MCQs Introduction to Statistics 21

The post is about MCQs introduction to Statistics. There are 20 multiple-choice questions in this quiz related to data, variables, measures of central tendencies, measures of dispersions, level of measurements, and measures of positions. Let us start with the MCQs Introduction to Statistics Quiz.

Online Multiple-Choice Questions Quiz about Introduction to Statistics with Answers

1. Ten students completed an exam. Their scores were: 5, 7, 2, 1, 3, 4, 8, 8, 6, 6. What is the interquartile range (IQR)?

 
 
 
 

2. A sample mean is unbiased.

 
 

3. A population mean estimates a sample mean.

 
 

4. A sample mean is a center of mass of what?

 
 
 
 

5. When you detect a value in your data set that is vastly different from other observations in the same data set, what would you report that as?

 
 
 
 

6. How many goals have the top strikers in a football competition scored? For the following 10 strikers, the information obtained is: 12, 10, 11, 12, 11, 14, 15, 18, 21, 11. The (1) ———— of the dataset equals 12, the mean equals (2) ———–, and the (3) ————– equals 11. The standard deviation equals (4) ———— Fill in the right words/numbers.

 
 
 
 

7. The grades for a statistics exam are as follows: 3, 5, 5, 6, 7.5, 6, 5, 1, 10, 4. Which score is an outlier? Use the interquartile range (IQR).

 
 
 
 

8. A researcher wants to measure physical height in as much detail as possible. Which level of measurement does s/he employ?

 
 
 
 

9. What is true about a variance of zero?

 
 
 
 

10. Suppose a researcher conducted a study on eye color and 550 people are questioned about it. 110 of them have brown eyes and 44% of them have blue eyes. What percentage of the people you questioned have blue or brown eyes?

 
 
 
 

11. Which of the following statements is true?
I. The larger the variance, the smaller the standard deviation.
II. The stronger the skew, the smaller the difference between the median and the mean.

 
 
 
 

12. The extent to which values are dispersed around central observation is considered as

 
 
 
 

13. A population mean is a center of mass of what?

 
 
 
 

14. If a Curve has a longer tail to the right, it is called

 
 
 
 

15. Data obtained from an organization’s internal CRM, HR, and workflow applications is classified as:

 
 
 
 

16. The more data that goes into the sample mean, the more concentrated its density/mass function is around the population mean.

 
 

17. What type of data refers to information obtained directly from the source?

 
 
 
 

18. The height of a student is 60 inches. This is an example of ——————?

 
 
 
 

19. A researcher wants to know what people think of football. He asks ten people to rate their attitude towards football on a scale from 0 (do not like football at all) to 10 (like football a lot). The ratings from ten people are as follows: 1, 10, 6, 9, 2, 5, 6, 6, 5, 10. What is the standard deviation?

 
 
 
 

20. What is the difference between variables and constants?

 
 
 
 

Online MCQs Introduction to Statistics

  • A researcher wants to measure physical height in as much detail as possible. Which level of measurement does s/he employ?
  • Suppose a researcher conducted a study on eye color and 550 people are questioned about it. 110 of them have brown eyes and 44% of them have blue eyes. What percentage of the people you questioned have blue or brown eyes?
  • Ten students completed an exam. Their scores were: 5, 7, 2, 1, 3, 4, 8, 8, 6, 6. What is the interquartile range (IQR)?
  • A researcher wants to know what people think of football. He asks ten people to rate their attitude towards football on a scale from 0 (do not like football at all) to 10 (like football a lot). The ratings from ten people are as follows: 1, 10, 6, 9, 2, 5, 6, 6, 5, 10. What is the standard deviation?
  • Which of the following statements is true? I. The larger the variance, the smaller the standard deviation. II. The stronger the skew, the smaller the difference between the median and the mean.
  • The grades for a statistics exam are as follows: 3, 5, 5, 6, 7.5, 6, 5, 1, 10, 4. Which score is an outlier? Use the interquartile range (IQR).
  • How many goals have the top strikers in a football competition scored? For the following 10 strikers, the information obtained is: 12, 10, 11, 12, 11, 14, 15, 18, 21, 11. The (1) ———— of the dataset equals 12, the mean equals (2) ———–, and the (3) ————– equals 11. The standard deviation equals (4) ———— Fill in the right words/numbers.
  • What is true about a variance of zero?
  • What is the difference between variables and constants?
  • A population mean is a center of mass of what?
  • A sample mean is a center of mass of what?
  • A population mean estimates a sample mean.
  • A sample mean is unbiased.
  • The more data that goes into the sample mean, the more concentrated its density/mass function is around the population mean.
  • What type of data refers to information obtained directly from the source?
  • Data obtained from an organization’s internal CRM, HR, and workflow applications is classified as:
  • When you detect a value in your data set that is vastly different from other observations in the same data set, what would you report that as?
  • The height of a student is 60 inches. This is an example of ——————?
  • If a Curve has a longer tail to the right, it is called
  • The extent to which values are dispersed around central observation is considered as
MCQs Introduction to Statistics with Answers

