a) Do not reject the null hypothesis (b) Do not reject the null hypothesis

It has long been stated that the mean temperature of humans is 98.6 F. However, two researchers currently involved in the subject thought that the mean temperature of humans is less than 98.6 F. They measured the temperatures of 148 healthy adults 1 4 times daily for 3 days, obtaining 600 measurements. The sample data resulted in a sample mean of 97.8 F and a sample standard deviation of 0.6 F. (a) Using the classical approach, judge whether the mean temperature of humans is less than 98.6 F at the a=0.01 level of significance. (b) Approximate the P-value

(a) Reject H0 since the test statistic is less than the critical value (b) 0

State the conditions required for a random variable X to follow a Poisson process.

-The number of successes in any interval is independent of the number of successes in any other interval provided the intervals are not overlapping -The probability of success is the same for any two intervals of equal length. -The probability of two or more successes in any sufficiently small subinterval is 0

Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable. (a) The number of people in a restaurant that has a capacity of 100. (b) The time it takes for a light bulb to burn out.

-The random variable is discrete. The possible values are x=0,1,2,...., 100 -The random variable is continuous. The possible values are t>0

What is a random variable?

A random variable is a numerical measure of the outcome of a probability experiment

A binomial experiment is performed a fixed number of times. What is each repetition of the experiment called?

Each repetition of the experiment is called a trial

Determine if the following probability experiment represents a binomial experiment A random sample of 15 high school seniors is obtained, and the individuals selected asked to stated their hair length.

No, this probability experiment does not represent a binomial experiment because the variable is continuous, and there are not two mutually exclusive outcomes

Determine whether the following probability experiment represents a binomial experiment and explain the reason for your answer Seven cards are selected from a standard 52 card deck without replacement. The number of nines selected is recorded.

No,because the trials of the experiment are not independent and the probability of success differs from trial to trial

A poll of 1125 adults in a certain country found that 23% identified themselves as the followers of some religion. The margin of error was 4 percentage points with 95% confidence

There is 95 % confidence that the proportion of adults in a certain country who identified themselves as the followers of some religion is between 19 % and 27%

Determine whether the distribution is a discrete probability distribution x 0 10 20 30 40 P(x) 0.2 0.2 0.2 0.2

Yes, because the probabilities meet all the conditions

Determine whether the distribution is a discrete probability distribution x P(x) 0 0.07 1 0.37 2 0.32 3 0.09 4 0.15 Is the distribution a discrete probability distribution?

Yes, because the sum of the probabilities is equal to 1 and each probability is between 0 and 1, inclusive

Suppose a sample of 0-rings was obtained and the wall thickness (in inches) of each was recorded. Use a normal probability plot to assess whether the sample data could have come from a population that is normally distributed

Yes, since the relationship between the expected z-values and the observed values is approximately linear.

What is the formula for the expected number of successes in a binomial experiment with n trials and probability of success p?

np

A _____ ________ is the value of a statistic that estimates the value of a parameter

point estimate