A random sample of n=25 is obtained from a population with variance σ^2, and the sample mean is computed. Test the null hypothesis H0 : μ = 110 versus the alternative hypothesis H1: μ>110 with α=0.01.
Compute the critical value (Xc overbar) and state your decision rule for the options below.
a. |
The population variance is σ^2=256. |
b. |
The population variance is
σ^2=400. |
c. |
The population variance is
σ^2=900. |
d. |
The population variance is
σ^2=500. |
Ans:
critical z values=+/-2.576
a)standard error of mean=sqrt(256/25)=3.2
lower limit=110-2.576*3.2=101.76
upper limit=110+2.576*3.2=118.24
b)standard error of mean=sqrt(400/25)=4
lower limit=110-2.576*4=99.70
upper limit=110+2.576*4=120.30
c)
standard error of mean=sqrt(900/25)=6
lower limit=110-2.576*6=94.54
upper limit=110+2.576*6=125.46
d)
standard error of mean=sqrt(500/25)=4.472
lower limit=110-2.576*3.2=98.48
upper limit=110+2.576*3.2=121.52
A random sample of n=25 is obtained from a population with variance σ^2, and the sample...
9, A random sample is obtained from a population with variance = 400 and the sample mean is computed to be 70, Consider the null hypothesis Ho: μ = 80 versus the alternative H1: Ho: μ < 80. Compute the p-value. If n 32, the p-value is
A random sample is obtained from a population with variance = 400 and the sample mean is computed to be 70. Consider the null hypothesis Ho: µ = 80 versus the alternative H1: Ho: µ < 80. Compute the p-value. If n = 16, the p-value is ?
If, in a sample of n=20 selected from a normal population, overbar X=54 and S=8, what are the critical values of t if the level of significance, α, is 0.10, the null hypothesis, H0, is μ=50, and the alternative hypothesis, H1, is μ≠50? The critical values of t are ± (Round to four decimal places as needed.)
To test Ho: σ=4.6 versus H1: σ≠4.6, a random sample of size n=11 is obtained from a population that is known to be normally distributed. (a) If the sample standard deviation is determined to be s=5.6, compute the test statistic. (b) If the researcher decides to test this hypothesis at the α=0.01 level of significance, use technology to determine the P-value. (c) Will the researcher reject the null hypothesis?
The observations from a random sample of n = 6 from a normal population are: 13.15, 13.72, 12.58, 13.77, 13.01, 13.06. Test the null hypothesis of H0:μ=13 against the alternative hypothesis of H1:μ<13. Use a 5% level of significance. Answer the following, rounding off your answer to three decimal places. (a) What is the sample mean? (b) What is the sample standard deviation? (c) What is the test statistic used in the decision rule? (d) Can the null hypothesis be...
#1 part A.) To test H0: μ=100 versus H1: μ≠100, a random sample of size n=20 is obtained from a population that is known to be normally distributed. Complete parts (a) through (d) below. (aa.) If x̅=104.4 and s=9.4, compute the test statistic. t0 = __________ (bb.) If the researcher decides to test this hypothesis at the α=0.01 level of significance, determine the critical value(s). Although technology or a t-distribution table can be used to find the critical value, in...
3. (25 points) To test Ho: σ 0.35 versus H1: σ < 0.35, a random sample of size n = 41 is obtained from a population that is known to be normally distributed a. If the sample standard deviation is determined to be s 0.23, compute the test statistic. (5 pts) b. If the researcher decides to test this hypothesis at the a 0.01 level of significance , determine the critical value. (5 pts) c. Draw a chi-square distribution and...
Suppose that X1, X2, . . . , Xn is an iid sample of N (0, σ2 ) observations, where σ 2 > 0 is unknown. Consider testing H0 : σ 2 = σ 2 0 versus H1 : σ 2 6= σ 2 0 ; where σ 2 0 is known. (a) Derive a size α likelihood ratio test of H0 versus H1. Your rejection region should be written in terms of a sufficient statistic. (b) When the null...
A sample of size 100, taken from a population whose standard deviation is known to be 8.90, has a sample mean of 51.16. Suppose that we have adopted the null hypothesis that the actual population mean is greater than or equal to 52, that is, H0 is that μ ≥ 52 and we want to test the alternative hypothesis, H1, that μ < 52, with level of significance α = 0.05. a) What type of test would be appropriate in...
A random sample of 16 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 9 and the sample standard deviation is 2. Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is 8.5. (a) Is it appropriate to use a Student's t distribution? Explain. Yes, because the x distribution is mound-shaped and symmetric and σ is unknown. No, the x distribution is skewed left. No, the...