BIG Corporation advertises that its light bulbs have a mean lifetime, μ, of 2800 hours. Suppose we have good reason to believe that μ is different from 2800hours and decide to do a statistical test of the claim. We choose a random sample of light bulbs manufactured by BIG and find that the mean lifetime for thissample is 2600 hours and that the sample standard deviation of the lifetimes is 600 hours.Based on this information, complete the parts below.(a)What are the null hypothesis Ho and the alternative hypothesis H₁ that should be used for the test?Ho :OH₁ :0(b) Suppose that we decide to reject the null hypothesis. What sort of error might we be making?(Choose one) ▼(c) Suppose the true mean lifetime of BIG's light bulbs is 2800 hours. Fill in the blanks to describe a Type I error.(Choose one)A Type I error would be (Choose one) the hypothesis that u is (Choose one)when, in fact, μ is (Choose one)▼μ0<0XXOSOΠΣΠ 0=05ロ<ロS

Given that Claim: We have good reason to believe that μ is different from 2800 hours. a)Hypothesis :…

Answered: BIG Corporation advertises that its…

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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An ecologist is studying the impact of local polluted waters on the growth of alligators. The length of adult male alligators typically follows a normal distribution with a standard deviation of 2 feet. The ecologist wants to estimate the mean length of this population of alligators. Suppose she samples n alligators at random and uses the sample mean, X to as an estimator for u. a. What is the bias and variance of the estimator? (Note, these may be a function of n.) b. If n = 4, what is the probability that the estimator is within one foot of the true mean? (I.e. find P(|X – µ| < 1). c. What sample size, n, is required for the estimator to be within one foot of the true mean with 95% probability? (I.e. find the value of n that satisfies P(|X – µ| < 1) = 0.95.) d. Suppose the ecologist ends up sampling n = 9 alligators and calculates a sample mean of ī = 10.4 feet. Construct a 95% confidence interval for the population mean. e. Give an interpretation for the interval obtained in (d).
An IQ test is designed so that the mean is 100 and the standard deviation is 10 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 95% confidence that the sample mean is within 2 IQ points of the true mean. Assume that σ=10 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.
BIG Corporation advertises that its light bulbs have a mean lifetime, µ, of 2800 hours. Suppose we have good reason to believe that µ is different from 2800 hours and decide to do a statistical test of the claim. We choose a random sample of light bulbs manufactured by BIG and find that the mean lifetime for this sample is 2980 hours and that the sample standard deviation of the lifetimes is 650 hours. Based on this information, complete the parts below. (a) What are the null hypothesis Ho and the alternative hypothesis H₁ that should be used for the test? H₂O Ho 0 H₁ :0 (b) Suppose that we decide not to reject the null hypothesis. What sort of error might we be making? (Choose one) (c) Suppose the true mean lifetime of BIG's light bulbs is 3000 hours. Fill in the blanks to describe a Type II error. A Type II error would be (Choose one) ▼the hypothesis that μ is (Choose one) (Choose one) when, in fact, u is (Choose one) μ 0<0 ロミロ × XI □<口 0=0 □≠ロ Ś
sisin, 2 Calculate Quartile Deviation and its Coefficient from the following data : Weight (in pounds) 140 150 160 120 122 124 126 130 No, of Students 1 1 3. 10 Solutian
A simple random sample of 25 has been collected from a normally distributed population for which it is known the standard deviation is 17. The sample mean has been calculated as 342 and the sample standard deviation of 14.9. Construct a 95% confidential interval for the population mean
The frequency distribution was obtained using a class width of 0.5 for data on cigarette tax rates. Use the frequency distribution to approximate the population mean and population standard deviation. Compare these results to the actual mean μ=$1.502 and standard deviation σ=$1.031.
The average age of trees in a large local park is 60 years with a standard deviation of 2.2 years A simple random sample of 4 trees is selected, and the sample mean age z of these trees is computed. The percentage of trees older than 60.1 years is
In the year 2033, Sarai Patterson is a leading traveling nurse. Sarai is interested in reducing the mean recovery time for patients after experiencing a serious injury (assume recovery times are normally distributed). Suppose the mean recovery time is presently 8.6 months. Sarai takes a random sample of 46 patients that have experienced serious injury to participate in a new treatment program and finds the sample mean is 8.1 months and a sample standard deviation of 1.2 months. Using α = 0.05, answer the following questions. a) What is the setup for your null and alternative hypothesis? b) What is the value of the test statistic? c) What is/are the critical value(s)?
if the population standard deviation is 1.6, then Find the standard deviation of x forb an SRS of 68 observations
a distribution with a mean of u=41 and a standard deviation of 4 is transformed into a standardized distribution with a mean of u=100 and a standardized deviation =20, find the new standardized score for each of the following values from the original population, x=39, x=36, x=45, x=50
D A small amount of the trace element selenium, 50-200 micrograms (ug) per day, is considered essential to good health. Suppose that random samples of 50 adults were selected from two regions of the United States and that each person's daily selenium intake was recorded. The means and standard deviations of the selenium daily intakes for the two groups are shown in the table. Sample Mean (ug) Sample Standard Deviation (ug) Find a 95% confidence interval for the difference (₁-₂) in the mean selenium intakes for the two regions. (Round your answers to three decimal places.) 49 Region Phase One-Tw_docx 1 167.4 22.8 ug to Interpret this interval, O The probability that the difference in the average daily selenium intake for the populations in Region 1 and Region 2 is exactly in the middle of the Interval is 95%. A 2 140.5 17.3 O The probability that the difference in the average daily selenium intake for the populations in Region 1 and Region 2 is within the interval is 95%. We are 95%…
a=1 b=8 c=6 d=0

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