EDUCBA

EDUCBA

MENUMENU
  • Free Tutorials
  • Free Courses
  • Certification Courses
  • 250+ Courses All in One Bundle
  • Login
Home Finance Finance Resources Finance Formula Z Test Statistics Formula
Secondary Sidebar
Finance Blog
  • Finance Formula
    • Skewness Formula
    • Fixed Asset Turnover Ratio Formula
    • Forecasting Formula
    • EBITDA Margin Formula
    • Accounting Ratio Formula
    • Deferred Annuity Formula
    • Capital Investment Formula
    • Ratio Analysis Formula
    • Loss Ratio Formula
    • Benefit-Cost Ratio Formula
    • Probability Distribution Formula
    • Cash Conversion Cycle Formula
    • Accrued Income
    • DCF Excel summary
    • Price to Earning Ratio Formula
    • Current Yield of Bond Formula
    • Earnings Per Share Formula
    • Manufacturing Overhead Formula
    • FCFF Formula
    • Predetermined Overhead Rate Formula
    • Times Interest Earned Ratio Formula
    • Bank Efficiency Ratio Formula
    • Capital Expenditure Formula
    • Expense Ratio Formula
    • WACC Formula
    • Activity Ratio Formula
    • Standard Error Formula
    • Forward Rate Formula
    • Gearing Formula
    • Prime Cost Formula
    • Productivity Formula
    • t-Test Formula
    • Risk Free Rate Formula
    • Tax Shield Formula
    • Sortino Ratio
    • Reserve Ratio Formula
    • Bond Formula
    • Annualized Rate of Return Formula
    • Conditional Probability Formula
    • Financing Formula
    • Future Value of an Annuity Formula
    • For Profit vs Non Profit
    • Deadweight Loss Formula
    • Inflation Formula
    • Amortized Loan Formula
    • Horizontal Analysis Formula
    • Marginal Utility Formula
    • Kurtosis Formula
    • Macaulay Duration Formula
    • Multiplier Formula
    • Modified Duration Formula
    • Operating Leverage Formula
    • Payout Ratio Formula
    • Statistics Formula
    • Sampling Error Formula
    • Trend Analysis Formula
    • Taylor Rule Formula
    • Put Call Parity Formula
    • Annual Return Formula
    • Discount Rate Formula
    • Cash Flow Formula
    • Dilution Formula
    • Attrition Formula
    • Operating Expense Formula
    • Interpolation Formula
    • Annuity Due Formula
    • Bond Yield Formula
    • Turnover Ratio Formula
    • Efficiency Formula
    • Revenue Per Employee
    • Regression Line Formula
    • Yield to Maturity
    • Pearson Correlation Coefficient Formula
    • Accounting Formula
    • Fiscal Deficit Formula
    • Tax Multiplier Formula
    • Efficiency Ratio Formula
    • Demand Elasticity Formula
    • Gross Margin Formula
    • Elasticity Formula
    • Marginal Benefit Formula
    • Depreciation Formula
    • Cost-Benefit Analysis Formula
    • Percentage Change Formula
    • Levered Beta Formula
    • Shares Outstanding Formula
    • Capital Gain Formula
    • Convexity Formula
    • Gross Income Formula
    • Net Exports Formula
    • Producer Surplus Formula
    • Accounting Rate of Return Formula
    • Net Cash Flow Formula
    • Labor Force Participation Rate Formula
    • Moving Average Formula
    • Net Worth Formula
    • Accounting Profit Formula
    • Disposable Income Formula
    • Discount Formula
    • Average Variable Cost Formula
    • Total Variable Cost Formula
    • Product Cost Formula
    • Marginal Product Formula
    • Break-Even Sales Formula
    • Return on Sales Formula
    • Cost of Goods Manufactured Formula
    • Average Fixed Cost Formula
    • Stock Turnover Ratio Formula
    • Operating Ratio Formula
    • Equity Ratio Formula
    • Net Present Value Formula
    • Aggregate Demand Formula
    • Volatility Formula
    • Marginal Product of Labor Formula
    • Z Test Statistics Formula
    • Standard Cost Formula
    • Velocity of Money Formula
    • Invested Capital Formula
    • Unlevered Beta Formula
    • Bank Reconciliation Formula
    • Portfolio Return Formula
    • Central Tendency Formula
    • Accumulated Depreciation Formula
    • Intrinsic Value Formula
    • Decile Formula
    • Vector Cross Product Formula
    • Effective Annual Rate Formula
    • CAGR Formula
    • Mode Formula
    • Arithmetic Mean Formula
    • Real GDP Formula
    • Gini Coefficient Formula
    • Expected Value Formula
