i) Show that the standard score of the sample mean X, is equal to Y. ii) Show that the mean and variance of the random variable Y are 0 and 1, respectively. iii) Show using the moment generating function technique that Y is a standard normal random variable.

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A: It is given that the initial standard deviation is really 20, and the sample size is 64.

Q: The following are the number of employees of 20 supermarkets:…

A: arrange data in accending order 35,45,55,55,56,56,60,65,67,69,70,71,75,76,88,89,89,90,90,103   here…

Q: . For the following set of scores: 7 5 6 4 4 3 8 9 4 7 5 5 6 9 4 7 5 10 6 8 5 6 3 4 8 5 a.…

A: Frequency is the number of times an observation occurred. Frequency distribution is used to tabulate…

Q: 1.2 canada Youth admissions to correctional services, by age and sex 2019-2020 Age at admission 12…

A: Given data: x y 12 6 13 62 14 194 15 343 16 492 17 548 18 83

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A: Type 1 error may be defined as the reject null hypothesis when null hypothesis is true.

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A: In OLS when the variance of errors are no longer constants that situation is called…

Q: a two-tailed test at the a = 0.1 ppropriate rejection regions. (Round your answers to two decimal…

A: Given a two-tailed test at the alpha = 0.1 Z critical value for two tailed test = ±1.645...........…

Q: A simple random sample of size n is drawn. The sample mean, x, is found to be 19.4, and the sample…

A:

Q: Based on a survey, assume that 28% of consumers are comfortable having drones deliver their…

A: It is given that 28% of the customers are comfortable having drones deliver their purchases.  Thus,…

Q: The accompanying table describes results from groups of 10 births from 10 different sets of parents.…

A: Formula used: The maximum value in this range = μ+2σ μ = E(X) = ∑X·P(X) E(X2) = ∑X2·P(X) σ =…

Q: Identify the type of sampling method used: AT&T selects every 40th iPod for testing and evaluation…

A: Note : There is two types of sampling methods probabilistic sampling and non probabilistic…

Q: 0 Below is a graph showing monthly average sea level observed in Key West, Florida from 1913 through…

A: The given graph shows the relationship between the monthly average sea level in Key West, Florida…

Q: s=1.99

A: Hypotheses: H0:μ=7Ha:μ<7 This is a left-tailed test as the direction of alternative hypothesis is…

Q: IQ is known to be normally distributed with a mean of 100 and standard deviation of 16. A small…

A: Given that, the sample mean is x̅= 105 sample size is n= 64 Population mean is μ= 100 and σ= 16…

Q: line​ read, "More Than Half of Americans Say Federal Taxes Too​ High." The headline was based on a…

A: given data,claim :p>0.5x=609n=1202p^=xn  =6091202  =0.5067α=0.01

Q: a) Suppose that Y₁, Y₂, ..., Y is a random sample from a normal distribution with parameter mean 0…

A:

Q: Suppose the salary of x-ray technicians is normally distributed with a population standard deviation…

A: Given,sample size(n)=55sample mean(x¯)=$61,880population standard…

Q: The following are the grades of 16 students in Life and Works of Manny Pacquiao subject:…

A: observations: 86,89,75,70,92,82,84,88,92,90,79,81,88,90,79,84   n = 16

Q: An estimate of the mean time taken by this group of workers is: A. 51.7 min B. 47.0 min C. 49.7 min…

A: First we convert histogram into frequency table,   class frequency(f) 10-20 0 20-30 2 30-40…

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A: Given that We have to find the 95% confidence interval for the difference between the two groups A…

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A: Assigning numbers to the selection unit is kind of randomization of units.Now each unit would be…

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A: Given Calculate Mean, Median, Mode mid range the following grouped data

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A: If any sales be in a 2 or 3 month interval then we know it is a seasonal.

Q: Prove if X~ N (1₁0) for M being any real number upe &o is greater than Zero, then Z= = (X-M)…

A: Given X~Nμ, σ, μ being any real number and σ is greater than zero.