Computer MCQs Online Test

Elementary Statistics Quiz 20

This Statistics Test is about MCQs Basic Elementary Statistics Quiz with Answers. There are 20 multiple-choice questions from Basics of Statistics, measures of central tendency, measures of dispersion, Measures of Position, and Distribution of Data. Let us start with the MCQS Basic Elementary Statistics Quiz with Answers

Please go to Elementary Statistics Quiz 20 to view the test

Elementary Statistics Quiz with Answers

  • What is the 25th percentile of the following data set; 1, 3, 3, 4, 5, 6, 6, 7, 8, 8
  • Which of the following is a measure of variability?
  • Which of the following measures of central tendency will always change if a single value in the data changes?
  • Which data sets have a mean of 10 and a standard deviation of 0?
  • What is meta data?
  • Which of the following is an example of categorical data?
  • The median represents a value in the data set where:
  • If the variance of a dataset is correctly computed with the formula using ($n – 1$) in the denominator, which of the following options is true?
  • Which of the following is NOT a descriptive statistic?
  • What is one of the common measures of Central Tendency?
  • What is a branch of mathematics dealing with the collection, analysis, interpretation, and presentation of numerical or quantitative data?
  • When you are calculating the middle value of a data field in a data set, actually, what are you calculating?
  • What is the general tendency of a set of data to change over time called?
  • The interquartile range (IQR) is which of the following?
  • Which dispersion is used to compare the variation of two series?
  • Which of the following is written at the top of the table?
  • The formula of mid-range is
  • Which one of the following is not included in measures of central tendency?
  • For the data 2, 3, 7, 0, -8. The Geometric mean will be
  • Under which of the following conditions would the standard deviation assume a negative value?
Basic Elementary Statistics Quiz with Answers

MCQs in Statistics

MCQs General Knowledge

Testing Population Proportion

Testing population proportion is a hypothesis testing procedure used to assess whether or not a sample from a population represents the true proportion of the entire population. Testing a sample population proportion is a widely used statistical method with various applications across different fields.

Purpose of Testing Population Proportion (one-sample)

The main purpose of testing a sample population proportion is to make inferences about an entire population based on the sample information. Testing a sample population proportion helps to determine whether an observed sample proportion is significantly different from a hypothesized population proportion.

Common Uses of Testing Population Proportion

The following are some common uses of population proportion:

  • Marketing research: To determine if a certain proportion of customers prefer one product compared to another.
  • Quality control: In manufacturing, population proportion tests can be used to test/check if the proportion of defective items in a production batch exceeds an acceptable threshold.
  • Medical research: To test the efficacy of a new treatment by comparing the proportion of patients who recover using the new treatment versus a standard treatment.
  • Political polling: To estimate the proportion of voters supporting a particular candidate or policy.
  • Social sciences: To examine the prevalence of certain behaviors or attitudes in a population.

Applications Population Proportion in Various Fields

  • Business: Testing customer satisfaction rates, conversion rates in A/B testing for websites, or employee retention rates.
  • Public health: Estimating vaccination rates, disease prevalence, or the effectiveness of public health campaigns.
  • Education: Assessing the proportion of students meeting certain academic standards or the effectiveness of new teaching methods.
  • Psychology: Evaluating the proportion of individuals exhibiting certain behaviors or responses in experiments.
  • Environmental science: Measuring the proportion of samples that exceed pollution thresholds.

Types of Testing Population Proportion

There are two types of population proportion tests.

  1. One-sample z-test for proportion: One-sample proportion tests are used when comparing a sample proportion to a known or hypothesized population proportion.
  2. Two-sample z-test for proportions: Two-sample proportion tests are used when comparing proportions from two independent samples.

