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STATISTICS 1

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Quiz on STATISTICS 1, created by raquel galindo on 07/06/2016.
raquel galindo
Quiz by raquel galindo, updated more than 1 year ago
raquel galindo
Created by raquel galindo almost 8 years ago
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Question 1

Question
The 68-95-99.7 rule applies:
Answer
  • Only to the standard normal distribution.
  • To any normal distribution
  • To any probability distribution
  • None of these answers is correct

Question 2

Question
Mark the correct statement:
Answer
  • 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.

Question 3

Question
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?
Answer
  • We do not know because we have to standardize.
  • 99.7%
  • 68%
  • 95%

Question 4

Question
Which of the following statements is true regarding the standard error of the mean?
Answer
  • 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.

Question 5

Question
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?
Answer
  • 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.

Question 6

Question
If a random sample of size n is drawn from a normal population, then the sampling distribution of sample means will be:
Answer
  • normal for all values of n.
  • normal only for n > 30.
  • approximately normal for all values of n.
  • approximately normal only for n > 30.

Question 7

Question
Which of the following statements is true regarding the standard error of the mean?
Answer
  • 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.

Question 8

Question
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?
Answer
  • 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.

Question 9

Question
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?
Answer
  • 99.7%
  • 95%
  • We do not know because we have to standardize.
  • 68%

Question 10

Question
Unbiassedness is:
Answer
  • 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.
  • None of the answers is correct.

Question 11

Question
In inferrential statistics the estimator:
Answer
  • 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

Question 12

Question
A hypothesis test:
Answer
  • 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

Question 13

Question
In a significance test, the null hypothesis:
Answer
  • 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

Question 14

Question
In a significance test, the alternative hypothesis:
Answer
  • Does not contain 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

Question 15

Question
Whenever we reject the null hypothesis, it means:
Answer
  • 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

Question 16

Question
β is
Answer
  • 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)

Question 17

Question
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.
Answer
  • 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.

Question 18

Question
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.
Answer
  • We cannot reject the null hypothesis. That is, the population mean is not 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 significantly different from 2 at a 95% confidence level.

Question 19

Question
α is:
Answer
  • 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 false (error type II)
  • 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 true (error type I)

Question 20

Question
The following hypothesis: μ = 4
Answer
  • 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

Question 21

Question
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.
Answer
  • We cannot reject the null hypothesis. That is, the population mean is not significantly different from 2 at a 95% confidence level.
  • 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.

Question 22

Question
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:
Answer
  • 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.

Question 23

Question
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:
Answer
  • 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.

Question 24

Question
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:
Answer
  • 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

Question 25

Question
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:
Answer
  • One tailed paired-samples two-means test
  • Two two tailed independent samples two-means test
  • One tailed independent samples two-means test
  • Two tailed paired-samples two-means test

Question 26

Question
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:
Answer
  • The average number of educated employees is not significantly larger in Company A than in Company B 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.
  • The test can indicate which company has a significantly larger proportion of educated employees 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.

Question 27

Question
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:
Answer
  • 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.

Question 28

Question
If we want to see whether a particular categorical variable with more than 2 categories follows an expected distribution, we will generally conduct:
Answer
  • 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

Question 29

Question
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:
Answer
  • We cannot conclude whether the variables are significantly associated or not.
  • 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.

Question 30

Question
If we want to test whether the percentage of women in Group 1 is bigger than in Group 2 we will have to conduct:
Answer
  • 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
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