The built-in data set, rock, is a data frame recording the measurements of rock sample from a petroleum reservoir. We are interested in the area column of rock. Using R we can convertthis column into the vector x by the assignment x<-rock$shape. Assume that the n area measurements x=(X₁, X₂,...,xn) are a random sample from a population with true unknownmean μ and true unknown variance 2. Remember, let x be defined by x<-rock$shape.a) Calculate, n, the number of elements in x. 48b) Calculate the sample standard deviation s, of x.c) Estimate true mean μ, using this data by calculating the sample mean.d) Calculate the sample variance of x.e) Calculate the interquartile range of x, using R.f) Calculate the 50th percentile of x using R.g) Calculate a trimmed mean for x using R.48h) Since the sample size is >30 we can create a confidence interval for μ using a normal critical value. If we want the confidence interval to be at the 94% level and we use a normalcritical value, then what critical value should we use?i) Calculate a 94% confidence interval(using a normal critical value) for μ.

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Answered: b) Calculate the sample standard…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Researchers conducted a study to determine whether magnets are effective in treating back pain. Pain was measured using the visual analog scale, and the results shown below are among the results obtained in the study. Higher scores correspond to greater pain levels. 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) to (c) below. Reduction in Pain Level After Magnet Treatment (u): n=22, x=0.58, s=0.89 Reduction in Pain Level After Sham Treatment (H2): n=22, x=0.51, s = 1.29 OA. Ho: H₁₂ H₁₁₂ H₁₁
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A magazine claims that the mean amount spent by a customer at Burger Stop is greater than the mean amount spent by a customer at Fry World. The results for samples of customer transactions for the two fast food restaurants are shown below. a= 0.10, can you support the magazine's claim? Assume the population variances are equal. Assume the samples are random and independent, and the populations are normally distributed. Complete parts (a) through (e) below. Burger Stop Fry World Xy = $9.13 5 = $0.78 X2 = $8.50 S2= $0.68 n= 17 n =8 (a) Identify the claim and state Ho and H. Which is the correct claim below? O A. "The mean amount spent by a customer at Fry World is greater than the mean amount spent by a customer at Burger Stop." "The mean amount spent by a customer at Burger Stop is greater than the mean amount spent by a customer at Fry World." Oc. "The mean amount spent by a customer at Burger Stop is not equal to the mean amount spent by a customer at Fry World." O D. "The mean amount…
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Assume the samples are random and independent, the populations are nomally distributed, and the population variances are equal. The table available below shows the prices (in dollars) for a sample of automobile batteries. The prices are classified according to battery type. At a = 0.10, is there enough evidence conclude that at least one mean battery price is different from the others? Complete parts (a) through (e) below. E Click the icon to view the battery cost data. (a) Let u1. P2. H3 represent the mean prices for the group size 35, 65, and 24/24F respectively. Identify the claim and state Ho and H. H Cost of batteries by type The claim is the V hypothesis. Group size 35 Group size 65 Group size 24/24F 101 111 121 124 D 146 173 182 278 124 140 141 89 (b) Find the critical value, Fo, and identify the rejection region. 90 79 84 The rejection region is F Fo, where Fo = (Round to two decimal places as needed.) (c) Find the test statistic F. Print Done F= (Round to two decimal places as…
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Researchers conducted a study to determine whether magnets are effective in treating back pain. Pain was measured using the visual analog scale, and the results shown below are among the results obtained in the study. Higher scores correspond to greater pain levels. 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) to (c) below. Reduction in Pain Level After Magnet Treatment (μ1): n=29, x=0.58, s=0.95 Reduction in Pain Level After Sham Treatment (μ2): n=29, x=0.48, s=1.56 Question content area bottom Part 1 a. Use a 0.05 significance level to test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment (similar to a placebo). What are the null and alternative hypotheses? A. H0: μ1≠μ2 H1: μ1<μ2 B. H0: μ1<μ2 H1:…
Find x °x and Ps for all possible samples of 187 values taken from a Normally distributed population with u = 66.34 and o = 44.02 What is the mean of the population consisting of all possible sample means? %3D What is the standard deviation of the population consisting of all possible sample means? What is the variance of the population consisting of all possible sample means? %3D What is the mean of the population consisting of all possible sample variances? %3D (Round to 4 decimal places as needed) Vi (1,1) More Clear all Ask my instructor
Researchers conducted a study to determine whether magnets are effective in treating back pain. Pain was measured using the visual analog scale, and the results shown below are among the results obtained in the study. Higher scores correspond to greater pain levels. 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) to (c) below. Reduction in Pain Level After Magnet Treatment (μ1): n=27, x=0.46, s=0.89 Reduction in Pain Level After Sham Treatment (μ2): n=27, x=0.42, s= 1.43 * Find the t stat * Find the p value * state the conclusion * Does the confidence interval support the conclusion of the test * Does it appear that magnets are effective in treating back pain? Is it valid to argue that magnets might appear to be effective if the sample sizes are larger? * Is it valid to argue that magnets might appear to be…

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b) Calculate the sample standard deviation s, of x. [ c) Estimate true mean μ, using this data by calculating the sample mean. d) Calculate the sample variance of x. |