QMB 3200 final practice

The mean of the sampling distribution of is always equal to the mean of the sampled population.

true

The correlation coefficient may assume any value between

-1 and 1

If all data points fell on a straight line, SSE would equal _____ and r would equal _____.

0, -1, or 1

If the random variable of x is normally distributed, 68.26% of all possible observed values of x will be within two standard deviations of the mean.

FALSE

Alpha (α) is the probability that the test statistic would assume a value as or more extreme than the observed value of the test.

False

Everything else being constant, increasing the sample size decreases the probability of committing a Type II error.

False

The point estimate of the variance in a regression model is

MSE

If we are testing the difference between the means of two normally distributed populations with samples of n1 = 10, n2 = 10, the degrees of freedom for the t statistic is ____.

18

If we are testing the hypothesis about the mean of a population of paired differences with samples of n1 = 10, n2 = 10, the degrees of freedom for the t statistic is ____.

9

Which of the following statements is not a property of the normal probability distribution?

95.44% of all possible observed values of the random variable x are within plus or minus three standard deviation of the population mean.

In testing for the equality of means from two independent populations, if the null hypothesis is rejected, the test could result in:

A Type I error.

If a two-sided null hypothesis is rejected for a single mean at a given significance level, the corresponding one- sided null hypothesis (i.e., the same sample size, the same standard deviation, and the same mean) will_________ be rejected at the same significance level.

Always

Which of the following is a violation of one of the major assumptions of the simple regression model?

As the value of x increases, the value of the error term also increases.

Another name(s) for the normal distribution is (are.

Bell Shapes and Gaussian

A students grade on an examination was transformed to a z value which is negative. Therefore, we know that he scored.

Below the mean

The ----------- distribution would most likely be used to describe the distribution of time between arrivals of customers at the grocery store.

Exponential

First a 90% confidence interval is constructed from a sample size of 100. Then, for the same identical data, a 92% confidence interval is constructed. The width of the 90% interval is wider than the 92% confidence interval.

False

In a simple linear regression model, the coefficient of determination not only indicates the strength of the relationship between independent and dependent variable, but also shows whether the relationship is positive or negative.

False

The correlation coefficient is the ratio of explained variation to total variation.

False

The null hypothesis always includes an equal (=) sign.

False

The null hypothesis is a statement that will be accepted only if there is convincing sample evidence that it is true.

False

The number of defective pencils in a lot of 1000 is an example of a continuous random variable.

False

The power of a statistical test is the probability of rejecting the null hypothesis when it is true.

False

The standard deviation of all possible sample proportions increases as the sample size increases.

False

There are two types of machines called type A and type B. Both type A and type B can be used to produce a certain product. The production manager wants to compare efficiency of the two machines. He assigns each of the fifteen workers to both types of machines to compare the hourly production rate of the 15 workers. In other words, each worker operates machine A and machine B for one hour each. These two samples are independent.

False

When comparing two independent population means by using large samples selected from populations with equal variances, the correct test statistic to use is t.

False

When comparing two independent population means, if n1 = 13 and n2 = 10, degrees of freedom for the t statistic is 22.

False

When conducting a hypothesis test about a single mean, other relevant factors held constant, increasing the level of significance from .05 to .10 will reduce the probability of a Type I error.

False

When the level of confidence and the sample size remain the same, a confidence interval for a population mean μ will be wider, when the sample standard deviation σ is small than when σ is large.

False

When the null hypothesis is true, there is no possibility of making a Type I error.

False

When using simple regression analysis, if there is a strong correlation between the independent and dependent variable, then we can conclude that an increase in the value of the independent variable causes an increase in the value of the dependent variable.

False

All continuous random variables are normally distributed.

False.

When carrying out a large sample test of H0: µ = 10 vs. Ha: µ > 10 by using a rejection point, we reject H0 at level of significance α when the calculated test statistic is:

Greater then Za

The average customer waiting time at a fast food restaurant has been 7.5 minutes. The customer waiting time has a normal distribution. The manager claims that the use of a new system will decrease average customer waiting time in the store. What is the null and alternative hypothesis for this scenario?

