J 1 To test Ho: μ = 33 versus H₁: µ#33, a simple random sample of size n = 40 is obtained. Complete parts (a) through (c) below.Click the icon to view the table of critical t-values.(a) Does the population have be normally distributed to test this hypothesis by using t-distribution methods? Why?O A. No-there are no constraints in order to perform a hypothesis test.OB. Yes-since the sample size is at not least 50, the underlying population does not need to be normally distributed.O C. No-since the sample size is at least 30, the underlying population does not need to be normally distributed.O D. Yes-the population must be normally distributed in all cases order to perform a hypothesis test.(b) Given sample evidence, x= 37.6 and s= 11.5, construct a 99% confidence interval to test the hypothesis.nd isThe lower bound iThe upper bound is.(Round to three decimal places as needed.)(c) Because the value lies(Type an integer or decimal. Do not round.)the confidence interval, wethe null hypothesis.fail to rejectreject

Given that: The null and alternative hypotheses is, H0:μ=33H1:μ≠33 This is two-tailed test. Sample…

Answered: To test Ho: μ = 33 versus H₁: μ#33, a…

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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In a survey of 180 females who recently completed high school, 75% were enrolled in college. In a survey of 160 males who recently completed high school, 70% were enrolled in college. At α=0.07, can you reject the claim that there is no difference in the proportion of college enrollees between the two groups? Assume the random samples are independent. Complete parts (a) through (e). Find the critical value(s) and identify the rejection region(s).
A snack food manufacturer estimates that the variance of the number of grams of carbohydrates in servings of its tortilla chips is 1.23. A dietician is asked to test this claim and finds that a random sample of 24 servings has a variance of 1.27. At α=0.10, is there enough evidence to reject the manufacturer's claim? Assume the population is normally distributed. (b) Find the critical value(s). I do not know how to calculate the critical value with my calculator. I have a TI83+.
From exercise 9-15 Find the boundary of the critical region if the type I error probability is a) alpha = 0.01 and n = 10 b) alpha = 0.05 and n=10 c) alpha = 0.01 and n=16 d) alpha = 0.05 and n=16 From exercise 9-15 standard deviation = 20 H0: mu = 175 H1: mu >175
A researcher is interested in testing whether annual house hold income in Philadelphia is normal. So she took a sample of 50 house holds and found that skewness (s)= 2.3190 and Kurtosis (k) = 6.7322. Use the Jarque- Bera Test to test , at alpha 0.05, whether income follows normal distribution. -Yes, population is normal because Chi-Square test is higher than critical value. -Yes, population is normal because Chi-Square test is less than critical value. -No, population is not normal because Chi-Square test is higher than critical value. -No, population is not normal because Chi-Square test is less than critical value.
Suppose that Y1,Y2,Y3 denote a random sample from an exponential distribution with density function f(y) = Consider the following four estimators of θ: ?1θe−y/θ, y>0,0, otherwise. θˆ =Y, θˆ =Y1+Y2, θˆ =Y1+2Y2, θˆ =Y1+Y2+Y3 =Y ̄. 11223343 Which estimators are unbiased? Among the unbiased estimators, which has the smallest variance?
A random sample of 22 women participated in a study testing whether a new banana boat sunscreen reduced their incident rate of sunburn during the summer. The average woman in the study reported getting burned 5.7 times over the past 3 months, with a SS = 179. Compare this incident rate to a rate of 7 times per 3 months. Use an alpha of .05, 2 tailed test. a) What is the t-critical value(s)? b) What is the estimated standard error? c) Compute the t-statistic. d) Make a decision regarding the null and provide a conclusion (explain what it means in regards to this particular study).
Consider a real random variable X with zero mean and variance σ2X . Suppose that wecannot directly observe X, but instead we can observe Yt := X + Wt, t ∈ [0, T ], where T > 0 and{Wt : t ∈ R} is a WSS process with zero mean and correlation function RW , uncorrelated with X.Further suppose that we use the following linear estimator to estimate X based on {Yt : t ∈ [0, T ]}:ˆXT =Z T0h(T − θ)Yθ dθ,i.e., we pass the process {Yt} through a causal LTI filter with impulse response h and sample theoutput at time T . We wish to design h to minimize the mean-squared error of the estimate.a. Use the orthogonality principle to write down a necessary and sufficient condition for theoptimal h. (The condition involves h, T , X, {Yt : t ∈ [0, T ]}, ˆXT , etc.)b. Use part a to derive a condition involving the optimal h that has the following form: for allτ ∈ [0, T ],a =Z T0h(θ)(b + c(τ − θ)) dθ,where a and b are constants and c is some function. (You must find a, b, and c in terms ofthe information…
Let X1, ..., Xn be a sample from an exponential population with parameter λ.(a) Find the maximum likelihood estimator for λ. (b) Is the estimator unbiased?(c) Is the estimator consistent?
Calculate the t-test statistic using the standard error from part a. t= At α=0.02 , Use the distribution table to find the critical values for the rejection regiontc=±____
To achieve statistical significance for a one-sample t-test, is which of the following? the t-obtained must be less than the t-critical. the t-obtained must be larger than the t-critical (farther into the region of rejection). the t-obtained must differ from the t-critical by .05. the t-obtained must equal the t-critical.
A random sampleY1 , Y 2 , ⋯,Yn is drawn from a distribution whose probability density function is given by: f (Y ) = βe − βY , Y  0 & β > 0 a). Obtain the maximum likelihood estimator (MLE) of β. b). Given that ∑ n Y i = 25 , ∑n Yi 2 = 50 , n = 50 calculate the maximum likelihood i =1 i =1 estimate of β. ( c). Using the same data as in part (b), test the null hypothesis that β =1against the alternative hypothesis that β ≠1at 5% level of significance
To test H0: σ=2.1versus H1: σ<2.1, a random sample of size n=21 is obtained from a population that is known to be normally distributed. If the sample standard deviation is determined to be s=1.9, compute the test statistic. χ20 If the researcher decides to test this hypothesis at the α=0.05 level of significance, determine the critical value. Draw a chi-squared distribution and depict the critical region Will the researcher reject the null hypothesis? Why? Choose the correct answer below. A. Yes,because χ20<χ20.95. B. No, because χ20<χ20.95. C.No, because χ20>χ20.95. D. Yes, because χ20>χ20.95

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