Benford's Law states the probability distribution (below) of the first significant digit in a number. Digit Probability 1 2 3 4 5 6 7 8 0.301 0.176 0.125 0.097 0.079 0.067 0.058 0.051 The Fibonacci Sequence, found in the number of pedals on a pine cone, the number of seeds on a sun- flower and many other places in nature is 1, 1, 2, 3, 5, 8, 13, 21... The next number in the sequence is found by summing up the previous two numbers. The distribution of the first significant digit of the first 85 numbers in the sequence is below. Does this distribution follow to Benford's Law? [Hint: Goodness of Fit] 1 Digit 2 3 Frequency 25 16 11 4 5 6 7 7 5 9 0.046 7 8 9 4 6 4

Q: 3. Calculate the mean, median, mode, variance, and standard deviation for each of the following two…

A: Given the data on two groups A and B.want to calculate the mean, median, mode, variance, and…

Q: A survey of 40 people was conducted to compare their self-reported height to their actual height.…

A: Solution-:Given: The mean difference  The sample mean The ssample standard deviation the sample size…

Q: A company providing mobile phone service plans has a list of phone numbers for their 250,000…

A: The provided information is as follows:The sample size is .The sample size is .The sample standard…

Q: Let x1, . . . , xn iid from N(µ, σ^2 ) where σ^2 = 1. (a) Show that the Jeffreys prior for the…

A: The provided information is as follows:The  are iid from  such as .

Q: The number of calls into a call center for any given interval often follows a Poisson distribution.…

A: The provided information is as follows:The number of calls to a call center for any particular day…

Q: 3.3-3. If Z is N(0, 1), find values of c such that a. P(Z > c) = 0.025. b. P(|Z| ≤ c) = 0.95.

A: Question 3.3-3)The standard normal variable is normally distributed with mean 0 and a variance 1.…

Q: The data show the chest size and weight of several bears. Find the regression equation, letting…

A: The data set is,Chest Size (inches)585065595948Weight (pounds)414312499450456260

Q: A study by researchers at a university addressed the question of whether the mean body temperature…

A: Given,Population mean, μ = 99.4°F.Sample size, n = 102Claim :- The mean body temperature of healthy…

Q: An article included data from a survey of a random sample of adults living in the United States. Of…

A: n=sample size=1300 X=700

Q: After a comprehensive survey is conducted, you are presented with the accompanying data on the total…

A: The total incomes of the “upper class”, the “middle class”, and the “lower class” in five parishes…

Q: Two catalysts may be used in a batch chemical process. Twelve batches were prepared using catalyst…

A: From the provided information,

Q: The test statistic is (Type an integer or a decimal. Do not round.) The critical value is (Round to…

A: The given data is as follows:

Q: In a poll of 200 randomly selected U.S. adults, 108 said they favored a new proposition. Based on…

A: Solution

Q: Two samples are taken with the following sample means, sizes, and standard deviations #1 = 37 52 =…

A: The objective of this question is to estimate the difference in population means using a 91%…

Q: 9.14. A pair of fair dice is rolled. Let { [1 if the sum of the dice is 6 0 otherwise X = and let y…

A: For random variable Y:Y takes values from 1 to 6 with equal probabilities since it represents the…

Q: USA Today reports that the average expenditure on Valentine's Day was expected to be $100.89. Do…

A: The question is about confidence interval.Given :No. of male consumers in a survey ( n1 ) = 54Sample…

Q: 1. Hypothesis testing: A local dog rescue organization claims that it rescues, on average μ = 55…

A: The given data is as follows:Population mean, Population standard deviation, Sample mean, Sample…

Q: Find the margin of error for the given values of c, s, and n. c=0.90, s = 4, n=9 Click the icon to…

A: Given,n=9s=4c=0.90 implies Critical value will be given by as follows:

Q: ]/v[ The final answer for the test statistic from technology is as follows: Round to 2 decimal…

A: The amount of sugar in a Krispy Kreme glazed donut is 10 g.  Want to test whether the mean amount of…

Q: esc V A private college advertised that last year their freshman students, on average, had a score…

A: The question is asking us to determine which of the given statements must be true based on the…

Q: Use a t-distribution to find a confidence interval for the difference in means using the relevant…

A: We have given a paired data set as follows: CaseTreatment 1Treatment 21211822831330254242252821We…

Q: Listed below are foot lengths (mm) and heights (mm) of males. Find the regression equation, letting…

A: Foot Lenth…

Q: Conduct the hypothesis test and provide the test statistic and the critical value, and state the…

