BNAD 277 Midterm 1

A company sold 1000 units in it's first year and 1400 in second year. What's the growth rate?

(1400-1000)/1000 = .40 or 40%

The required sample size for estimating a population proportion is largest when p hat equals

.5

A population has a mean of 50 and a SD of 10. A random sample of 256 is selected. The standard deviation of X bar is equal to

.625 (standard deviation of x bar is equal to sigma/square root of n.)

Chebyshev formula

1-1/ksquared where k is the number of standard deviations from the mean

confidence interval for 90%

1.645

The confidence level is equal to

100 x (1-a)%

Confidence interval for 99%

2.575

Nadia purchased 200 shares of stock at $20 per share. The purchased 300 shares at $15. What's the weighted average?

200/500($20) + 300/500($15) = $17

If exponential distribution has an expected value equal to 5, then the standard deviation equals

5

A random sample of 80 observations results in 50 successes. What is the point estimate of the population proportion of successes

50/80 = .625

Which is most useful as a relative measure of dispersion? (SD, range, Coefficient of variation, or variance)

Coefficient of variation

Suppose you were told that the delivery time of your new washing machine is equally likely over the time period 9 am to noon. If we define the random variable X as delivery time, then X follows the

Continuous normal distribution

The Poisson random variable does what?

Counts the number of occurrences of an event over a given interval of time or space

True or false? A discrete random variable can assume an uncountable number of values

False

Investment A: mean of 10 and SD of 5. Investment B: mean of 15 and SD of 10. Which has higher return and less risk?

Investment B has higher return while investment A has less risk because smaller SD.

We can use the finite population correction factor when

N>_ .05N

Which of the following is an example is an example of a continuous random variable? (Bernoulli trials, normal random variable, binomial random variable, and discrete uniform random variable)

Normal random variable

The probability that the normal random variable Z is greater than 1.5 is equal to

P(Z<-1.5)

The square root of the average of the sum of squared deviations from the mean is known as the

Standard deviation

The exponential distribution is related to which distribution?

The Poisson distribution

A confidence interval narrows if

The chosen confidence level decreases and the sample size increases

What can be said about the expected value and standard deviation of an exponential distribution?

The expected value is equal to the standard deviation

The exponential distribution is used to describe

The time that elapsed between such occurrences

True or false: A confidence interval provides a range of values that should contain a population parameter with a certain level of confidence

True

Lower Standard deviation means lower

Variability

The confidence interval provides

a range of values that, with a certain level of confidence, contains the population parameter of interest.

What greek letter denotes the level of significance

alpha

The probability that a discrete random variable X assumes a particular value x is

between zero and one

Sampling distribution p bar is closely related to the _____ distribution

binomial distribution

A random variable X with an equally likely chance of assuming any value within a specified range is said to have which distribution?

continuous uniform distribution

The numerical measure that reveals only the direction of the linear relationship between two variables, but not the strength of the linear relationship is referred to as the

covariance

Expected value x bar is the same as the

expected value

If X is normally distributed with expected value mu and standard deviation sigma, then x bar is normally distributed with

expected value mu and standard deviation sigma over square root of n.

For a given confidence level and sample size, the width of the interval is wider for a ...

larger Standard deviation

For a given confidence level and sample size, the width of the interval is wider for a

larger standard deviation (a larger SD increases the margin of error. Increasing the margin of error leads to a wider interval)

The variability between sample means is _____ the variability between observations

less than

The parameter p represents the

population proportion

When estimating the population mean the t distribution is used when the

population variance is unknown

The probability distribution of a continuous random variable is called its

probability density function

Which of the following is a descriptive measure for a qualitative variable? (mean, median, proportion, or standard deviation)

proportion

The expected value of p bar is the

proportion of successes in the population

Stratified sampling is preferred to cluster sampling when the objective is

to increase precision

Margin of error

z score times (SD/ square root of n)

The exponential random variable is bounded below by

zero

Confidence interval for 95%

1.96

The ______ is the multiplicative average of a data set

Geometric mean

X bar is a random variable whose value depends on the

chosen random sample

The correlation coefficient

describes both the direction and the strength of the linear relationship between two random variables.

When we construct a confidence interval for the population mean, the margin of error includes the standard error of x bar and the

desired level of confidence

For a continuous random variable X, the cumulative distribution function F(x) provides the probability that X is

less than or equal to any value x

alpha is referred to as the

level of significance

The probability distribution of a discrete random variable is called its probability ________

mass function

Equation for p bar

number in the sample that satisfied the criteria/ sample number

The exponential distribution is based entirely on how many parameters?

one

The population parameter is a constant while the sample statistic is a

random variable whose value depends on the choice of the random sample.

The width of the confidence interval is influenced by the

sample size n, standard deviation sigma, and confidence level 100(1-a)%

The probability distribution of the sample mean is commonly referred to as the

sampling distribution of x bar

The standard deviation of the sample mean x bar is referred to as the

standard error of the sample mean (SD/square root of n)

The standard deviation of the sample proportion p bar is referred to as the

standard error of the sample proportion

The expected value of X bar is equal to

mu

We use the finite population correction factor to

reduce the sampling variation of x bar and p bar

The sharpe ratio can be characterized as a measure of the relationship between

risk and reward

The probability distribution of the sample mean is commonly referred to as the

sampling distribution of x bar.

In _____ sampling, the population is divided up into strata and then randomly selected observations are taken proportionately form each stratum

stratified random sampling

Binomial distribution describes the number of `

successes X in n trials

The sample proportion p bar is the estimator of

the population proportion p

The two pieces of information that are necessary to determine the value of t are

the sample size df and significant level

Z subscript a/2 is the z value associated with the probability a/2 in the

upper-tail

Suppose you are constructing a confidence interval for the population mean. For a given sample size and standard deviation, the width of the confidence interval is _____ for a greater confidence level

wider

The mean of the standard normal distribution is equal to

zero

The probability that a continuous random variable X assumes a particular value x is

zero

Steps to calculate mean absolute deviation (MAD)

1. Calculate the arithmetic mean for the data set 2. Find the absolute difference between each value and the mean 3. Sum the absolute differences 4. Divide by the sample size

Steps for finding the mean of grouped data

1. Find the midpoint foreach of grouped data 2. Multiply the midpoint of each class by the number of observations in its class 3. Sum the products of the midpoints and observations 4. Divide by the total number of observations

The average of the absolute differences between the values of the data set and the mean is the

mean absolute deviation

Equation for confidence interval

mean plus or minus margin of error

Which of the following is an example of a population parameter (mu, s squared, x bar, or s)

mu

The exponential distribution is

not symmetric

The total area under the normal curve is

equal to 1

For a continuous random variable, one characteristic of its probability density function f(x) is that teh area under f(x) over all values x is

equal to one

The sample mean is commonly referred to as the

estimator

For a continuous random variable X it is only meaningful to calculate the probability that the value of the random variable

falls within some specified interval

Use finite population if n is

greater than 5% of N

When constructing a confidence interval for the population mean, the factors that affect the width of the confidence interval for a given SD are

the confidence interval and sample size

Binomial distribution describes what

the number of successes X in n trials where p is the probability of success

Sample mean X bar is estimator of

the population mean mu