IEE 380

E ( X^2 ) − μ^2 is the equation for (population) variance.

true

Events are said to be independent when the occurrence of one event does not affect the probability of another.

true

The standard method for estimating the parameters in a simple linear regression model is the method of least squares

true

1 − α is the probability that we fail to reject the null hypothesis when the null hypothesis is __________________. Enter one word as your answer.

true / correct

Consider the following set of data: 5. 4. 5. 6. 3. 7. Calculate the sample mean. Round your answer to two decimal places.

use excel

Assume X is a normally distributed random variable, where X ~N(58.3,9.2). What is the standard deviation of X? Round your answer to two decimal places.

~N(mu,variance) therefore sigma=sqrt(variance)

X is a continuous uniform random variable between the values 3.6 and 13.2. What is the probability X is more than or equal to 7.2? Round your answer to two decimal places.

0.63 * use Prob density function

The cumulative distribution function is the limit of the probability density function.

FALSE The Cumulative Distribution Function (CDF), is the probability that a random variable X is less than or equal to a specific numerical value, x.

An experiment that results in the same outcome when replicated is referred to as a random experiment.

False

The notation, p(x), has the same meaning as P(X = x) P(X < x) F(x) F(X) None of these other choices

P(X = x)

A continuous random variable is a variable that takes on values in an uncountable set.

TRUE

Continuous random variables can be described by a probability density function (pdf) and a cumulative distribution function (CDF).

TRUE

If both the response and regressor variables are random variables, we can calculate a correlation coefficient that reflects the linear relationship between these two variables.

True

A statistical hypothesis is a statement about the parameters of one or more samples.

false

An automatic filling machine is used to fill bottles with liquid detergent. A random sample of 18 bottles results in a sample standard deviation of fill volume s =0.037 oz. Assume that fill volume is approximately normal. Determine the upper bound of a two-sided 97.5% confidence interval on the population variance, σ 2. Round your answer to four decimal places.

X^2_alpha/2 (chi square) dist test UB=(n-1)*(s^2)/X^2_alpha/2

1 − β is the probability that we reject the null hypothesis when the null hypothesis is ________________? Enter one word as your answer.

false

For a function to be considered a probability mass function (pmf), the following must be true: p ( xi ) = 0 ∑ i = 1 p ( xi ) = 1 p(x)=P(x=xi) term-17

false

When determining the sample size for a specified error on the mean, we use conventional rounding methods to determine the integer value of n.

false

The totality of all observations is a sample

false The totality of all observations is a population.

A random variable is a function that assigns a probability to each outcome in the sample space of a random experiment.

false A random variable is a function that assigns a real number to each outcome in the sample space of a random experiment.

The correlation coefficient and the slope provide equivalent information in simple linear regression.

false (also need B0)

When determining the sample size for a specified error on the mean, we use conventional rounding methods to determine the integer value of n.

false round up

Suppose that a random variable X is continuously uniform between the values of 4 and 14. Find the mean of the distribution of the sample mean of a random sample of size 39. Round your answer to two decimal places.

mu=(b+a)/2

If T is a random variable with a t distribution, how many degrees of freedom does T have?

n-1

Consider the following set of data: 3. 9. 6. 2. 2. 2 Calculate the sample variance. Round to two decimal places.

sample variance = sum(xi-xbar)^2/(n-1)

Consider the following data: 29 18.4 15.9 16 28 Determine the lower bound of a two-sided 95% confidence interval on μ. Round your answer to two decimal places.

xbar-t_(alpha/2)*(s/sqrt(n)

A fitted linear regression model is yhat=10+2x. If x = 1 and the corresponding observed value of y = 11, the residual at this observation is:

yi-yhat ->(11-(10+2*1))=-1

Discrete random variables:

-Number of scratches on a surface. -Proportion of defective parts among 100 tested. -Number of transmitted bits received in error. -Number of common stock shares traded per day.

Suppose that a random variable X is continuously uniform between the values of 5 and 11. Find the variance of the distribution of the sample mean of a random sample of size 37. Round your answer to four decimal places. You Answered

A) var(x) = (b-1)^2/n B) Var(x) on dist of sample mean = var(x)/N

When testing H0: σ = σ0 against H1: σ > σ0, which option best describes the p-value? Area to the right of the test statistic under the Chi Square pdf. Area to the left of the test statistic under the Chi Square pdf. Two times the area to the right of the test statistic under the Chi Square pdf. Area to the right of the test statistic under the F pdf

Area to the right of the test statistic under the Chi Square pdf.

Cans of frozen orange juice are weighed to ensure they are not underfilled. Cans are independent, and the probability that a can is underfilled is 0.025. Three cans are weighed sequentially. What is the probability that all three cans are not underfilled? Express your answer to four decimal places using conventional rounding methods.

BINOMIAL DISTRIBUTION (nCx)(0.025^x)(0.975)^n-x - prob that 3 are filled, x=0 & n=3

Continuous random variables:

Continuous random variables: -Electrical current and voltage. -Physical measurements, e.g., length, weight, time, temperature, pressure.

Which one of the following is used to measure the center of a distribution? Kurtosis Mean Variance Skewness Standard Deviation

Correct! Mean

Given p(y) = 0.10 for y = -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 Determine the variance of the random variable. Express your answer to two decimal places.

Discrete uniform distribution have a set of consecutive integers as the possible values for x each with equal probability. use formula from image, b=5, a=-4

If two events are independent of one another then the probability of their intersection is zero.

FALSE - mutually exclusive has intersection of zero

A random variable is said to be discrete if it has an infinite number of values in a finite interval of its range.

False A discrete random variable is one with a finite or countably infinite range. Its values are obtained by counting. A continuous random variable is one with an interval (either finite or infinite) of real numbers for its range. Its values are obtained by measuring.

Assume X is normally distributed with mean 12 and standard deviation 6. What is the probability X is greater than 11.5? Round your answer to four decimal places.

NORM dist (CASIO) for P(z>Z) : lower = x upper=Z mu= 12 sigma=6 x>11.5? p(z>Z) where Z=(x-mu/sigma)

How many outcomes can a Bernoulli Trial have?

2

If a random variable, X, measuring the number of customers that enter a bank is assumed to be Poisson distributed, then the distribution of inter-arrival times to that bank is normal.

False The Poisson process is one of the most widely-used counting processes. It is usually used in scenarios where we are counting the occurrences of certain events that appear to happen at a certain rate, but completely at random (without a certain structure). For example, suppose that from historical data, we know that earthquakes occur in a certain area with a rate of 22 per month. Other than this information, the timings of earthquakes seem to be completely random

Which of the following is not true? If S is the sample space, then the P(S) = 0 Probabilities are numbers in the [0,1] interval. A continuous random variable is one with an interval of real numbers for its range. A discrete sample space can be made up of a finite set of outcomes. All of these options are not true.

If S is the sample space, then the P(S) = 0 The set of all possible outcomes of a random experiment is called the sample space and is denoted by the letter 𝑆.

The residuals from a linear regression model can be used to check the underlying assumptions and to investigate model adequacy.

True