You would like to construct a 95% confidence interval to estimate the population mean PCB (Polychlorinated biphenyl) level in white croaker fish from the SanFrancisco Bay. The random sample we select has a mean of 628 parts per million and a standard deviation of 50 parts per million.(a) What is the best point estimate, based on the sample, to use for the population mean?parts per millionSampling scenario(b) For each of the following sampling scenarios, determine which distribution should be used to calculate the critical valuefor the 95% confidence interval for the population mean.(In the table, Z refers to a standard normal distribution, and t refers to a t distribution.)The sample has size 14, and it is from a normally distributedpopulation with an unknown standard deviation.The sample has size 15, and it is from a normally distributedpopulation with a known standard deviation of 48.The sample has size 100, and it is from a non-normally distributedpopulation.NXtŚCould useeither Z or tUnclearXS

Sample mean = 628Standard deviation = 50

Answered: You would like to construct a 95%…

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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The composite ACT scores for Idaho students who took the test in 2019 have average 22.3 with the standard deviation 2.25 and approximately normal distributed. In a random sample of 49 students who took the exam in 2019, the average composite ACT score is 23.5 with standard deviation 1.06. Suppose 49 is a large sample size, the sampling distribution of the average composite ACT scores of 49 students in Idaho is approximately:___________________(give the mean and standard deviation. For random samples of 49 students who took the exam in 2019, what is the probability that the average composite ACT score is 22 or less? For random samples of 49 students who took the exam in 2019, what is the probability that the average composite ACT score is 23 or more? Find the 85th percentile for the average of composite ACT score of sample 49 students.
An article in the San Jose Mercury News stated that students in the California state university system take 4.5 years, on average, to finish their undergraduate degrees. Suppose you believe that the mean time is longer. You conduct a survey of 43 students and obtain a sample mean of 5.1 with a sample standard deviation of 1.2. Do the data support your claim at the 1% level?Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) a. State the null and alternative hypotheses b. In words, state what your random variable X represents. c. State the distribution to use for the test. (enter your answer in the form z or tdf)
Question: A paper manufacturer requires a minimum strength of 20 pounds per square inch. To check on the quality of the paper, a random sample of 10 pieces of paper is selected each hour from the previous hour’s production and a strength measurement is recorded for each. Assume that the strength measurements are normally distributed with a standard deviation ? = 2 pounds per square inch. Required: What is the approximate sampling distribution of the sample mean of ? = 10 test pieces of paper? If the mean of the population of strength measurements is 21 pounds per square inch, what is the approximate probability that, for a random sample of ? = 10 test pieces of paper, ?̅ = 20?
You are interested in estimating the the mean weight of the local adult population of female white- tailed deer (doe). From past data, you estimate that the standard deviation of all adult female white-tailed deer in this region to be 23 pounds. What sample size would you need to in order to estimate the mean weight of all female white-tailed deer, with a 97% confidence level, to within 8 pounds of the actual weight? Type your answer in the following format: [xxx,xxx] with no space inside the brackets. An alternative is to type a single number (not in brackets) if the system marks you incorrect, bear in mind that I do check all answers. Sample Size:
You are interested in testing whether the average age of household heads is higher in the suburbs than in inner city neighbourhoods. A survey is conducted, and the following results are obtained. In the suburbs, the household heads of the 45 households surveyed had a mean age of 44 with a standard deviation of 15. In the inner city, the mean age of the 40 household heads surveyed was 38 with a standard deviation of 13. Assuming that the populations from which these samples were drawn have equal variances, can you conclude that the difference between the two means is significant at the 95% level of confidence? (d) Calculate the value of t* (e) What is the p-value associated with the test statistic? (f) What conclusion do you reach about the null hypothesis? Explain.
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Ideal Number of Children Frequency 0. 11 27 528 262 63 10 4. 8. 6. 0. 10 11 H23456
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An article in the San Jose Mercury News stated that students in the California state university system take 4.5 years, on average, to finish their undergraduate degrees. Suppose you believe that the mean time is longer. You conduct a survey of 42 students and obtain a sample mean of 5.1 with a sample standard deviation of 1.2. Do the data support your claim at the 1% level?Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)
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According to the Center for Disease Control and Prevention (CDC), the mean life expectancy in 2015 for non‑Hispanic black females was 78.1 years. Assume that the standard deviation was 15 years, as suggested by the Bureau of Economic Research. The distribution of age at death, ?, is not normal because it is skewed to the left. Nevertheless, the distribution of the mean, x¯, in all possible samples of size ?n is approximately normal if ? is large enough, by the central limit theorem. Let x¯ be the mean life expectancy in a sample of 100 non‑Hispanic black females. Determine the interval centered at the population mean ? such that 95% of sample means x¯ will fall in the interval. Give your answers precise to one decimal What are the upper and lower limits?
Use the given information to find the number of degrees of freedom, the critical values χL2(chi_L^2), χR2 (chi_R^2), and the confidence interval estimate of σ. It is reasonable to assume that a simple random sample has been selected from a population with a normal distribution. Platelet Counts of Women 99% confidence; n=40, s=65.9. What should replace the question marks. Round to 3 decimal places if necessary. df = ? χL2= ? χR2= ? The confidence interval estimate of σ is ?<σ<?

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