4. It is desired to test H0 : µ = 20 Vs H1 : µ <...
4. It is desired to test H0 : µ = 20 Vs H1 : µ < 20, on the basis of a random sample of size 64 from normal distribution with population standard deviation σ = 2.4. The sample mean and sample standard deviation are found to be 19.5 and 2.5, respectively.
(a) Test the hypothesis at α = 0.05. Compute the test statistics, critial regions, and perform the test. Will the result be difference if α is changed to 0.01?
(b) Test the null hyposthesis against a 2-sided alternative hypothesis, i.e., H1: µ is not equal to 20, at significance level α 0.05.
Homework Answers
For the hypothesis test H0: µ = 10 against H1: µ < 10 with variance unknown...
For the hypothesis test H0: µ = 10 against H1: µ < 10 with variance unknown and n = 20, let the value of the test statistic be t0 = 1.25. Find the approximate the P-value.
For the hypothesis test H0: µ = 10 against H1: µ > 10 with variance known...
For the hypothesis test H0: µ = 10 against H1: µ > 10 with variance known and n = 15, find the P-value for each of the following values of test statistic. (1) z0 = - 2.05 and (2) z0 = 1.84
A researcher is interested in testing the hypothesis H0 : μ = 8 vs H1 : μ...
A researcher is interested in testing the hypothesis H0 : μ = 8 vs H1 : μ > 8, using a sample of size 81. The population standard deviation is known to be σ = 5. The researcher decides to reject H0 if X ≥ 9. What is the significance level of this hypothesis test? Assume that the population is normal. Express your answer as a decimal (not as a percentage).
To test H0: σ = 40 versus H1: σ < 40
To test H0: σ = 40 versus H1: σ < 40, a random sample of size n=27 is obtained from a population that is known to be normally distributed. (a) If the sample standard deviation is determined to be s = 28.8, compute the test statistic (b) if the researcher decides to test this hypothesis at the a=0.05 level of significance, use technology to determine the P-value.(c) Will the researcher reject the null hypothesis?
Given a known standard deviation of 0.5, n=25, H0: µ=12, H1: µ<12, a sample mean of...
Given a known standard deviation of 0.5, n=25, H0: µ=12, H1: µ<12, a sample mean of 11.8 and a level of significance of 0.05, what is an appropriate confidence interval on µ?
Consider the hypothesis test H0: σ1 = σ2 against H1: σ^21 ≠ σ^22 with known variances...
Consider the hypothesis test H0: σ1 = σ2 against H1: σ^21 ≠ σ^22 with known variances s1 ^2= 2.3 and s^2 2 = 1.9. Suppose that sample sizes n1 = 15 and n2 = 15. Use α = 0.05. a. Parameter of Interest b. Null and Hypothesis c. test statistic d. reject Ho if e. computation f. conclusion
We are looking to calculate the power of a one-sided test from n independent observations xi...
We are looking to calculate the power of a one-sided test from n independent observations xi from a N (µ, σ2 ) distribution with a null hypothesis of H0 : µ = µ0 and an alternative H1 : µ > µ0. Supposing that we know σ2, we can form a test statistic T = (x¯ − µ0)/(σ/√n) and reject the null hypothesis when T > 1.645. This test has level α = 0.05. We want a formula for the power...
Use the following to answer questions 1 and 2. Consider the hypothesis test H0: µ ≥...
Use the following to answer questions 1 and 2. Consider the hypothesis test H0: µ ≥ 65, Ha: µ < 65. From a sample of 15 observations, the sample mean was 63 and the sample standard deviation was 4. Use level of significance 0.01. Compute the test statistic. Give your answer to 2 decimal places.
Consider the test of H0:σ^2=7 against H1:σ^2>7. What is the critical value for the test statistic...
Consider the test of H0:σ^2=7 against H1:σ^2>7. What is the critical value for the test statistic X02 for the significance level α=0.05 and sample size n=19? Give your answer with two decimal places (e.g. 98.76). Enter your answer in accordance to the question statement Thank you!
Suppose you want to test the following hypotheses: H0: p ≥ 0.4 vs. H1: p <...
Suppose you want to test the following hypotheses: H0: p ≥ 0.4 vs. H1: p < 0.4. A random sample of 1000 observations was taken from the population. Answer the following questions and show your Excel calculation for each question clearly: (a) Let p ̂ be the sample proportion. What is the standard error of sample proportion (i.e., σ_p ̂ ) if H0 is true? (b) If the sample proportion obtained were 0.38 (i.e., p ̂=0.38), what is its p-value?...
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