**Transcription:**"Under what two conditions will a sampling distribution be normally distributed?"**Explanation:**This text prompts a discussion typically found in statistics or probability theory, related to the normal distribution of sampling distributions. It likely leads to an explanation of the Central Limit Theorem, which states that the sampling distribution of the sample mean will tend to be normal under two conditions:1. **Sample Size:** The sample size is sufficiently large (usually n ≥ 30 is considered adequate).2. **Population Distribution:** The population from which samples are drawn is normally distributed, or the sample size is large enough to ensure normality regardless.No graphs or diagrams are present in this image.

Answered: Under what two conditions will a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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An amusement park keeps track of the percentage of individuals with season passes according to age category. An independent tourist company would like to show that this distribution of age category for individuals buying season passes is different from what the amusement park claims. The tourist company randomly sampled 200 individuals entering the park with a season pass and recorded the number of individuals within each age category. Age Category Child (under 13 years old) Teen (13 to 19 years old) Adult (20 to 55 years old) Senior (56 years old and over) Number of Individuals 56 86 44 14 The tourist company will use the data to test the amusement park’s claim, which is reflected in the following null hypothesis. H0:pchild=0.23H0:pchild=0.23, pteen=0.45pteen=0.45, padult=0.20padult=0.20, and psenior=0.12psenior=0.12. What inference procedure will the company use to investigate whether or not the distribution of age category for individuals with season passes is…
The standard deviation of any sampling distribution is called a: A. Standard error B. Type- I error C. Non-sampling error D. Type II-error
a)Determine the mean of sample means distribution b) Determine the standard deviation (standard error) of sample means distributionc) Draw a Normal (bell-shaped) graph for sample means distribution byhand on a paper showing x and y axes without any values marked on them. However,label the values of mean and standard deviation as described below. The adult male heights in a country vary normally with mean of 70 inches and standarddeviation of 4 inches. We draw many samples of size 100 from the above populationusing repeated random sampling and record the mean height for each sample to constitutea sample means distribution (?̅ -distribution). Do the above for the distribution.
Let x1, x2, . . . , x100 denote the actual net weights (in pounds) of 100 randomly selected bags of fertilizer. Suppose that the weight of a randomly selected bag has a distribution with mean 75 lbs and variance 1 lb2. Let x be the sample mean weight (n = 100). (a) Describe the sampling distribution of x. The distribution is approximately normal with a mean of 75 lbs and variance of 1 lb2.The distribution is approximately normal with a mean of 75 lbs and variance of 0.01 lbs2. The distribution is unknown with a mean of 75 lbs and variance of 0.01 lbs2.The distribution is unknown with a mean of 75 lbs and variance of 1 lb2.The distribution is unknown with unknown mean and variance. (b) What is the probability that the sample mean is between 74.65 lbs and 75.35 lbs? (Round your answer to four decimal places.) P(74.65 ≤ x ≤ 75.35) = (c) What is the probability that the sample mean is greater than 75 lbs?
Which of the following is NOT one of the assumptions for the independent-samples t-test? A)The corresponding populations are normal. B)The corresponding populations for the samples have equal variances c)None D)The participants in the samples are independent.
Is the distribution of marital categories in the GSS representative of their distributions in the population? Let’s assume that in the U.S.: married = 48%, widowed = 6%, divorced = 12%, separated = 2%, never married = 32%. In the 2018 GSS, MARITAL is coded: 1=married, 2=widowed, 3=divorced, 4=separated, and 5=never married. Interpret the output and provide the output from this test as a part of your answer. Discuss your interpretation of the results using APA format. 1.) Assumption? 2.) Level of measurement? 3.) Null hypothesis? 4.) Research hypothesis? 5.) Select the sampling distribution and establish the critical region? 6.) Compute the test statistics? 7.) Interpret the results using APA format? *Use the graphs inserted below in images.
Suppose that 70% of residents in a certain city own at least one pet. You select a random sample of 30 city residents. Let X = the number of residents that own at least one pet. Would it be appropriate to use a normal distribution to model the sampling distribution of X? No, there are at least 10 "successes" expected, but there are not at least 10 "failures" expected. It is not appropriate to use a normal distribution to model the sampling distribution of X. No, the sample size is greater than 10, so it is not appropriate to use a normal distribution to model the sampling distribution of X. Yes, the sample size is at least 30, so it is appropriate to use a normal dist bution to model the sampling distr ution of X. Yes, there are at least 10 "successes" expected and 10 "failures" expected so it is appropriate to use a normal distribution to model the sampling distribution of X. No, there are not at least 10 "successes" expected, although there are at least 10 "failures" expected. It is…
When should a s distribution be used? When there are how many cases in a sample? When should a t distribution be used? When there are how many cases in a sample?
Suppose heights, in inches, of male orangutans have an unknown distribution with mean 60 and standard deviation 3 inches. A sample of size n = 49 is randomly taken from the population and the mean is taken. Using the Central Limit Theorem for Means, what is the sample mean distribution?
According to a recent survey of 1400 people, 65% feel that the president is doing an acceptable job. We are interested in the population proportion of people who feel the president is doing an acceptable job. NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Please label each part
In a t distribution, the critical values will always be the same (not dependent on sample size).TrueFalse
B. Explain the following: 1. What is a t-distribution? 2. When is a z-test and the t-test used?

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Under what two conditions will a sampling distribution be normally distributed? I