Assumptions and Considerations

The following are assumptions and considerations when testing population proportion:

  • The sample should be randomly selected and representative of the population.
  • The sample size (number of observations in the sample) should be large enough (typically $np$ and $n(1-p)$ should both be greater than 5, where $n$ is the sample size and $p$ is the proportion).
  • For two-sample tests, the samples should be independent of each other.
  • Interpretation: The results of these tests are typically interpreted using p-values or confidence intervals, allowing researchers to make statistical inferences about the population based on the sample data.

Data Frive Decisions from Proportion Tests

By using tests for population proportions, researchers and professionals can make data-driven decisions, validate hypotheses, and gain insights into population characteristics across a wide range of fields and applications.

Suppose, a random sample is drawn and the population proportion (say) $\hat{p}$ is measured and $n\hat{p}\ge 5$, $n\hat{q}\ge5$, the distribution of $\hat{p}$ is approximately normal with $\mu_{\hat{p}} =p$ and $\sigma_{\hat{p}}=\sqrt{\frac{pq}{n}}$. Also, suppose that one of the possible null hypotheses of the following form, when testing a claim about a population proportion is:

$H_o: p=p_o$
$H_o:p\ge p_o$
$H_o\le p_o$

For simplicity, we will assume the null hypothesis $H_o:p=p_o$. The standardized test statistics for a one-sample proportion test is

\begin{align*}
Z&=\frac{\hat{p} – \mu_{\hat{p}}}{\sigma_{\hat{p}}}\\
&=\frac{\hat{p} -p_o }{\sqrt{\frac{p_oq_o}{n}}}
\end{align*}

This random variable will have a standard normal distribution. Therefore, the standard normal distribution will be used to compute critical values, regions of rejection, and p-values, as we use it to test a mean using a large sample.

Testing Population Proportion

Example 1 (Defective Items): Testing Population Proportion

A computer chip manufacturer tests microprocessors coming off the production line. In one sample of 577 processors, 37 were found to be defective. The company wants to claim that the proportion of defective processors is only 4%. Can the company claim be rejected at the $\alpha = 0.01$ level of significance?

Solution:

The null and alternative hypotheses for testing the one-sample population proportion will be

$H_o:p=0.04$
$H_1:p\ne 0.04$

By focusing on the alternative hypothesis symbol ($\ne$), the test is two-tailed with $p_o=0.04$.

The $\hat{p} = \frac{37}{577} \approx 0.064$.

the standardized test statistics is

\begin{align*}
Z &= \frac{\hat{p} – p_o}{\sqrt{\frac{p_oq_o}{n}}}\\
&=\frac{0.064 – 0.04}{\sqrt{\frac{(0.04)(0.96)}{577}}}\\
&=\frac{0.024}{0.008}\approx 3.0
\end{align*}

Looking up $Z=3.00$ in the standard normal table (area under the standard normal curve), we get a value of 0.9987. Therefore, $P(Z\ge 3.00) = 1-0.9987) = 0.0013$.
Note that the test is two-tailed, the p-value will be twice this amount or $0.0026$.

Since the p-value ($0.0026$) is less than the level of significance ($0.01$), that is $0.0025 < 0.01$ (p-value < level of significance), we will reject the company’s claim. It means that the proportion of defective processors is not 4%, it is either less than 4% or more than 4%.

Example 2 (Opinion Poll): Testing Population Proportion

An opinion poll of 1010 randomly chosen/selected adults finds that only 47% approve of the president’s job performance. The president’s political advisors want to know if this is sufficient data to show that less than half of adults approve of the president’s job performance using a 5% level of significance.

Solution:

The null and alternative hypothesis of the problem above will be

$H_o:p\ge 0.50$
$H_1:p< 0.50$

By focusing on the alternative hypothesis symbol (<), the test is left-tailed with $p_o=0.50$.

The $\hat{p} = 0.47$. The standardized test statistics for one-sample population proportion will be

\begin{align*}
Z &= \frac{\hat{p} – p_o}{\sqrt{\frac{p_oq_o}{n}}}\\
&=\frac{0.47 – 0.50}{\sqrt{\frac{(0.5)(0.5)}{1010}}}\\
&=\frac{-0.03}{0.01573}\approx -1.91
\end{align*}

For a left-tailed test (for $\alpha = 0.05$), the $Z_o=-1.645$. Since $-1.91 < -1.645$, the null hypothesis should be rejected. So the data does support the claim that $p<0.50$ at the $\alpha=0.05$ level of significance.

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