Muhammad Imdad Ullah

Currently working as Assistant Professor of Statistics in Ghazi University, Dera Ghazi Khan. Completed my Ph.D. in Statistics from the Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan. l like Applied Statistics, Mathematics, and Statistical Computing. Statistical and Mathematical software used is SAS, STATA, Python, GRETL, EVIEWS, R, SPSS, VBA in MS-Excel. Like to use type-setting LaTeX for composing Articles, thesis, etc.

Important Testing of Hypothesis MCQs 8

by

The quiz is about Testing of Hypothesis MCQs with Answers. The quiz contains 20 questions about hypothesis testing. It covers the topics of formulation of the null and alternative hypotheses, level of significance, test statistics, region of rejection, and decision about acceptance and rejection of the hypothesis. Let us start with the Testing of Hypothesis MCQs quiz.

Online multiple choice questions about Testing of Hypothesis with Answers

1. What determines how close the computed sample statistic has come to the hypothesized population parameter?

 
 
 
 

2. What is the region of rejection for a one-tail Z test?

 
 
 
 

3. If the p-value is greater than alpha in a two-tail test, what conclusion should you draw?

 
 
 
 

4. Which of the following does not need to be known to compute the P-value?

 
 
 
 

5. A hypothesis test in which rejection of the null hypothesis occurs for values of the point estimator in either tail of the sampling distribution is called

 
 
 
 

6. For finding the p-value when the population standard deviation is unknown, if it is reasonable to assume that the population is normal, we use

 
 
 
 

7. If you reject a true null hypothesis, what does this mean?

 
 
 
 

8. When the null hypothesis has been true, but the sample information has resulted in the rejection of the null, a ———- has been made.

 
 
 
 

9. Which of the following statements is false?

 
 
 
 

10. A Type II error is the error of

 
 
 
 

11. The maximum probability of a Type I error that the decision-maker will tolerate is called the

 
 
 
 

12. When testing the following hypotheses at a level of significance

$H_o: p \le 0.7$

$H_a: p > 0.7$

The null hypothesis will be rejected if the test statistic $Z$ is

 
 
 
 

13. How do you commit a Type II error?

 
 
 
 

14. If a one-tail Z test for a proportion is performed and the upper critical value is +2.33 and the test statistic is equal to +1.37, then what conclusion can you draw?

 
 
 
 

15. If the p-value is less than alpha in a one-tail test, what conclusion can you draw?

 
 
 
 

16. In a hypothesis test, the probability of obtaining a value of the test statistic equal to or even more extreme than the value observed, given that the null hypothesis is true, is referred to as what?

 
 
 
 

17. In hypothesis testing, the hypothesis which is tentatively assumed to be true is called the

 
 
 
 

18. In hypothesis testing, $\beta$ is

 
 
 
 

19. What test should a researcher use to determine whether there is evidence that the mean family income in the U.S. is greater than $30,000?

 
 
 
 

20. In hypothesis testing, the level of significance is

 
 
 
 

Testing of Hypothesis MCQs with Answers

Hypothesis Testing procedure
  • In hypothesis testing, the hypothesis which is tentatively assumed to be true is called the
  • When the null hypothesis has been true, but the sample information has resulted in the rejection of the null, a ———- has been made.
  • The maximum probability of a Type I error that the decision-maker will tolerate is called the
  • A Type II error is the error of
  • In hypothesis testing, the level of significance is
  • For finding the p-value when the population standard deviation is unknown, if it is reasonable to assume that the population is normal, we use
  • In hypothesis testing, $\beta$ is
  • A hypothesis test in which rejection of the null hypothesis occurs for values of the point estimator in either tail of the sampling distribution is called
  • When testing the following hypotheses at a level of significance $H_o: p \le 0.7$ $H_a: p > 0.7$ The null hypothesis will be rejected if the test statistic $Z$ is
  • Which of the following does not need to be known to compute the P-value?
  • Which of the following statements is false?
  • If you reject a true null hypothesis, what does this mean?
  • How do you commit a Type II error?
  • What test should a researcher use to determine whether there is evidence that the mean family income in the U.S. is greater than $30,000?
  • In a hypothesis test, the probability of obtaining a value of the test statistic equal to or even more extreme than the value observed, given that the null hypothesis is true, is referred to as what?
  • If the p-value is greater than alpha in a two-tail test, what conclusion should you draw?
  • If the p-value is less than alpha in a one-tail test, what conclusion can you draw?
  • If a one-tail Z test for a proportion is performed and the upper critical value is +2.33 and the test statistic is equal to +1.37, then what conclusion can you draw?
  • What is the region of rejection for a one-tail Z test?
  • What determines how close the computed sample statistic has come to the hypothesized population parameter?
Testing of Hypothesis MCQs Quiz