    • Price Elasticity of Supply Formula
    • Net Operating Income Formula
    • Profit Percentage Formula
    • GDP Per Capita Formula
    • Altman Z Score
    • Quartile Deviation Formula
    • Return on Capital Employed Formula
    • Consumer Price Index Formula
    • Economic Profit Formula
    • Market Share Formula
    • Real Interest Rate Formula
    • Income Elasticity of Demand Formula
    • Income From Operations Formula
    • Indexation Formula
    • Sales Formula
    • Money Multiplier Formula
    • GDP Deflator Formula
    • Residual Income Formula
    • Effective Interest Rate Formula
    • Coupon Bond Formula
    • Current Account Formula
    • Total Cost Formula
    • Total Expense Ratio Formula
    • Net Sales Formula
    • Percentage Decrease Formula
    • Uncertainty Formula
    • Nominal GDP Formula
    • Effect Size Formula
    • Delta Formula
    • Cost of Sales Formula
    • Fixed Cost Formula
    • Unemployment Rate Formula
    • Present Value of Annuity Formula
    • Compounding Formula
    • Geometric Distribution Formula
    • National Income Formula
    • Accounts Receivables Turnover Formula
    • Integer Formula
    • Ending Inventory Formula
    • Owner's Equity Formula
    • Capacity Utilization Rate Formula
    • Interest Formula
    • Nominal Interest Rate Formula
    • Risk Premium Formula
    • Interest Coverage Ratio Formula
    • Gross Profit Margin Formula
    • Diluted EPS Formula
    • Return On Average Equity Formula
    • Return on Average Assets Formula
    • Working Capital Formula
    • Revenue Per Employee Ratio Formula
    • Capital Employed Formula
    • Rule of 72 Formula
    • Inventory Turnover Ratio Formula
    • Preferred Dividend Formula
    • Retention Ratio Formula
    • Present Value Factor Formula
    • Equity Multiplier Formula
    • Continuous Compounding Formula
    • Return on Assets (ROA) Formula
    • Portfolio Variance Formula
    • Weighted Average Formula
    • Net Working Capital Formula
    • Tax Equivalent Yield Formula
    • Poisson Distribution Formula
    • Current Ratio Formula
    • Debt Ratio Formula
    • Quick Ratio Formula
    • Payback Period Formula
    • Marginal Cost Formula
    • Debt to Income Ratio Formula
    • Book Value Per Share Formula
    • Asset Turnover Ratio Formula
    • Perpetuity Formula
    • Bid-Ask Spread Formula
    • Price to Book Value Formula
    • Capital Gains Yield Formula
    • Net Profit Margin Formula
    • DuPont Formula
    • Bond Pricing Formula
    • Binomial Distribution Formula
    • Sustainable Growth Rate Formula
    • Average Collection Period Formula
    • Net Income Formula
    • CAPM Formula
    • Cost of Goods Sold Formula
    • Economic Order Quantity (EOQ) Formula
    • Amortization Formula
    • Enterprise Value Formula
    • Beta Formula
    • Cost of Equity Formula
    • Rate of Return Formula
    • Revenue Formula
    • Markup Price Formula
    • Cash Flow from Operations Formula
    • Simple Interest Rate Formula
    • Consumer Surplus Formula
    • Asset to Sales Ratio Formula
    • Debt Service Coverage Ratio Formula
    • Capitalization Rate Formula
    • Cost of Debt Formula
    • Straight Line Depreciation Formula
    • Variable Costing Formula
    • Return on Invested Capital Formula
    • Profitability Index Formula
    • Expected Return Formula
    • Cost of Capital Formula
    • Price Index Formula
    • Average Total Cost Formula
    • Discount Factor Formula
    • Price Elasticity Formula
    • Profitability Ratios Formula
    • Financial Leverage Formula
    • Contribution Margin Formula
    • Time Value of Money Formula
    • Balance Sheet Formula
    • Opportunity Cost Formula
    • Current Assets Formula
    • Operating Cycle Formula
    • Operating Margin Formula
    • Bond Equivalent Yield Formula
    • Marginal Revenue Formula
    • Sales Revenue Formula
    • Net Debt Formula
    • Times Interest Earned Formula
    • Gordon Growth Model Formula
    • Required Rate of Return Formula
    • Break Even Analysis Formula
    • Inventory Formula
    • Marginal Propensity to Consume Formula
    • Debt to Asset Ratio Formula
    • Solvency Ratio Formula
