The 68-95-99.7 rule applies:
Only to the standard normal distribution.
To any normal distribution
To any probability distribution
None of these answers is correct
Mark the correct statement:
The standard normal distribution has a population mean of 0, a standard deviation of 1 and a variance of 1.
Any normal distribution has a population mean of 0, a standard deviation of 1 and a variance of 1.
The standard normal distribution is a family of different distributions depending on the mean and the dispersion of data.
None of the answers is correct.
Imagine a variable X with population mean of 0 and a variance of 1. What is the probability that the sample mean is between -3 and 3?
We do not know because we have to standardize.
99.7%
68%
95%
Which of the following statements is true regarding the standard error of the mean?
It is equal to the population standard deviation divided by the sample size n.
It is equal to the population standard deviation divided by the square root of n.
It is equal to the population variance divided by the square root of n.
It is equal to the population variance divided by n -1.
If all possible random samples of size n are taken from a population, and the mean of each sample is determined, what can you say about the mean of the sample means?
It is larger than the population mean.
It is smaller than the population mean.
It is exactly the same as the population mean.
None of the above.
If a random sample of size n is drawn from a normal population, then the sampling distribution of sample means will be:
normal for all values of n.
normal only for n > 30.
approximately normal for all values of n.
approximately normal only for n > 30.
Imagine a variable X with population mean of 0 and a variance of 1. What is the probability that the sample mean is between -1 and 1?
Unbiassedness is:
A desirable property of point estimators according to which the expected value of the statistic equals the parameter.
A desirable property of point estimators according to which the bias decreases when the sample size increases.
A desirable property of point estimators according to which the estimator has the smallest variance possible.
In inferrential statistics the estimator:
Provides an approximate value for the population parameter which we call estimate
Is a random variable (not a unique value) with which we estimate population caracteristics
I the random variable from which we find point estimates (by using a unique sample).
All of the above are correct
A hypothesis test:
Tests a statement regarding a parameter (which we place in the null hypothesis) based on the sample data
Tests a statement regarding a statistic (which we place in the alternative hypothesis) based on the sample data
Tests a statement regarding a parameter (which we place in the alternative hypothesis) based on the sample data
Tests a statement regarding a statistic (which we place in the null hypothesis) based on the sample data
In a significance test, the null hypothesis:
Always contains the equality sign
Corresponds to the statement complementary (contrary) to the problem being explored
May never be accepted (we, at most, fail to reject it)
All of the answers are correct
In a significance test, the alternative hypothesis:
Does not contain the equality sign
Whenever we reject the null hypothesis, it means:
We cannot make any conclusion regarding the alternative hypothesis.
We find support for the alternative hypothesis
We fail to find support for the alternative hypothesis
We accept the null hypothesis
β is
the probability associated to rejecting the null hypothesis when it is true (error type I)
the probability associated to not rejecting the null hypothesis when it is true (error type II)
the probability associated to not rejecting the null hypothesis when it is false (error type II)
the probability associated to not rejecting the null hypothesis when it is true (error type I)
If we are conducting a 2-tailed significance test for the mean (we want to test whether the mean is different from 2) and the critical value (for a 95% confidence level) is 2 whereas the standardized sample mean is 3.
We cannot reject the null hypothesis. That is, the population mean is significantly different from 2 at a 95% confidence level.
We reject the alternative hypothesis. That is, the population mean is significantly different from 2 at a 95% confidence level.
We reject the null hypothesis. That is, the population mean is significantly different from 2 at a 95% confidence level.
We cannot reject the null hypothesis. That is, the population mean is not significantly different from 2 at a 95% confidence level.
If we are conducting a 2-tailed significance test for the mean (we want to test whether the mean is different from 2) and the critical value (for a 95% confidence level) is 3 whereas the standardized sample mean is 2.
α is:
The following hypothesis: μ = 4
Can either be a null or an alternative hypotesis in a significance test
Cannot be a hypothesis of a significance test
Can only be an alternative hypothesis in a significance test
Can only be a null hypothesis in a significance test
If we are conducting a 1-tailed significance test for the mean (we want to test whether the mean is different from 2) and the p-value (for a 95% confidence level) is 0.027.
If we have conducted a one-tailed two-means test where we want to find if the average number of educated employees is larger in Company A than in Company B and we find that the critical value is 1,96 (at a 95% confidence level) and the standardized difference in means value is 1, we conclude that:
The test can indicate which company has a significantly larger proportion of educated employees at a 95% confidence level.
The average number of educated employees is significantly larger in Company A than in Company B at a 95% confidence level.
There is a significant difference between the average number of educated employees in Company B and in Company A at a 95% confidence level.
The average number of educated employees is not significantly larger in Company A than in Company B at a 95% confidence level.
If we have conducted a one-tailed two-proportions test where we want to find if the proportion of educated employees is larger in Company A than in Company B and we find that the critical value is 1,96 (at a 95% confidence level) and the standardized difference in proportions is 3, we conclude that:
The proportion of educated employees is significantly larger in Company B than in Company A at a 95% confidence level.
There is no significant difference between the proportion of educated employees in Company B and in Company A at a 95% confidence level.
The test cannot indicate which company has a significantly larger proportion of educated employees at a 95% confidence level.
The proportion of educated employees is significantly larger in Company A than in Company B at a 95% confidence level.
If we want to test whether the average grade of a Group of students increase when we compare grades at the beginning of the course and at the end, we have to conduct a:
One tailed paired-samples two-means test
One tailed independent samples two-means test
Two tailed independent samples two-means test
Two tailed paired-samples two-means test
If we want to test whether the average grade of Group 1 is larger than the average Grade of Group 2, we will have to conduct a:
Two two tailed independent samples two-means test
The test can indicate which company has a significantly larger proportion of educated employees at a 95% confidence level
In an Independence Chi-squared test, when the critical value is smaller than the chi-squared statistic that we compute from our cross-tabulation we conclude:
There is some significant association between the two variables that we have cross-tabulated.
We would need to know the expected distribution to take a conclusion.
There is no significant association between the two variables that we have cross-tabulated.
We cannot conclude whether the variables are significantly associated or not.
If we want to see whether a particular categorical variable with more than 2 categories follows an expected distribution, we will generally conduct:
There is no test appropriate for this kind of problem
An independence Chi-squared test
An association test using the Chi-squared distribution
A goodness-of-fit chi-squared test
In an Independence Chi-squared test, when the critical value is larger than the chi-squared statistic that we compute from our cross-tabulation we conclude:
We cannot reject that the two variables that we have cross-tabulated are independent.
The two variables that we have cross-tabulated need to be not associated at any level.
There is a significant association between the two variables that we have cross-tabulated.
If we want to test whether the percentage of women in Group 1 is bigger than in Group 2 we will have to conduct:
A one tailed two proportions test
A two tailed two proportions test
A one tailed paired-samples two means test
A two tailed paired-samples two means test
