Explore BrainMass


A Z-test is a type of parametric statistical test utilized for comparing two populations, which have large population sizes and the same variance values, to determine if their population means differ. It is a common test used for hypothesis testing, along with the Student’s t-test. A Z-test is an approximation which is based from the probability distribution of the test statistic.

A basic Z-test, using standard units, corresponds to the following formula:

Z = Xbar – μ0 /σ


μ= mean of the population

Xbar = mean of the samples

σ = standard deviation

A Z-test is used often for large populations in which the variance is known. For populations where the population is small and the variance is unknown, a t-test is more appropriate. Furthermore, histograms are often constructed before computing a Z-test in order to verify that the sample being used comes from a normally distributed population.

When conducting a Z-test, the first step is to state the null and alternative hypotheses. After this, a decision needs to be made on whether the test is a right-tailed test, a left-tailed test or a 2-tailed test. This is dependent upon the structure of the null hypothesis.

Additionally, Z-tests have a single critical value for different significance levels. Typically the significance value required is stated initially. The following displays the critical regions for testing the population means using a Z-test1:

μ < μ0 - Reject the null if: Z < -zα

μ > μ0  - Reject the null if: Z > zα

μ does not equal μ0 - Reject the null if Z < -zα/2 or Z > zα/2




1. Miller, I. and Freund, J.E. (2011). Probability and Statistics for Engineers, 8th Edition. Boston, MA. 

Do Americans drink enough water?

Do Americans drink enough water? A sample of 42 professionals was selected and their water consumption was monitored over a 24 hour period. The mean amount consumed was 39.3 oz with a standard deviation of 11.2 oz. If the recommendation is for Americans to drink 4.6 8 oz servings a day, do Americans' consumption significantly

One Sample Hypothesis Test

I have completed the answer I need help putting them to be put on the guided format as requested for me to do so. One attachment is my answers and the other is the guide. I am not looking for you to change my answer. COMPLETE PROBLEM 1: It is pretty common across most schools to find the grades at the MBA level divided betwe

Parametric vs. Non-parametric Testing

Gerber Biotech Industries was testing three different drugs namely Breath-Easy, Fresh Mint and Sober Breath, meant for neutralizing the alcohol content in the breath so that the (drunken) drivers can pass the breath analyzer test. The three drugs are tested on randomly selected volunteers and the time taken for each of the drugs

Z-score for a college basketball game

In N=25 games last season the college basketball team averaged u= 76 points with a standard deviation of o= 6. in their final game of the season, the team scored 89 points. based on this information, the number of points scored in the final games was: -there is not enough information - -far above average - above average bu

Migraine vs. headache

The formal hypotheses - a detailed outline of the hypotheses of how caffeine correlates to migraine headaches. Complete a proposal of the statistical procedure that will employ a test of the hypothesis Section on the experimental design and the identification of the appropriate "variables" involved in the process Section o

How does the cellphone service compare between different cities?

How does the cellphone service compare between different cities? a. At the .05 level of significance, is there evidence of a difference in the mean cell phone service rating between Verizon and AT&T? b. What assumption is necessary about the population distribution in order to perform this test? c. Use a graphical method to

Conversion to Z-scores

Using the database created in W1 Assignment 2, convert each subject's age and height into a z-score. Using the z-score of ±1.645 for the 5 percent cutoff and the z-score of ±1.96 for the 2.5 percent in the tail, identify the subject identification (ID) number for subjects who are closest to the cutoff for the upper 2.5 perc

Using a Z-Score to Describe an Individual's Performance

Explain the general rationale behind using a z-score for describing how an individual performed on an exam compared to just stating the overall mean and the individual's score. How does the information differ in the two situations? What additional information are you gaining with a z-score? Imagine you are in charge of review

PEWs internet use survey

According to the Pew Internet & American Life Project, 75% of American adults use the Internet (Pew Internet website, April 19, 2008). The Pew project authors also reported on the percentage ofAmericans who use the Internet by age group. The data in the file AgeGroup are consistent with their findings. These data were obtaine

Finding the T-Score on the Risk Taking Scale

T-scores are used on some psychological tests, such as the MMPI. T-scores have a mean of 50 and a standard deviation of 10, and therefore a z-score of -1 (one standard deviation below the mean) would be converted to a T-score of 40. What is George's T-score on the Risk-Taking scale? a. 45 b. 56 c. 58 d. 66 Known facts:

Sampling plans and population

1. A handler loads one item every 5 minutes, so 480 items are completed in his first week of work. His manager checks his work by randomly selecting a day of the week, then reviewing all the item she completed that day. Does this sampling plan result in a random sample? Does this sampling plan result in a random sample? a)

Solving for Z

I am trying to solve some of my homework problems solving for Z, however in Excel 2007 it will not allow me to do the probabilities any suggestions. I am using the normsdist function.

