b) what is the test statistic? give your answer to four decimal places.

Z Test Statistics Formula (Table of Contents)

• Formula
• Examples
• Calculator

What is the Z Test Statistics Formula?

Z Examination statistics is a statistical procedure used to examination an alternative hypothesis confronting the nada hypothesis. Information technology is whatsoever statistical hypothesis used to decide whether two samples means are different when variances are known and the sample is large. Z Test determines if at that place is a significant deviation between sample and population means. Z Test normally used for dealing with problems relating to big 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 examination must be performed. Mathematically z test formula is represented every bit,

Z Examination = ( x̄ – μ) / (σ / √due north)

Here,

• x̄ = Mean of Sample
• μ = Mean of Population
• σ = Standard Difference of Population
• due north = Number of Observation

Examples of Z Examination Statistics Formula (With Excel Template)

Let's take an example to sympathize the adding of Z Test Statistics formula in a ameliorate way.

You can download this Z Examination Statistics Formula Excel Template here – Z Exam Statistics Formula Excel Template

Z Test Statistics Formula – Example #one

Suppose a person wants to check or test if tea and coffee both are equally popular in the metropolis. In that example, 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 employ z test method.

Principal at school claims that students in his school are to a higher place average intelligence and a random sample of xxx 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?

Solution:

Z Test Statistics is calculated using the formula given below

Z Examination = ( x̄ – μ) / (σ / √northward)

• Z Exam = (112.5 – 100) / (fifteen / √xxx)
• Z Test = four.56

Compare the z exam results with z test standard table and y'all tin can come up to the conclusion in this example null hypothesis is rejected and the master claim is right.

Z Test Statistics Formula – Example #2

Suppose an investor looking to clarify the average daily return of the stock of one the company is greater than i% or non? So investors picked upwards a random sample of 50 and render is calculated and has a mean of 0.02 and investors considered standard deviation of mean is 0.025.

So, in this instance, the null hypothesis is when the mean is iii% and the culling hypothesis is that of mean render is higher than 3%. Investors assume alpha of 0.05% is selected as a two-tailed exam and 0.025% of the sample in each tail and alpha critical value is either 1.96 or -one.96. So if the event of the Z examination is less or greater than 1.96 zero hypothesis will be rejected.

Solution:

Z Examination Statistics is calculated using the formula given below

Z Test = ( x̄ – μ) / (σ / √n)

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

Then from the above adding 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 boilerplate daily return of the stock is more than ane%.

Z Test Statistics Formula – Example #three

An insurance visitor is currently reviewing its current policy rates when originally settings the charge per unit they believe that the boilerplate claim amount will be a maximum of Rs 180000. The company is business organization about that true mean actually higher than this. The company randomly select twoscore sample claim and calculate sample mean of Rs 195000 assuming a standard deviation of Merits is Rs 50000 and set alpha as 0.05. So z test to exist performed to see insurance company should be concerned or not.

Solution:

Z Exam Statistics is calculated using the formula given below

Z Exam = ( x̄ – μ) / (σ / √north)

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

Step – 1 Set the Null hypothesis

Footstep – 2 summate the examination statistics

So if you put all bachelor figures in z test formula information technology will give usa z exam results as ane.897

Footstep – 3 Set Rejection region

Because blastoff as 0.05 permit'due south say rejection region is 1.65

Pace – 4 Conclude

As per z test results, we can see that 1.897 is greater than the rejection region of 1.65 then the company fails to have the nothing hypothesis and the insurance company should be concerned about their current policies.

Caption

• Commencement, determine the average of the sample (It is a weighted average of all random samples).
• Decide the average mean of the population and subtract the average mean of the sample from information technology.
• So divide the resulting value by the standard deviation divided by the square root of a number of observations.
• One time the above steps are performed z examination statistics results are calculated.

Relevance and Utilise 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 exam is best on the assumption that the distribution of sample hateful is normal. Z test is applied if certain weather are made otherwise nosotros accept to employ other tests and fluctuations do non 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 examination is i of the bases of statistical hypothesis testing methods and often acquire at an introductory level. Some fourth dimension z tests tin be used where the data is generated from other distribution, such as binomial and Poisson.

Z Test Statistics Formula Calculator

Yous can utilize the following Z Examination Statistics Computer

Recommended Manufactures

This has been a guide to Z Exam Statistics Formula. Hither nosotros discuss How to Summate Z Test Statistics along with practical examples. We also provide Z Test Statistics Calculator with a downloadable excel template. You may too await at the post-obit articles to acquire more than –

1. What is Hypergeometric Distribution Formula?
2. Hypothesis Testing Formula | Definition | Estimator
3. Examples of Coefficient of Determination Formula
4. How to Summate Sample Size Using Formula?
5. Statistics Formula | Calculator | Excel Template

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