A: Answer Given The level of significance = 0.10degree of freedom = n-1 = 6-1 = 5Total sample size [N]…

Q: Suppose 239 subjects are treated with a drug that is used to treat pain and 53 of them developed…

A: The objective of this question is to test the claim that more than 20% of users develop nausea after…

Q: Consumer Reports uses a survey of readers to obtain customer satisfaction ratings for the nation's…

A: We have given sample data representative of independent samples of Publix and Trader Joe's…

Q: Use the accompanying paired data consisting of weights of large cars (pounds) and highway fuel…

A: The given data is as follows: Weight (pounds)Highway Fuel Consumption…

Q: Find the critical values X and x for the given confidence level c and sample size n. c=0.99, n=15…

A: Confidence level : c=0.99Sample size: n=15

Q: The mean price for used cars is $10,955. A manager of a Kansas City used car dealership reviewed a…

A: Given the data on sales price.want to test

Q: Table 1 Chi-Square Results of the Percent of Students Exhibiting Each Quantitity- Frequency Level…

A: The observed percentages for the quantitative frequency level of all students and the gender from…

Q: The p-value for the hypothesis test  The test statistic for the hypothesis test

A: The data shows the marital status and location of residence.

Q: A dietitian wishes to see if a person's cholesterol level will change if the diet is supplemented by…

A: The given data is as follows:Subject BeforeAfter1210190220517032082104192188517817362442287211198

Q: Words were displayed on a computer screen with background colors of red and blue. Results from…

A:

Q: Use the contingency table to the right to (a) calculate the marginal frequencies, and (b) find the…

A: Given :Observed frequency table:ExcellentFairPoorSeats 100 or fewer181209168Seats over 100185312153

Q: Find the critical value ze necessary to form a confidence interval at the level of confidence shown…

A: The confidence level is 0.80.

Q: You wish to test the following claim (H) at a significance level of a = 0.02. Ho: p=79.9 Ha : μ <…

A: We have to test the hypothesisThe population is normally distributed, and the population standard…

Q: 3.3-2. If Z is N(0, 1), find c. P(-2.31 ≤ Z ≤ -0.65). e. P(Z 2).

A: Z∼N(0,1)Objective:Find the following probabilities:

Q: The incomes of a group of 10,000 persons were found to be normally distributed with mean equal to…

A: Given that, the income of the group is normally distributed.Total number of people: Mean: Standard…

Q: A researcher wants to know if there is a difference between the mean amount of sleep that people get…

A: Answer Given,Total sample size [N] = 9+7+8 = 24

Q: ANOVA results CHEST Between Groups Within Groups Total Sum of Squares 223.750 860.167 1083.917 Print…

A: The claim is that the different car sizes have the same mean amount of chest compression.

Q: Under the last-in, first-out (LIFO) inventory valuation method, a price index for inventory must be…

A: The quantity weights are given below:ProductQ1P0P1A5000.150.21B501.61.8C1004.54.2D401113.20

Q: The following frequency distribution reports the number of frequent flier miles, reported in…

A: Note: “Since you have posted a question with multiple sub parts, we will provide the solution only…

Q: Compute the Poisson distribution P(v) for µ = 0.5 and v = 0, 1, . . ., 6. ar histogram of Pos(v)…

A: Given that

Q: A liquid soap bottle is advertised with a content of 310 milliliters​ (mL). Ten bottles are randomly…

A: x313306309299297317315296304308

Q: Based on the data shown below, calculate the correlation coefficient (to three decimal places) X y…

A: The data values…

Q: Q4: It is said that a fully charged cell phone battery can last about 9 hours on average with a…

A: For the distribution of the lifetime (in hours) of a fully charged cellphone battery, it is given…

Q: 1. Prove that e²+1 = (1 - ₁)²e²+ n²

A: It is to be proven that

Q: The times of the finishers in the Toronto City 10km run are normally distributed with mean of 51…

A: The times of the finishers in the Toronto City 10km run are normally distributed with mean of 51…

Q: 12.7  Determine the test statistic.   Determine the​ P-value.   Determine the proper conclusion…

A: Right-HandedLeft-HandedFemale857871879857874886785847896813Male94410019099169031030913915947977

Q: The table below includes results from polygraph (lie detector) experiments conducted by researchers.…

A: The given data is as follows: Did the Subject Actually Lie ?NoYesPolygraph test indicated that the…

Q: Annual high temperatures in a certain location have been tracked for several years. Let X represent…

A: The formula of correlation is,where,SSXX denotes the sum of squares of XSSXY denotes the product of…