Statistics questions***

I. Jane Smith is a student in the MBA 751 Econometrics course and she received an 83.6% on her final exam grade. The mean of exam scores is expected to be a 75% with a standard deviation of 8.5%. Compute a Z-score for Jane. II. John Doe is looking at an investment in Acme, Inc. bond offering. Acme, Inc.'s bonds have an ann

Statistics - Z Score

1. Assuming a normal distribution, What is the z-score associated with the second quartile? 2. Find the following: P(z>2.43) 3. If we wish to have 95% confidence interval, what would be the value of the confidence coefficient? 4. In your own words, describe the relationship between the standard erro (of the mean) a

Statistics: Quartiles, Distribution

1. Find the third quartile Q3 of the list of 24 sorted values shown below. 35 35 42 42 43 43 43 45 46 47 49 50 51 54 55 56 57 59 63 64 67 69 74 77 The third q2uartile Q3 is _____ (type an integer or a decimal.) 2. Which is relatively better: a score of 81 on a psychology test or a score of 50 on a economics test? Scores

z-test, t-test or ANOVA

If a researcher wishes to study the effect of, for example, a new drug on blood pressure, what type of testing should be used and why? Should it be a z-test, a t-test, or an ANOVA for the analysis? Please help. What would the choice of test depend on? Would the hypothesis be directional or non-directional? Would the tes

Assessing Z-Scores and Outliers

1. Thousands of students apply for admission to graduate schools in economics each year with the intention of obtaining a PhD. The mean and standard deviation of these 129 productivity scores were used to compute a z score for each economics program. Harvard University had the highest z score (z=5.08) and hence was the top ranke

Comparing Z-scores in a Population

1) Compute the z score corresponding to each of the following values of x a. x=40, s=5, x with a bar=30 b. x=90, mean= 89, sigma=2 c. mean=50, sigma= 5, x =50 d. s=4, x=20, x with a bar =30 e. in parts a-d state whether the z score locates x within a sample or a population f. in parts a-d state whether each value of x lies

Compute the Z-Score for Rocket Company

Current assets $ 30,000 Total assets 88,000 Current liabilities 18,000 Book value of total debt 38,000 Retained earnings 42,000 Sales 125,000 Earnings before interest and tax

Computation of z score

working capital $ 90,000 total assets 620,000 retained earning 30,000 earnings before interest and taxes 55.000 market value of equity

Z test statistics and scores

What differentiates a z test statistic for a population from the z statistic for a sampling of means? Why is there a difference? Consider a normal population with ? = 43 and ? = 5.2. Calculate the z-score for an x ? of 46.5 from a sample of size 16.

Z Scores

1. What are the characteristics of the normal curve? What human behavior, trait, or characteristic can you think of that is distributed normally? 2. Standard scores, such as z scores, allow us to make comparisons across different samples. Why? 3. Why is a z score a standard score, and why can standard scores be used to com

Z-Test and Critical Values

If the critical values for a statistical test are 1.96 and 1.96, determine if you would reject or fail to reject the null hypothesis in each of the following cases: a. z  1.06 b. z  2.06 c. A z score beyond which 7% of the data fall in each tail

Z-Score Corresponding to Values of 'x'

1) Compute the z-score corresponding to each of the following values of x: a. x=40, s=5, x (with line over) = 30 b. x=90, (weird u for subtracting x with line over) = 89, (weird o with line over it for dividing the result by s) = 2 c. (weird u for subtracting x with line over) = 50, (weird o with line over it for dividing

Finding the z-score

A department store, on average, has daily sales of $29,876.76. The standard deviation of sales is $1000.00. On Tuesday, the store sold $34,893.71 worth of goods. Find Tuesday's z-score.

Z-Score Calculation

The mean age of adult learners in a chosen class of 31 students is 33.8 years. The standard deviation is equal to 7 years. You are a member of the class and are 26 years old. What is your z-score? What does this tell us?