    • Interest Expense Formula
    • Leverage Ratio Formula
    • Dividend Payout Ratio Formula
    • Operating Profit Margin Formula
    • PEG Ratio Formula
    • Net Interest Margin Formula
    • Return on Equity (ROE) Formula
    • Overhead Ratio Formula
    • Future Value Formula
    • Days in Inventory Formula
    • Market Capitalization Formula
    • Sharpe Ratio Formula
    • Cash Ratio Formula
    • Retained Earnings Formula
    • Average Rate of Return Formula
    • Current Liabilities Formula
    • Equity Value Formula
    • Relative Risk Reduction Formula
    • Capital Adequacy Ratio Formula
    • Debtor Days Formula
    • DPMO Formula
    • Average Formula
    • Exponential Growth Formula
    • Net Realizable Value Formula
    • Range Formula
    • Shareholders' Equity Formula
    • Sinking Fund Formula
    • Doubling Time Formula
    • Salvage Value Formula
    • Coupon Rate Formula
    • Simple Interest Formula
    • Correlation Formula
    • R - Squared Formula
    • MTBF Formula
    • Change in Net Working Capital Formula
    • Midrange Formula
    • Normal Distribution Formula
    • Mean Formula
    • Population Mean Formula
    • Median Formula
    • Central Limit Theorem Formula
    • Free Cash Flow Formula
    • Stockholder's Equity Formula
    • Acid-Test Ratio Formula
    • Percentile Rank Formula
    • Purchasing Power Parity Formula
    • Harmonic Mean Formula
    • Relative Standard Deviation Formula
    • T Distribution Formula
    • Normalization Formula
    • Operating Income Formula
    • Markup Percentage Formula
    • Relative Change Formula
    • Maturity Value Formula
    • Salary Formula
    • High Low Method
    • Income Statement Formula
    • Market to Book Ratio Formula
    • Dividends Per Share Formula
    • Daily Compound Interest Formula
    • Working Capital Turnover Ratio Formula
    • Weighted Mean Formula
    • Compounded Annual Growth Rate Formula
    • Regression Formula
    • Margin of Error Formula
    • Hypergeometric Distribution Formula
    • Standard Normal Distribution Formula
    • NOPAT Formula
    • Effective Tax Rate Formula
    • Degree of Operating Leverage Formula
    • Outliers Formula
    • Information Ratio Formula
    • Percent Error Formula
    • Hypothesis Testing Formula
    • Activity Based Costing Formula
    • Coverage Ratio Formula
    • Market Risk Premium Formula
    • Degree of Financial Leverage Formula
    • Absorption Costing Formula
    • Future Value of Annuity Due Formula
    • Internal Growth Rate Formula
    • F-Test Formula
    • Covariance Formula
    • Population Variance Formula
    • Coefficient of Determination Formula
    • Adjusted R Squared Formula
    • Compound Interest Formula
    • Gross Profit Formula
    • Accounting Equation Formula
    • Sample Size Formula
    • Sample Standard Deviation Formula
    • Quartile Formula
    • Variance Analysis Formula
    • Correlation Coefficient Formula
    • Z Score Formula
    • Variance Formula
    • Present Value Formula
    • Coefficient of Variation Formula
    • Net Asset Value Formula
    • Profit Margin Formula
    • Holding Period Return Formula
    • Capital Asset Pricing Model Formula
    • Present Value of Annuity Due Formula
    • Depreciation Expenses Formula
    • Annuity Formula
    • Taxable Income Formula
    • Profit Formula
    • Monthly Compound Interest Formula
    • Equity Formula
    • Return on Total Assets Formula
    • Alpha Formula
    • Debt to Equity Ratio Formula
    • EBITDA Formula
    • Accrued Interest Formula
    • Dividend Formula
    • Common Stock Formula
    • Mortgage Formula
    • Growth Rate Formula
    • Absolute Value Formula
  • Accounting fundamentals (700+)
  • Asset Management Tutorial (200+)
  • Banking (44+)
  • Corporate Finance Basics (373+)
  • Credit Research Fundamentals (6+)
  • Economics (88+)
  • Financial Modeling in Excel (17+)
  • Investment Banking Basics (140+)
  • Investment Banking Careers (29+)
  • Trading for dummies (69+)
  • valuation basics (27+)
  • Insurance Resources (14+)
  • Top Finance Books (7+)
Finance Blog Courses
  • Investment Banking Course
  • Investment Banking Online Course
  • Financial Modeling Certification

