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