An Introduction to Mathematical Statistics and Its Applications (6th Edition)
6th Edition
ISBN: 9780134114217
Author: Richard J. Larsen, Morris L. Marx
Publisher: PEARSON
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Chapter 6.4, Problem 8Q
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A random sample of size 36 from a population with known
variance, o = 9, yields a sample mean of x = 17. Find ß, for
testing the hypothesis H,: u = 15 versus H1 : =16. Assume
a 0.05.
%3D
%3D
Consider the test of hypothesis H0: mu=1150 against the alternative Ha: mu > 1150. Suppose n = 100 samples X1, ... , Xn were selected from a normal distribution with mean mu and variance 900. Determine the rejection region for this test at the level of significance alpha=0.025
Let T = (bar{X} - 1150) / (30/sqrt{n} )
where
bar{X} = (X1, ... , Xn)/n is the sample mean
sqrt{n} is the square root of n.
Answer choice
A. T > -1.645
B. T < -1.96
C. T > 1.96
D. T < -1.645
According to a researcher, the average level of mercury uptake in wading birds in Everglades has
declined over the past several years. Ten years ago, the average level was 15 parts per million (ppm).
Suppose we are interested in testing whether the average level today is less than 15 ppm. Describe
the type I error for the test of hypothesis.
O The mean mercury level is equal to 15 ppm when in fact the mean is less than 15 ppm.
O The mean mercury level is less than 15 ppm when in fact the mean is equal to 15 ppm.
O The mean mercury level is greater than 15 ppm when in fact the mean is equal to 15 ppm.
Chapter 6 Solutions
An Introduction to Mathematical Statistics and Its Applications (6th Edition)
Ch. 6.2 - State the decision rule that would be used to test...Ch. 6.2 - An herbalist is experimenting with juices...Ch. 6.2 - (a) Suppose H0:=0 is rejected in favor of H1:0 at...Ch. 6.2 - Company records show that drivers get an average...Ch. 6.2 - If H0:=0 is rejected in favor of H1:0, will it...Ch. 6.2 - A random sample of size 16 is drawn from a normal...Ch. 6.2 - Recall the breath analyzers described in Example...Ch. 6.2 - Calculate the P-values for the hypothesis tests...Ch. 6.2 - Suppose H0:=120 is tested against H1:120. If =10...Ch. 6.2 - As a class research project, Rosaura wants to see...
Ch. 6.2 - As input for a new inflation model, economists...Ch. 6.3 - Commercial fishermen working certain parts of the...Ch. 6.3 - Efforts to find a genetic explanation for why...Ch. 6.3 - Defeated in his most recent attempt to win a...Ch. 6.3 - Suppose H0:p=0.45 is to be tested against H1:p0.45...Ch. 6.3 - Recall the median test described in Example 5.3.2....Ch. 6.3 - Among the early attempts to revisit the death...Ch. 6.3 - What levels are possible with a decision rule of...Ch. 6.3 - Suppose H0:p=0.75 is to be tested against H1:p0.75...Ch. 6.4 - Recall the Math for the Twenty-First Century...Ch. 6.4 - Carry out the details to verify the decision rule...Ch. 6.4 - For the decision rule found in Question 6.2.2 to...Ch. 6.4 - Construct a power curve for the =0.05 test of...Ch. 6.4 - If H0:=240 is tested against H1:240 at the =0.01...Ch. 6.4 - Suppose n=36 observations are taken from a normal...Ch. 6.4 - If H0:=200 is to be tested against H1:200 at the...Ch. 6.4 - Will n=45 be a sufficiently large sample to test...Ch. 6.4 - If H0:=30 is tested against H1:30 using n=16...Ch. 6.4 - Suppose a sample of size 1 is taken from the pdf...Ch. 6.4 - Polygraphs used in criminal investigations...Ch. 6.4 - Prob. 12QCh. 6.4 - Prob. 13QCh. 6.4 - A sample of size 1 is taken from the pdf...Ch. 6.4 - Prob. 15QCh. 6.4 - Prob. 16QCh. 6.4 - Prob. 17QCh. 6.4 - Prob. 18QCh. 6.4 - Prob. 19QCh. 6.4 - Suppose that one observation from the exponential...Ch. 6.4 - Prob. 21QCh. 6.4 - Prob. 22QCh. 6.4 - Prob. 23QCh. 6.4 - Given the pdf fY(y;)=2y2,0y. Take a sample of size...Ch. 6.5 - Let k1,k2,...,kn be a random sample from the...Ch. 6.5 - Let y1,y2,...,y10 be a random sample from an...Ch. 6.5 - Let y1,y2,...,yn be a random sample from a normal...Ch. 6.5 - Let k denote the number of successes observed in a...Ch. 6.5 - Suppose a sufficient statistic exists for the...
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- random sample of size 36 from a population with known variance = 9 yields a sample mean of 17. The Z value that corresponds to α = 0.05 that is used to test H0: μ=μ0 versus Ha: μ>μ0 is (The answer must be rounded to three decimal places.)arrow_forwardA sample of n = 16 scores is selected from a normal population with σ = 32. If the sample mean of M = 81 produces a z-score of z = -1.75, then what is the population mean (μ)?arrow_forwardRandom samples of size n₁ = 60 and n₂ = 70 were drawn from populations 1 and 2, respectively. The samples yielded P₁ = 0.6 and P₂ = 0.4. Test Hỏ: (P₁ – P₂) = 0.1 against Hå: (P₁ − P2₂) > > 0.1 using α = 0.05. Find the test statistic. The test statistic is z = (Round to two decimal places as needed.) ***arrow_forward
- On average, a sample of n = 36 scores from a normal population with σ= 10 will provide a better estimate of the population mean than a researcher would get with a sample of n = 9 scores from a normal population with σ= 10.arrow_forwardAssume that you have a sample of n1=7 , with the sample mean X1=44 , and a sample standard deviation of S1=6 , and you have an independent sample of n2=6 from another population with a sample mean of X2=32 and the sample standard deviation S2=5 . Assuming the population variances are equal, at the 0.01 level of significance, is there evidence that μ1>μ2?arrow_forwardA random sample of n = 25 scores is selected from a normal population with a mean of μ = 40. After a treatment is administered to the individuals in the sample, the sample mean is found to be M = 44. If the population standard deviation is σ = 5, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a one-tailed test with α = .05.Calculate the Cohen’s d.arrow_forward
- A random sample of n = 25 individuals is selected from a population with µ = 20, and a treatment is administered to each individual in the sample. After treatment, the sample mean is found to be M = 22.2 with SS = 384. Find the estimated standard error (this is the denominator of the t-statistic.arrow_forwardA simple random sample of size n=40 is drawn from a population. The sample mean is found to be 107.6, and the sample standard deviation is found to be 20.2. Is the population mean greater than 100 at the α=0.025 level of significance? Determine the null and alternative hypotheses. H0: mu equals 100μ=100 mu less than 100μ<100 mu equals 100μ=100 mu greater than 100μ>100 mu less than 107.6μ<107.6 mu equals 107.6μ=107.6 mu greater than 107.6μ>107.6 H1: mu greater than 100μ>100 mu less than 100μ<100 mu equals 100μ=100 mu greater than 100μ>100 mu less than 107.6μ<107.6 mu equals 107.6μ=107.6 mu greater than 107.6μ>107.6 Compute the test statistic. t 0t0 t 0t0 z 0z0 = (Round to two decimal places as needed.) Determine the P-value. The P-value is . (Round to three decimal places as needed.) What is the result of the hypothesis test? the null hypothesis because the P-value is the level of significance.…arrow_forward
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