Z Test Statistics Formula

By Madhuri ThakurMadhuri Thakur

Z Test Statistics Formula

Z Test Statistics Formula (Table of Contents)

  • Formula
  • Examples
  • Calculator

What is the Z Test Statistics Formula?

Z Test statistics is a statistical procedure used to test an alternative hypothesis against the null hypothesis. It is any statistical hypothesis used to determine whether two samples means are different when variances are known and the sample is large. Z Test determines if there is a significant difference between sample and population means. Z Test normally used for dealing with problems relating to large samples. The name ‘z test’ drive from that interference is made from a standard normal distribution and ‘Z’ is the traditional symbol used to denote standard normal random variable. Z test formula computed by the Sample means minus population means divided by population standard deviation and sample size. When the sample size is more than 30 units than in that case the z test must be performed. Mathematically z test formula is represented as,

Z Test = (x̄ – μ) / (σ / √n)

Here,

  • x̄ = Mean of Sample
  • μ = Mean of Population
  • σ = Standard Deviation of Population
  • n = Number of Observation

Examples of Z Test Statistics Formula (With Excel Template)

Let’s take an example to understand the calculation of Z Test Statistics formula in a better manner.

Start Your Free Investment Banking Course

Download Corporate Valuation, Investment Banking, Accounting, CFA Calculator & others

You can download this Z Test Statistics Formula Excel Template here – Z Test Statistics Formula Excel Template

Z Test Statistics Formula – Example #1

Suppose a person wants to check or test if tea and coffee both are equally popular in the city. In that case, he can use a z test statistics method to obtain the results by taking a sample size say 500 from the city out of which suppose 280 are tea drinkers. So to test this hypothesis he can use z test method.

All in One Financial Analyst Bundle(250+ Courses, 40+ Projects)
Financial ModelingInvestment BankingUS GAAPCFA-Level 1 & 2
Equity ResearchM & A ModelingPrivate Equity ModelingForex Trading
Price
View Courses
250+ Online Courses | 40+ Projects | 1000+ Hours | Verifiable Certificates | Lifetime Access
4.9 (86,641 ratings)

Principal at school claims that students in his school are above average intelligence and a random sample of 30 students IQ scores have a mean score of 112.5 and mean population IQ is 100 with a standard deviation of 15. Is there sufficient evidence to support the principal claim?

Z Test Statistics Formula Example 1-1

Solution:

Z Test Statistics is calculated using the formula given below

Z Test = (x̄ – μ) / (σ / √n)

Z Test Statistics Formula Example 1-2

  • Z Test = (112.5 – 100) / (15 / √30)
  • Z Test = 4.56

Compare the z test results with z test standard table and you can come to the conclusion in this example null hypothesis is rejected and the principal claim is right.

Z Test Statistics Formula – Example #2

Suppose an investor looking to analyze the average daily return of the stock of one the company is greater than 1% or not? So investors picked up a random sample of 50 and return is calculated and has a mean of 0.02 and investors considered standard deviation of mean is 0.025.

So, in this case, the null hypothesis is when the mean is 3% and the alternative hypothesis is that of mean return is higher than 3%. Investors assume alpha of 0.05% is selected as a two-tailed test and 0.025% of the sample in each tail and alpha critical value is either 1.96 or -1.96. So if the result of the Z test is less or greater than 1.96 null hypothesis will be rejected.

Daily return of the stock Example 2-1

Solution:

Z Test Statistics is calculated using the formula given below

Z Test = (x̄ – μ) / (σ / √n)

Z Test Statistics Formula Example 2-2

  • Z Test = (0.02 – 1%) / (0.025/ √50)
  • Z Test = 2.83

So from the above calculation investors will come to conclusion and he will reject the null hypothesis because the result of z is greater than 1.96 and come to an analysis that the average daily return of the stock is more than 1%.

Z Test Statistics Formula – Example #3

An insurance company is currently reviewing its current policy rates when originally settings the rate they believe that the average claim amount will be a maximum of Rs 180000. The company is concern about that true mean actually higher than this. The company randomly select 40 sample claim and calculate sample mean of Rs 195000 assuming a standard deviation of Claim is Rs 50000 and set alpha as 0.05. So z test to be performed to see insurance company should be concerned or not.

Insurance Company Example 3-1

Solution:

Z Test Statistics is calculated using the formula given below

Z Test = (x̄ – μ) / (σ / √n)

Z Test Statistics Formula Example 3-2

  • Z Test = (195000 – 180000) / (50000 / √40)
  • Z Test = 1.897

Step – 1 Set the Null hypothesis

Step – 2 calculate the test statistics

So if you put all available figures in z test formula it will give us z test results as 1.897

Step – 3 Set Rejection region

Considering alpha as 0.05 let’s say rejection region is 1.65

Step – 4 Conclude

As per z test results, we can see that 1.897 is greater than the rejection region of 1.65 so the company fails to accept the null hypothesis and the insurance company should be concerned about their current policies.

