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. 

Excel: binomial distribution, normal distribution, uniform

I need assistance solving these problem sets in excel format. A large company must hire a new president. The Board of Directors prepares a list of five candidates, all of whom are equally qualified. Two of these candidates are members of a minority group. To avoid bias in the selection of the candidate, the company decides to

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 va

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 versus 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

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

Statistics for Econometrics Course

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: 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

Assessing Z-Scores and Outliers

See the attached file. 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) a

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-score and Standard Normal Distributions

If the random variable z is the standard normal score and a > 0, is it true that P(z < -a) = P(z > a)? Why or why not? Find the z-score for the standard normal distribution where: Area = 0.32 in the left tail

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

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?

How to Find the Z-Score

Scores on a particular test have a mean of 64.6. The distribution of sample means for samples of size 100 is normal with a mean of 64.6 and a standard deviation of 1.9. Suppose you take a sample of size 100 of test scores and find that the mean is 63. What is the z-score corresponding to this sample mean?

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

A car dealership is worried that Hondas are getting lower sales than Hyundai. Two independent random samples have been selected 630 observations from population 1 (Hondas) and 610 from population 2 (Hyundai). The sample means obtained are X1(bar)=$46 k and X2(bar)=$47 k. It is known from previous studies that the population variances are 4.1 and 5.0 respectively. Using a level of significance of .05, is there evidence that the Hondas are receiving lower sales? Fully explain your answer

A car dealership is worried that Hondas are getting lower sales than Hyundai. Two independent random samples have been selected 630 observations from population 1 (Hondas) and 610 from population 2 (Hyundai). The sample means obtained are X1(bar)=$46 k and X2(bar)=$47 k. It is known from previous studies that the population var

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

Examples of z-score calculations for statistics students

1. The weight of cans of fruit is normally distributed with a mean of 1,000 grams and a standard deviation of 50 grams. What percent of the cans weigh 860 grams or less? a) 0.0100 b) 0.8400 c) 0.0026 d) 0.0001 2). The mean amount spent by a family of four on food per month is $500 with a standard

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

Solver one proportion z test

Suppose that 50% of all adult Americans believe the federal budget deficits at recent levels cause long-term harm to the nations's ecomony. What is the probability that more than 58% of a random sample of 250 adults Americans would hold this belief? If the sample of 250 was made up of adults randomly selected from each of

Determining the Corresponding Z-Score

Find the z-score corresponding to a score of X = 100 for each of the following distributions: a. ? = 80 and ? = 10 b. ? = 80 and ? = 5 c. ? = 105 and ? = 10 d. ? = 105 and ? = 5 Make sure to indicate the direction (sign) of the z-scores.