Q: Course: Statistics A study conducted on the number of vehicles arriving per hour at a toll booth…

A: Solution:  Let X represent the number of vehicles per hour.  The mean number of vehicles arriving…

Q: success is p, determine the value of p approximate to three (3) decimal places. A. 0.084 / B. 0.400…

A: It is given that  Sample size, n = 10 P( X = 3 ) = 0.215 P( X = x ) = 0.251

Q: Below is a graph showing monthly average sea level observed in Key West, Florida from 1913 through…

A: The given graph shows the relationship between the monthly average sea level in Key West, Florida…

Q: The following are the grades of 16 students in Life and Works of Manny Pacquiao subject:…

A: Average=sum of the observationsno.of observations

Q: A simple random sample of size n is drawn from a population that is normally distributed. The sample…

A: Given that simple random sample of size n is drawn from a population that is normally distributed.…

Q: Consumer Research, Inc., is an independent agency that conducts research on consumer attitudes and…

A: Since you have posted a question with multiple subparts, we will solve first three subparts for you.…

Q: The table lists the smoking habits of a group of college students. Sex Non-smoker Regular Smoker…

A: sex non smoker regular smoker heavy smoker total man 135 57 5 197 woman 187 21 12 220 total…

Q: The following are data regarding number of minutes to accomplish a certain task: 121, 134, 145, 212,…

A: From the provided information, The data values are as follow: 121, 134, 145, 212, 289, 306, 367,…

Q: what does the provided table say.

A: From the given data, the table provides information about Economic prosperity.  "Not economically…

Q: Assuming the population has an approximate normal distribution, if a sample size n=16 has a sample…

A: It is given that  Sample mean = 31 Sample standard deviation = 5 Sample size = 16 Confidence level =…

Q: An investigator polls a representative sample of common cold sufferers, asking them to estimate the…

A: Given : An estimates approximate a normal curve with a mean of 91 hours and a standard deviation of…

Q: - Let X₁, he pdf is x₁ be a random sample from a normal distribution N(µ‚σ²) " 50 1 f (x | μ41₂0² )…

A: Given Xi~N(μ, σ2 ); i=1,2,...,n

Q: What is the standard error of the estimate? A) 1.595 B) 1.666 C) 0.970 D) 1.920   If there was no…

A: Close Friends Self-Esteem Mean 8.90 5.20 SD 3.75 2.15 a = 2.904  and b = 0.258

Q: Youth admissions to correctional services, by age and sex 2019-2020 Age at admission 12 year old 13…

A: Given data: Age (x) number of admissions (y) 12 6 13 62 14 194 15 343 16 492 17 548…

Q: denotes the proportion of defective products in the population. It is desirable to the the…

A:

Q: Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those…

A: given data, normal distribution , μ=100σ=15we have to find out the shaded region for the given…

Q: If Z is a normal random variable with mean 0 and standard deviation 1, find the following…

A:

Q: 2. Water samples were taken at four different locations in a river to determine whether the quantity…

A: The question is about ANOVA Given : F value = 1.81 Sig. = 0.007 Level of signif. ( α ) = 0.01   To…

Q: ➤ Let X₁,. the pdf is , Xn „be a random sample from a normal distribution N(µ,0²) SO ƒ(x|μ‚σ²)=-…

A: Given  Xi~N(population mean μ, standard deviations σ); i=1,2,...,n

Q: Answer number 1 & 2  only, provide the sampling technique, justificatio

A: Note: Hello! Thank you for your query. Because RRLs fall under the subjective category, we are only…

Q: A firm purchases a very large quantoty of metal off-cuts and wishes to know the average weight of an…

A: The information provided in the question are as follows : Sample size (n) = 625 Sample mean (x̄) =…

Q: 23. The numbers of tourists (in thousands) visiting Table Mountain in Cape Town per quarter, for…

A: From the above data table,

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A: We have given that A company producing steel nails receives an order for 5000 nails of length 50 mm…

Q: What is a measure that summarizes how well the sample regression equation fits the data? O…

A: The measure that summarizes how well the sample regression equation fits the data is…

Q: Derive the mean and variance of a Student's T distribution

A: Let us assume X is a random variable following standard normal distribution and Y is a random…

Q: In a test of the effectiveness of garlic for lowering​ cholesterol,64 subjects were treated with raw…

A: Given: n = 64 d = 0.7 sd = 1.51 α = 0.01 Formula Used: Test-statistic-t = d-μdsdn