https://rfaqs.com

https://gmstat.com

Index Number in Statistics: made easy

by

An index number in statistics is a tool used to track changes in a variable or a group of related variables, typically over time. Index Numbers condense the complex data into a single number (expressed as a percentage) for easier comparison between different periods or situations.

Example: A factory manager may wish to compare this month’s per-unit production cost with that of the past 6 months.

An index number measures how much a variable changes over time.

Simple Relatives Index Numbers

A simple relative is a ratio of the value of a variable in a given period to its value in the base (or reference) period.

If $x_0$ and $x_n$ are the values of a variable during the base period and a given period, respectively, then the simple relative, denoted by $x_{0n}$ is
$$x_{0n}=\frac{x_n}{x_0}$$

A relative is usually expressed as a percentage by multiplying by 100.

Simple Price Relative

If $p_0$ and $p_n$ are the prices of a commodity \texturdu{مفید شے، مال اسباب} during the base period and a given period, respectively, then the simple price relative, denoted by $p_{0n}$ is
$$p_{0n}=\frac{p_n}{p_0}$$
The price is generally defined as “money per unit quantity” and is usually taken as the average price for a period because the prices are not constant throughout a period.

Simple Quantity (Volume) Relative

If $q_0$ and $q_n$ are quantities of a commodity (produced, consumed, purchased, sold, exported, or imported, etc.) during the base period and a given period, respectively, then the simple quantity relative, denoted by $q_{0n}$ is
$$q_{0n}=\frac{q_n}{q_0}$$

Value

If $p$ is the price of a commodity and $q$ is its quantity during a period, then the value $v$ is given by $v=p\,q$. For example, if a quantity of 560kg of a commodity is purchased at the rate of Rs. 5 per Kg then
$$v=pq=5\times 560 = 2800$$

Simple Value Relative

If $v_0$ and $v_n$ are the values of a commodity during the base period and a given period, respectively, then the simple value relative, denoted by $v_{0n}$ is
$$v_{0n}=\frac{v_n}{v_0}=\frac{p_nq_n}{p_0q_0}=\frac{p_n}{q_n}\times \frac{q_n}{q_0}=p_{0n}\times q_{0n}$$

Index Number in Statistics

Uses of Index Number in Statistics

  • Functions: Measure changes in variables like prices, production levels, or stock values.
  • Benefits:
    • Simplifies complex data comparisons
    • Tracks trends over time
    • Provides a benchmark for analysis (often using a base period as a reference point at 100)
  • Examples:
    • Consumer Price Index (CPI) tracks inflation by measuring changes in the prices of a basket of goods and services.
    • Stock market indices like the S&P 500 track the overall performance of a specific stock market section.

Note that there are various types of index numbers used for different purposes. Computing the index numbers involves specific formulas and functions that take into account the chosen base period and the way different variables are weighted within the index.

https://itfeature.com Statistics and Data Analysis

https://gmstat.com

https://rfaqs.com

Describing Data Discover Story (2024)

by

Describing data effectively involves summarizing its key characteristics and highlighting interesting patterns or trends. Therefore, to extract information from the sample one needs to organize and summarize the collected data. The arrangement (organization) of data into a reduced form which is easy to understand, analyze, and interpret is known as the presentation of data.