Explanation

  • First, determine the average of the sample (It is a weighted average of all random samples).
  • Determine the average mean of the population and subtract the average mean of the sample from it.
  • Then divide the resulting value by the standard deviation divided by the square root of a number of observations.
  • Once the above steps are performed z test statistics results are calculated.

Relevance and Use of Z Test Statistics Formula

Z test is used to compare the average of a normal random variable to a specified value. Z test is useful or to be used when the sample is more than 30 and population variance is known. Z test is best on the assumption that the distribution of sample mean is normal. Z test is applied if certain conditions are made otherwise we have to use other tests and fluctuations do not exist in z test. Z test for a single means is used to test the hypothesis of the specific value of the population mean. Z test is one of the bases of statistical hypothesis testing methods and often learn at an introductory level. Some time z tests can be used where the data is generated from other distribution, such as binomial and Poisson.

Z Test Statistics Formula Calculator

You can use the following Z Test Statistics Calculator

x̄
μ
σ
√n
Z Test
 

Z Test =
x̄ − μ
=
σ / √n
0−0
= 0
0 / 0

Recommended Articles

This has been a guide to Z Test Statistics Formula. Here we discuss How to Calculate Z Test Statistics along with practical examples. We also provide Z Test Statistics Calculator with a downloadable excel template. You may also look at the following articles to learn more –

  1. What is Hypergeometric Distribution Formula?
  2. Hypothesis Testing Formula | Definition | Calculator
  3. Examples of Coefficient of Determination Formula
  4. How to Calculate Sample Size Using Formula?
  5. Statistics Formula | Calculator | Excel Template
Popular Course in this category
All in One Financial Analyst Bundle- 250+ Courses, 40+ Projects
  250+ Online Courses |  1000+ Hours |  Verifiable Certificates |  Lifetime Access
4.9
Price

View Course

Related Courses

Investment Banking Course (123 Courses, 25+ Projects)4.9
Investment Banking Course (123 Courses, 25+ Projects)4.8
Financial Modeling Course (7 Courses, 14 Projects)4.7
0 Shares
Share
Tweet
Share
Primary Sidebar
Footer
About Us
  • Blog
  • Who is EDUCBA?
  • Sign Up
  • Live Classes
  • Corporate Training
  • Certificate from Top Institutions
  • Contact Us
  • Verifiable Certificate
  • Reviews
  • Terms and Conditions
  • Privacy Policy
  •  
Apps
  • iPhone & iPad
  • Android
Resources
  • Free Courses
  • Investment Banking Jobs Offer
  • Finance Formula
  • All Tutorials
Certification Courses
  • All Courses
  • Financial Analyst All in One Bundle
  • Investment Banking Training
  • Financial Modeling Course
  • Equity Research Course
  • Private Equity Training Course
  • Business Valuation Course
  • Mergers and Acquisitions Course

ISO 10004:2018 & ISO 9001:2015 Certified

© 2022 - EDUCBA. ALL RIGHTS RESERVED. THE CERTIFICATION NAMES ARE THE TRADEMARKS OF THEIR RESPECTIVE OWNERS.

EDUCBA
Free Financial Modeling Course

3 Statement Model Creation, Revenue Forecasting, Supporting Schedule Building, & others

*Please provide your correct email id. Login details for this Free course will be emailed to you

By signing up, you agree to our Terms of Use and Privacy Policy.

EDUCBA Login

Forgot Password?

By signing up, you agree to our Terms of Use and Privacy Policy.

EDUCBA
Free Investment Banking Course

Corporate Valuation, Investment Banking, Accounting, CFA Calculator & others

*Please provide your correct email id. Login details for this Free course will be emailed to you

By signing up, you agree to our Terms of Use and Privacy Policy.

EDUCBA

*Please provide your correct email id. Login details for this Free course will be emailed to you

By signing up, you agree to our Terms of Use and Privacy Policy.

Let’s Get Started

By signing up, you agree to our Terms of Use and Privacy Policy.

EDUCBA

Download Z Test Statistics Formula Excel Template

EDUCBA

डाउनलोड Z Test Statistics Formula Excel Template

This website or its third-party tools use cookies, which are necessary to its functioning and required to achieve the purposes illustrated in the cookie policy. By closing this banner, scrolling this page, clicking a link or continuing to browse otherwise, you agree to our Privacy Policy

Loading . . .
Quiz
Question:

Answer:

Quiz Result
Total QuestionsCorrect AnswersWrong AnswersPercentage

Explore 1000+ varieties of Mock tests View more