10Benford's Law states that the first nonzero digits of numbers drawn at random from a large complex datafile have the following probability distribution.tFirstNonzeroDigitProbabili10.30120.176First Nonzero Digit 1Sample FrequencyUSE SALT30.1252 380 55 33State the null and alternate hypotheses.Ho: The distributions are different.H: The distributions are different.H: The distributions are the same.H: The distributions are different.H₁: The distributions are the same.0.0974Are all the expected frequencies greater than 5?Yes NoWhat sampling distribution will you use?uniform binomialWhat are the degrees of freedom?422normal chi-square50.079tySuppose that n = 275 numerical entries were drawn at random from a large accounting file of a majorcorporation. The first nonzero digits were recorded for the sample.60.067Ho: The distributions are the same.Ho: The distributions are the same.Ho: The distributions are different.(c) Estimate the P-value of the sample test statistic.P-value > 0.100 0.050 < P-value < 0.1000.005< P-value < 0.010 P-value < 0.0055621 18713Use a 1% level of significance to test the claim that the distribution of first nonzero digits in thisaccounting file follows Benford's Law.(a) What is the level of significance?Student's t70.05888170.051(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at leastthree decimal places. Round the test statistic to three decimal places.)91690.046(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis ofindependence?0.025 < P-value < 0.050 0.010 < P-value < 0.025Since the P-value > a, we fail to reject the null hypothesis. Since the P-value > a, we reject the nullhypothesis.Since the P-value s xx, we reject the null hypothesis. Since the P-values a, we failto reject the null hypothesis.(e) Interpret your conclusion in the context of the application.At the 1% level of significance, the evidence is sufficient to conclude that the distribution of first nonzerodinite in the secounting file do not follow Danford'e LowAt the 10 laual of signifinonan the suidonea.

Given that sample size (n) = 275 Non-zero digit Sample frequency (O) Probability according to…

Answered: Use a 1% level of significance to test…

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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Given the below is a bivariate distribution for the random variables x and y P(x,y) x Y 0.20 30 80 0.50 40 50 0.30 50 60 A. Draw a histogram of the probability distribution for both x and y B. Compute the covariance and correlation for x and y C. Are x and y positively related, negatively related, or unrelated Please do not solve using Microsoft Excel. My professor is not teaching using excel. I would like to see the steps taken to getting the solution for my own reference to study.
S - A study was done using a treatment group and a placebo group. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.01 significance level for both parts. a. Test the claim that the two samples are from populations with the same mean. What are the null and alternative hypotheses? OA. Ho: H₁ = 42₂ H₁: Hy > H₂ @ View an example Get more help. 2 C. Ho: H₁ = 4₂ H₁: Hy #4₂ The test statistic, t, is -1.32. (Round to two decimal places as needed.) The P-value is (Round to three decimal places as needed.) W S X command # 3 80 F3 E D с $ 4 a FA R F % 5 V FS T G 6 B MacBook Air & FG Y H & 7 N 8 41 F7 U J OB. Ho: 2 Η.: μη Σμη OD. Ho: H₁ H₂ H₁ H₁ H₂ * 8 M DII FO I ( 9 K DD F9 O < I ) O L command 4 F10 P . - : t ; Clear all option F11 { [ + ? 1 = 3CX5 Treatment Placebo H₂ 35 an Check answer…
How is the t distribution different from the Z distribution? a. The t distribution does not have any negative numbers. b. The t distribution is asymmetrical; that is, it is not a mirror image on each side of the population mean. c. The t distribution is wider than the Z distribution due to lower sample size. d. All of the above are differences between the t and Z distributions
Each of the boxplots shown summarizes 24 student scores on a recent test in two different classes. The boxplots are drawn using a common numerical scale. Which of the following must be true? 1. The lower 25% of Class B are much more spread out than the lower 25% of Class A 2. More people scored below the lower quartile for Class A than Class B 3. The distribution for Class B is skewed left and has a noticeable outlier as well, while the distribution for Class A is somewhat skewed right 4.Class A had more people between the median and the lower quartile than Class B. 3.The distribution for Class A is somewhat symmetric, while the distribution for Class B is skewed right with a noticeable outlier as well
Which one of the following statements is false? O 4 statistical hypothesis is a statement about the parameters of one or more populations. T = has a t- distribution with n – 1 degrees of freedom. s/ n P(type I error) = P(reject H, when H, is true) Failing to reject the null hypothesis when it is false is defined as a type II error.
Is it possible for the 50th percentile of a distribution to be equal to the 60th percentile? Why or why not? A. No, because you won’t get the same result multiplying by 50 as you do by 60. B. No, because there will always be some values of the distribution in between the 50th and 60th percentiles. C. Yes, this can happen if the distribution is uniform. D. Yes, this can happen if there are many members of the population with the same value.
A weight-loss clinic advertised that last month its patients, on average, lost 6 lb. Assuming that average refers to the mean, which of the following claims must be true based on this information? Note: More than one statement could be true. If none of the statements is true, mark the appropriate box. Last month, the number of their clients who lost 6 lb or more was equal to the number of their clients who lost 6 lb or less. Last month at least one of their patients lost exactly 6 lb. Last month at least one of their patients lost less than 10 lb. Two months ago some of their patients lost at least 6 lb. Last month all of their patients lost 6 lb or more. None of the above statements are true. X Ś A 181 Aa ?
Which of the following statements about Chebyshev's theorem is correct? B. Chebyshev's theorem states that all data points lie within three standard deviations of the mean in A. Chebyshev's theorem is only applicable to discrete distributions. any distribution. C. Chebyshev's theorem applies only to positively skewed distributions. D. Chebyshev's theorem applies to any distribution, regardless of its shape. E. Chebyshev's theorem is limited to normal distributions only. F. Chebyshev's theorem guarantees that at least 75% of data lie within three standard deviations of the mean in any distribution. 6. If a data set has a standard deviation of 18 and mean of 70, according to Chebyshev's theorem, what is the interval that must contain at least 19% of the data? A 50 to 90 3 B. 55 to 85 C. 20 to 80 D. 40 to 60 E. 35 to 65 F. None of the above Fina
I need help with parts 2,3, and 6
Which of the following is the best statement of the Law of Large Numbers? If the parent population (from which the data are drawn) is normally distributed, then the sample mean, , will follow a normal distribution. For bell-shaped data, approximately 68% of the data will be within one standard deviation of the mean, about 95% of the data will be within two standard deviations of the mean, and approximately 99.7% of the data will be within three standard deviations of the mean. If the sample size is large, the sample mean will be close to the population mean µ If the sample size is large, the shape of the sampling distribution of the sample mean will be approximately normal.
If the null hypothesis is true in a test of the Pearson’s correlation between X and Y, then __________. a. higher scores of X are paired with higher scores of Y b. none of mentioned here c. higher scores of X are paired with low and high scores of Y d. higher scores of X are paired with lower scores of Y e. lower scores of X are paired with higher scores of Y
The following data are from a completely randomized design. In the following calculations, use a = 0.05. Treatment Treatment Treatment 2 3 64 82 69 47 71 53 54 87 60 35 64 46 50 76 57 2 148.67 108.67 96.67

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