H0:µ ≥ 7.5 and HA < 7.5

A random variable is said to be discrete if:

Its outcome are countable

For the following hypothesis test where H0: µ ≤ 10 vs. Ha: µ > 10, we reject H0 at level of significance α and conclude that the true mean is greater than 10 when the true mean is really 14. Based on this information we can state that we have:

Made a correct decision

For the following hypothesis test where H0: ≤ 10 vs. Ha: > 10, we reject H0 at level of significance ? and conclude that the true mean is greater than 10 when the true mean is really 8. Based on this information we can state that we have:

Made a type 1 error

In order to test the effectiveness of a drug called XZR designed to reduce cholesterol levels, 9 heart patients' cholesterol levels are measured before they are given the drug. The same 9 patients use XZR for two continuous months. After two months of continuous use the 9 patients' cholesterol levels are measured again. The comparison of cholesterol levels before vs. after administering the drug is an example of testing the difference between:

Matched pairs from two dependent populations.

When using simple linear regression, we would like to use confidence intervals for the _____ and prediction intervals for the _____ at a given value of x.

Mean y-value, individual y-value

When the level of confidence and sample standard deviation remain the same, a confidence interval for a population mean based on a sample of n = 100 will be ______________ a confidence interval for a population mean based on a sample of n = 50.

Narrower than

If a one-sided null hypothesis for a single mean cannot be rejected at a given significance level, then the corresponding two-sided null hypothesis (i.e., the same sample size, the same standard deviation, and the same mean) will_________ be rejected at the same significance level.

Never

The normal approximation of the binomial distribution is appropriate when.

Np> 5 and n(1-p) >5

The simple linear regression ( least squares method) minimizes

SSE

A confidence interval increases in width as

The level of confidence increases, n decreases, s increases

The exact spread of the t-distribution depends on ________.

The number of degrees of freedom

The relationship between the standard normal random variable Z and normal random variable X is that:

The standard normal variable Z counts the number of standard deviations that the value of the normal random variable X is away from its mean

The relationship between the standard normal random variable Z and normal random variable X is that:

The standard normal variable Z counts the number of standard deviations that the value of the normal random variable X is away from its mean.

A continuous probability distribution having a rectangular shape where the probability is evenly distributed over an interval of numbers is called a uniform probability distribution.

True

As the level of significance α increases, we are more likely to reject the null hypothesis.

True

Everything else being constant, increasing the sample size decreases the probability of committing a Type II error.

True

For a binomial probability experiment, with n=150 and p=.2, it is appropriate to use the normal approximation to the binomial distribution.

True

If r = -1, then we can conclude that there is a perfect relationship between X and Y.

True

The actual weight of hamburger patties is an example of a continuous random variable.

True

The error term is the difference between an individual value of the dependent variable and the corresponding mean value of the dependent variable.

True

The estimated simple linear regression equation minimizes the sum of the squared deviations between each value of Y and the line.

True

The sampling distribution of the sample mean is developed by repeatedly taking samples of size n and computing the sample means and reporting the resulting sample means in the form of a probability distribution.

True

The slope of the simple linear regression equation represents the average change in the value of the dependent variable per unit change in the independent variable (X).

True

The standard deviation of a standard normal distribution is always equal to 1.

True

The z value tells us the number standard deviations that a value x is from the mean.

True

When the null hypothesis is not rejected, there is no possibility of making a Type I error.

True

In testing for the equality of means from two independent populations, if the null hypothesis is false, the test could result in:

Type 2 error

When conducting a hypothesis test about a single mean, at a given level of significance, as the sample size n increases, the power of the test:

Will Increase

A standard normal distribution has a mean of ---------- and standard deviation of --------.

ZERO, ONE.

In a simple linear regression analysis, the correlation coefficient (a) and the slope (b) _____ have the same sign.

always

The mean of a standard normal distribution is always equal to 1.

false

In simple regression analysis the quantity that gives the amount by which Y (dependent variable) changes for a unit change in X (independent variable) is called the

slope in the regression line

For the same value X (independent variable), the confidence interval for the average value of Y (dependent variable) is __________________ the prediction interval for the individual value of Y.

smaller than

When the population is normally distributed, population standard deviation σ is unknown, and the sample size is n = 15; the confidence interval for the population mean µ is based on:

the T distribution