Recall that Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Now suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 218 numerical entries from the file and r = 51 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. (i) Test the claim that p is less than 0.301. Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. О н р- 0.301; н,: р> 0.301 О но: р - 0.301; н,: р < 0.301 О но: р< 0.3013B н,: р - 0.301 О но: р- 0.3013B н,: р#0.301 (b) What sampling distribution will you use? O The standard normal, since np > 5 and ng > 5. O The Student's t, since np < 5 and ng < 5. O The standard normal, since np < 5 and ng < 5. O The Student's t, since np > 5 and ng > 5. What is the value of the sample test statistic? (Round your answer to two decimal places.) (c) Find the P-value of the test statistic. (Round your answer to four decimal places.)

Q: answers were wrong.

A: X Frequency 0 2 1 6 2 8 3 36 4 50 5 68 6 55 7 36 8 19 9 10 10 4

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Q: ARE YOU SURE ABOUT PART 2 ?

A: which is constant.

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A: From the obtained results, the p-value is 0.0676.

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A:

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A: Our objective is given below:

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A:

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Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related. 

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.