Remember: our goal is to construct tables, charts, and graphs that will help to quickly reveal the concentration and shape of the data. Graphical Presentation of Data help in making wise decisions.

Visualizations: Describing Data Visually/ Graphically

Charts and graphs are powerful tools for showcasing data patterns and trends. In this article, we will discuss bar graphs and histograms only.

Describing Data Using Bar Graph

Bar diagrams can be used to get an impression of the distribution of a discrete or categorical data set. They can also be used to compare groups, and categories in explanatory data analysis (EDA) to illustrate the major features of the data distribution in a convenient form.

A graphical representation in which the discrete classes are reported on the horizontal axis and the class frequencies on the vertical axis and the class frequencies are proportional to the heights of the bars. It is a way of summarizing a set of categorical data.

Note that a distinguishing characteristic of a bar chart is that there is a distance or a gap between the bars i.e. the variable of interest is qualitative and the bars are not adjacent to each other. Thus a bar chart graphically describes a frequency table using a series of uniformly wide rectangles, where the height of each rectangle is the class frequency.

There are different versions of bar graphs such as clustered bar graphs, stacked bar graphs, horizontal bar graphs, and vertical bar graphs.

Describing Data: Bar Graphs

Describing Data in Histogram

A histogram is a similar graphical representation to bar graphs. It is used to summarize data that are quantitative i.e. measured on an interval or ratio scale (continuous). Histograms are constructed from the grouped data by taking class boundaries along the x-axis and the corresponding frequencies along the y-axis. The heights of the bars represent the class frequencies.

Note that the horizontal axis represents all possible values because the nature of data is quantitative which is usually measured using continuous scales, not discrete. That is why, histogram bars are drawn adjacent to each other to show the continuous nature of data. It is generally used for large data sets (having more than 100 observations) when stem and leaf plots become tedious to construct. A histogram can also help in detecting any unusual observations (outliers) or gaps in the data set.

Describing Data: Histogram

Data (in its raw form) is a collection of numbers, characters, or observations that might seem overwhelming or meaningless. Describing data is the crucial step in unlocking its potential. In essence, describing data is like laying the groundwork for a building. It provides a clear understanding of the data’s characteristics, empowers informed decision-making, and paves the way for further analysis to extract valuable insights.

MCQs Economics

R Frequently Asked Questions

Data View in SPSS (2024)

by

The IBM SPSS has two main windows (i) Data View and (ii) Variable View. Data View in SPSS is one of the primary ways of looking at a data file in Data View so that you can see each row as a source of data and each column as a variable. The data view in SPSS is the most useful way to look at the actual values of the data presented in the data set.

By default, SPSS launches in Data View mode.

Data View in SPSS

The following diagram of the SPSS workplace highlights the data view in SPSS and the variable view in SPSS.

Data View in SPSS

If you are not in Data View, click the Data View Tab to enter the data view and the data edit mode. Typically, one should enter the data after establishing the names and other properties of the variables in a data set. Many of the features of Data View are similar to the features that are found in spreadsheet-like applications (such as MS Excel). There are, however, several important distinctions:

SPSS Data view
  • Rows are cases: Each row in a data view represents a case or an observation. For example, each respondent to a questionnaire is a case.
  • Columns are variables: Each column represents a variable or characteristic being measured. For example, each item on a questionnaire is a variable.
  • Cells contain values. The cross-section of the row and column makes a cell. Each cell contains a single value of a variable for a case. The cell is where the case and the variable intersect. Cells contain only data values. Unlike spreadsheet programs, cells in the Data Editor cannot contain formulas.

In summary, the Data View in SPSS is the primary workspace for viewing, manipulating, and understanding the actual values in the dataset. It plays a vital role in data exploration, cleaning, and analysis.

Statistics Help: Itfeature.com

Simulating a Coin Tossing