Consider testing H0: mu = 45 vs. H1: mu <> 45 at the alpha = 0.01 level of significance ('<>' means 'not equal'). A sample of size n = 50 is taken and a 99% confidence interval for mu is calculated as (33.4, 44.7). Then the test conclusion is:
Reject H0 |
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Do not reject H0 |
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There is not enough information to determine the test conclusion |
Since claimed population mean does not contained in confidence interval, we have sufficient evidence to
reject the null hypothesis.
Reject H0
Consider testing H0: mu = 45 vs. H1: mu <> 45 at the alpha = 0.01...
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).
Use the sample data below to test the hypotheses: H0: p1=p2=p3 H1: Not all population proportions are equal The calculated test statistic is 6.082 9.249 8.851 10.950 At 2.5% level of significance, the conclusion is fail to reject H0 No test No decision Reject H0
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...
Suppose that you are testing the hypotheses H0: μ=70 vs. HA: μ≠70. A sample of size 41 results in a sample mean of 65 and a sample standard deviation of 1.7. a) What is the standard error of the mean? b) What is the critical value of t* for a 99% confidence interval? c) Construct a 99% confidence interval for μ. d) Based on the confidence interval, at α=0.010 can you reject H0? Explain.
H0: theta <= theta0 vs. H1: theta > theta0. Let’s say we are testing this based on one observation of X from a Beta distribution with PARAMETERS (1,theta). Reject H0 if X<= c for some c. Write an expression for the power function of the test and sketch a plot of it. Find c so that the test has size alpha0. alpha0=0.05 and theta0=. Find c, the probability of Type 1 error if theta = 0.9, and the power of...
Multiple Choice: In testing the hypotheses H0: B1 = 0 vs. Ha: B1 ≠ 0 with alpha = 0.05, the calculated value of our test statistic is T = 3.45. The critical value from our t-table is t0.025 = 2.306. What conclusion should be made? a) Do not reject H0, there is evidence that X contributes information to the prediction of Y. b) Reject H0, there is evidence that X contributes information to the prediction of Y. c) Do not...
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?...
To test H0: mean = 80 vs. H1: mean < 80, a simple random sample of size n = 22 is obtained from a population that is known to be normally distributed. (a) If x-hat = 76.9 and s = 8.5 compute the test statistic (b) If the researcher decides to test the hypothesis at the a = 0.02 level of significance, determine the critical value. (c) Draw a t-distribution that depicts the critical region (d) Will the researcher reject...
Let T have a (Student's) t distribution with 10 degrees of freedom. If P(T < k) = 0.95, what is the value of k? Let mu be the unknown mean of a Normal distribution. I take 20 observations randomly from this distribution, and want to test H0: mu = 15 vs H1: mu is not equal to 15 at the 5% level of significance. If I observe a p-value of 0.11, what decision can I make? Write mu for the...
Consider testing H0: (p1-p2)=0 versus a two-tailed research hypothesis (H1: (p1-p2) not equal 0). Suppose you obtain a z test statistic equal to -2.37. Recalling that researchers typically report the best significance level reached among the conventional significance levels, the difference is statistically significant at a _____ percent level. (Type either 1, 5 or 10 to correctly fill in the blank.)