Fundamentals of Statistics (5th Edition)
5th Edition
ISBN: 9780134508306
Author: Michael Sullivan III
Publisher: PEARSON
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Textbook Question
Chapter B.2, Problem 7AYU
In Problems 5–8, find the critical values
7. 98% confidence, n = 23
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A sample of n = 25 scores is selected from a population with μ = 70 and σ = 20. It is very unlikely that the sample mean will be greater than 72.
True or False
If a =0.05 and df=26
for a left-tailed test,
what is the critical value of x??
A.
Xổ 05 = 38.885
Xổ.05
В.
15.379
C.
Xã.95 = 38.885
2
D.
Xá.95 = 15.379
1. In a random sample of 400 observations from a population whose variance is o?=100, we
calculated F= 75. Find the 95% confidence interval estimate of the population mean µ.
Chapter B.2 Solutions
Fundamentals of Statistics (5th Edition)
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- For a value of population parameter 0 equal to 2, which one of the following cases corresponds to an unbiased estimator with higher precision? E(Ô ) = 2 and Var(Ô) = 2 E(ô – 0) = 0 and Var( ô ) = 2 E(ô – 0 ) = 2 and Var(ô ) = 1 E(Ô) = 2 and Var( Ô ) = 1 ||arrow_forwardA population has µ = 60 and σ = 10. For a sample of n = 25 scores from this population, a sample mean of M = 55 would be considered an extreme value. True Falsearrow_forwardYou are conducting a left-tailed test of a claim about a population mean when sigma is unknown with a sample size of 37.If α=.05α=.05, find the critical value, to two decimal places.arrow_forward
- Please help me to explain these questions. Thank you.arrow_forwardIF n < 30 AND T = Ý−µ -H, √n SHOW HOW THE 100(1-2x)% CONFIDENCE INTERVAL FOR U IS DERIVEDarrow_forwardSuppose that X1,..., X, is a random sample from a normal distribution with mean u and variance o?. Two unbiased estimators of o? are ởf = s° = E(x, - Xy°, and ô = (X1 - 2 Find the efficiency of ở relative to ôž.arrow_forward
- 1. A sample of data is collected from a group of college students (X = 112, Sx = 12, N = 58). It is hypothesized that members of this group have higher test scores than the general population (u = 100, o = 15). What test do you conduct? Don't do the test, just name the test and list the relevant equation for the test statistic. %3Darrow_forward3. A research assistant is asked to draw two independent normally distributed samples. The first sample, X has a 10 observations with a mean of 1 and sample variance of 2. The second sample, Y has 20 observations with a mean of 0.5 and a sample variance of 3. Test the following hypotheses: (a) X = Ý (b) X > Y (c) Var(X) Var(Y) %3D (d) Var(X) = 1.5 (e) Var(Y) = 2.5 %3Darrow_forward3 For an SRS 4:³;=, from the normal distribution 7/2/2 (Y-M) ² 2 fy (y;u, 0²) - ▷ TIN 1 vážvože е Show that the sample mean I is an efficient estimator.arrow_forward
- A random sample of n= 4 individuals is selected from a population with μ = 35, and a treatment is administered to each individual in the sample. After treatment, the sample mean is found to be M = 40.1 with SS = 48. How much difference is there between the mean for the treated sample and the mean for the original population? (Note: In a hypothesis test, this value forms the numerator of the t statistic.) If there is no treatment effect, how much difference is expected between the sample mean and its population mean? That is, find the standard error for M. (Note: In a hypothesis test, this value is the denominator of the t statistic.) Based on the sample data, does the treatment have a significant effect? Use a two-tailed test with α = .05.arrow_forwardSuppose we wish to test Ho: μ = 36 vs. H₁: μ 36 based on a sample of size 31. USE SALT Which of the following sample results yields the smallest p-value? Ox= 34, s = 6 x = 33, s = 4 x = 38, s = 2 Ox= 32, s = 9 Why? The sample results with an observed mean farthest from the hypothesized mean will yield the smallest p-value. The sample results with the test statistic of largest magnitude will yield the smallest p-value. The sample results with the test statistic of smallest magnitude will yield the smallest p-value. The sample results with an observed mean closest to the hypothesized mean will yield the smallest p-value. The sample results based on the largest sample size will yield the smallest p-value. The sample results based on the smallest sample size will yield the smallest p-value.arrow_forward1. The mean and standard deviation of a process are expected to be about μ = 400 and σ = 16. An experiment is required to estimated the true mean with precision 8 = 10 with 95% confidence, i.e. a confidence interval for the population mean of the following form is required: P(x-8<< x+6) = 0.95 where x will be determined from the sample data. Calculate the sample size for the experiment assuming that the distribution is normal and that the population standard deviation will be estimated from the sample standard deviation.arrow_forward
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