Share
Explore BrainMass

Z-Test

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

Variables:

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

 

 

References:

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

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)

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

Computation of Z score

Given the following numbers: Working capital $ 90,000 Total assets 620,000 Retained earning 30,000 Earnings before interest and taxes 55.000 Market va

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

Probability

Suppose that people's heights (in centimeters) are normally distributed, with a mean of 165 and a standard deviation of 6. We find the heights of 40 people. (a) How many would you expect to be between 157 and 173 cm tall? (b) How many would you expect to be taller than 160 cm? For a particular value, this table gives th

Statistics

I need some help with approaching the following problem: A recent study conducted by the state government attempts to determine whether the voting public supports further increase in cigarette taxes. The opinion poll recently sampled 1500 voting age citizens. 1035 of the sampled citizens were in favor of an increase in cigare

Standard Norm Distribution

1) When comparing data from different distributions, what is the benefit of transforming data from these distributions to conform to the standard distribution? 2) What role do z-scores play in this transformation of data from multiple distributions to the standard normal distribution? 3) What is the relationship between

Statistics problem

Management is considering adopting a bonus system to increase production. One suggestion is to pay a bonus on the highest 5 percent of production based on past experience. Past records indicate that, on the average, 4,000 units of a small assembly are produced during a week. The distribution of the weekly production is approxima

Sampling and Sampling Distributions

I need help with some practice problems that were given to us, to help prepare for a quiz next week. Please provide detailed steps as to how you came by your answer (include any notes, calculations, or anything that may be pertinent to the solution). As always, your help would be greatly appreciated! Thanks, E

Need help with a couple of easy problems

1.The number of pizzas delivered to students each month is a random variable with the following probability distribution: X 0 1 2 3 P (x) 0.1 0.3 0.4 0.2 A) Find the mean number of pizzas delivered. B) Calculate the variance in the number of pizzas delivered. C) Determine the standard deviation. 2. It is

Descriptive Stats-additions, corrections, additions

Hi Martin! Here is the part I need your help, and I will also add the feedback below. 1) Compute the high scores on the RCMAS that would correspond to an extremely low score. 2) Demonstrate a conceptual understanding of z-scores in a write up. 3) Calculate the high and low score values **Include an interpretation of resul

Descriptive statistics/ Describing variation Z-score

I need assistance I keep getting 2.53333 as an answer =(10-8.1)/0.75=2.53333 The problem is as follows: A pizza franchise specifies that the amount of cheese on a large pizza should be on average 10 ounces with a standard deviation of 0.75 ounces. An inspector measures the amount of cheese on a large pizza and finds the a

Normal Distribution and Normal curve

Describe the basic characteristics of a normal distribution and the normal curve. What are z scores and how are they used in relation to distributions and raw scores? What is the difference between population and sampling distributions? Provide at least one example for each concept, explaining how the chosen example illustrates

Applied Statistics Health Care

I am new at a job and I have been given instructions that focused on Population and Sampling Distributions I need support in proving that the use of z-scores to describe the location of a score within a distribution and to standardize scores from different populations. In addition to that, I also need to explain basic probabi

Statistical Analysis

Student ID IQ SCORE GPA 1 84 2.5 2 71 2.1 3 62 1.9 4 89 3.1 5 66 1.9 6 109 3.5 7 107 3.2 8 92 3.3 9 67 2 10 112 3.4 11 74 2.5 12 66 2 13 103 2.9 14 114 3.1 15 76 2.2 16 97 2.9 17 70 2.6 18 108 3.9 19 66 1.8 20 88 2.8 21 113 3.8 22 107 3.5 23 82 3 24 110 3.6 25 94 2.9 26 76 2.4 26 82 2.9 28 74 2 29 88