Answered: Whether testing a hypothesis or…

Whether testing a hypothesis or constructing a confidence interval, t assumes that both underlying populations are normally distributed with equal variances. What are the assumptions?

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter9: Sequences, Probability And Counting Theory

Section9.7: Probability

Problem 1SE: What term is used to express the likelihood of an event occurring? Are there restrictions on its...

See similar textbooks

Related questions

Q: On average, 1 in 800 computer crashes during a severe thunderstorm. A certain company had 4,000…

A: Solution: Let X be the random variable that the number of crashed computers. The probability of of…

Q: What statistical distribution is used for testing the difference between two population variances? a…

A: Answer- ● d F-Fisher distribution

Q: What assumption(s) must hold true to use the normal distribution to make a confidence interval for…

A: Assume that p as the true proportion and n is the sample size.

Q: Automotive Engineers tested the gas mileage in kilometers per Liter (km/L) of a certain passenger…

A: The provided information is x¯=15s2=2.5s=1.58n=25α=0.001 df =n-1=25-1 df=24 The critical value is…

Q: In a hypothetical study, it has been investigated whether pain tolerance differs between people with…

A: a) As we van see in the boxplot provided in the question, the pain tolerance levels are not same for…

Q: EXERCISE Show that for a random sample from a normal population, the sample variance S² is a…

Q: The filling machine at a bottling plant is operating correctly when the variance of the fill amount…

A: Solution: Let X be the fill amounts. From the given information, X follows normal distribution with…

Q: Estimate the population (pop'n) variance and population (pop'n) standard deviation of the duration…

A: Given that n=10 s=8.54 α=0.05 level of significance We have to find population variance and…

Q: Packages of food whose average weight is 16 ounces with a standard deviation of 0.6 ounces are…

A: Given: n=24, μ=16, σ=0.6, x¯=392 The z-score is obtained by the formula:

Q: (a) Is X a complete sufficient statistic?

Q: In a t-distribution, the standard deviation is affected by: a. Researcher's chosen alpha level b.…

A: The formula of t distribution can written as:

Q: 17. Which is not assumed in ANOVA? A) Observations are independent. B) Populations are normally…

A: Answer: Option D) Population variances are known.

Q: What is the mean and standard deviation of the number of pedestrians waiting to cross? What is the…

Q: Which of the following is not desired property of the point estimator? A. maximum likelihood B.…

A: Point estimators are functions that are used to estimate a population parameter's estimated value…

Q: Calculate the mean (mu) and variance (sigma squared) of the probability distribution

Q: Which assumption can be violated when conducting a chi-square test of independence, yet still allow…

A: Chi-square test of independence: A single simple random sampling is done with each individual being…

Q: The normal distribution is always used when the null hypothesis involves population mean. A)…

A: Given: The normal distribution is always used when the null hypothesis involves population mean.

Q: If you were to use the normal approximation for the binomial distribution with probability of…

A: From the provided information, The probability of success = p Number of trials = n

Q: a) Compute the standard deviation for each of the variables. b) Compute the covariance between…

A: Given Data : 1) Variable : Grade Count, N: 6 Sum, Σx: 393 Mean, x̄ = Σx / N 65.5…

Q: Exercise 5 (-) Suppose that the random variable X has a negative binomial distribution with a p =…

A: (a) Obtain the probability that X equals 9. The probability that X equals 9 is obtained below…

Q: Two 6-sided dice are rolled and the two resulting values X and Y are multiplied together to form the…

A: In the given case outcomes of two dice are considered to be represented by random variables X and Y.…

Q: Explain when a random variable might be modelled using a Normal distribution, and give an example of…

A: Mathematically, Whenever a random variable is formed by adding a number of other individual…

Q: When conducting a hypothesis test for the population mean when sigma is known and the sample size is…

A: For the given Select the correct choice?

Q: Develop a research question from the data collected that requires a chi square distribution test.…

A: Given information: The data represents the values of the required variables.

Q: Write and sketch the pdf of the Gaussian (normal) distribution for different mean and variance…

A: Probability density function of normal distribution: A continuous random variable X is said to…

Q: When applying one-way analysis of variance (ANOVA), all the following are key assumptions that…

A: Solution.

Q: The standard deviation of a continuous random variable is its expected value. O True O False

A: Given : The standard deviation of a continuous random variable is its expected value.

Q: Construct a 90% confidence interval for u-2 with the sample statistics for mean cholesterol content…

Q: wind data acquisition system located at certain site, measures 7 m/s 24 times, 8 m/s 72 times, 9 m/s…

A: In probability theory, an event is an outcome or a set of outcomes of a random experiment to which a…

Q: 3. Derive the variance of the F distribution.

Q: A Paired t-Test reduces to the Chapter 9 case of hypothesis test on a mean, variances unknown. True…

A: A hypothesis which is tested for plausible rejection is called the Null Hypothesis (typically…

Q: A major application of analytics in marketing is determining customer retention. Suppose that the…

A: Wh have given that P(The customer leaves) = 0.14

Q: What does the Empirical Rule say? Can you use the Empirical Rule for ALL probabilities in a normal…

A: 1. What does the Empirical Rule say? 2. Can you use the Empirical Rule for ALL probabilities in a…

Q: A fair coin is flipped 80 times and the number of heads that occur is noted. A random variable x is…

Q: Let x be a random variable that follows normal distribution with mean 5 and variance 16. Find P (2…

A: Let X denote the random variable that follows normal distribution with mean μ=5 and variance σ2=16…

Q: In a log normal distribution. What is the expected value of the mean and the Std. And what is the…

A: The mean and standard deviation of log normal distribution is to be found out. The log normal…

Q: a. What is the expected weekly demand for the alarm clock radio? b. What is the variance and…

A: The provided information is x (weekly demand) Probability p(x) x*p(x) x2*p(x) 0 0.05 0 0 1…

Q: Cybersecurity When using the data from Exercise 1 to test for goodness-of-fit with the distribution…

Q: Fit a binomial distribution for which the Mean is 6, and the Variance is 4.

Q: persons required to recover Assume the population variances are not equal

A: Given: A recent study of 20 individuals. That is sample size n1=20 the average number of therapy…

Q: Aquatic Biology (Vol. 9, 2010) studied green sea turtles inhabiting the Grand Cayman South Sound…

A: From the given information, μ=55.7 σ=11.5

Q: (a) Test the hypothesis that p-0, using a=0.05 (b) Construct a 95% confidence interval for the…

A: From provided information, weight and systolic blood pressure of 26 males is given below. It is…

Q: What type of distribution is referred to test the equal assumption of variance? 1. T distribution…

A: Given σ12= σ22 (assume population variances are equal)

Q: We toss a symmetric coin five times. Let X denote the number of eagles tossed. Determine the…

A: The random variable X is defined as the number of eagles tossed. Conditions for using the binomial…

Q: Knowledge of this type of distribution allows us to construct a confidence interval for the ratio of…

Q: 2. During my office hours (from 12pm to 6pm), an average of about 1 student per hour comes in for…

Q: In a study using 14 samples, and in which the population variance is unknown, the distribution that…

A: population variance unknown with sample size n = 14

Q: When specifying the probability distribution for the input variables, which approach is most useful…

A: Introduction: Different types of distributions are useful at the different stages in a simulation…

Q: Construct a 99% confidence interval for H1 - H2 with the sample statistics for mean cholesterol…

Question

Whether testing a hypothesis or constructing a confidence interval, t assumes that both underlying populations are normally distributed with equal variances. What are the assumptions?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Hypothesis Tests and Confidence Intervals for Equality of Variances$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.