QUESTION 1:
You are testing H0: µ = 100 against Ha: µ < 100 based on an SRS of 18 observations from a Normal population. The data give x¯¯¯x¯ = 8.3 and s = 5.
The value of the t statistic (±0.01)
is
QUESTION 2:
You have an SRS of 14 observations from a Normally distributed population.
What critical value (±±0.001) would you use to obtain a 99.5%
confidence interval for the mean μμ of the population?
QUESTION 1: You are testing H0: µ = 100 against Ha: µ < 100 based on...
You are testing H0: μ = 100 against Ha: μ < 100 based on an SRS of 21 observations from a Normal population. The data give x̄ = 9.1 and s = 3.6. The value of the t statistic (±0.01) is _______
You are testing H0: u=100 against HA: u>100 based on an SRS of 16 observations from a Normal population. The t-statistic is t = 2.13 1. The degrees for the t statistic are: A. 15 B. 16. C. 17 2. The p-value for the statistic in the previous exercise: A. falls between 0.05 and 0.10 B. falls between 0.01 and 0.05 C. is less than 0.01
3. You are testing H0: u 500 against Ha: u < 500 based on an SRS of 16 observations from a Normal population. The data give-=498 and s-4. The value of the t statistic is (c) 2 (b)4 (a) 16 500
In testing H0: µ = 100 versus Ha: µ ╪ 100 versus using a sample size of 325, the value of the test statistic was found to be 2.16. The p-value (observed level of significance) is best approximated by 0.0154 0.9692 0.4846 0.0308 0.007
Suppose the null hypothesis is Ho : µ = 500 against Ha : > µ = 500 , and the significance level for this testing is 0.05. The population in question is normally distributed with standard deviation 100. A random sample of size n=25 will be used. If the true alternative mean is 550, then the probability of committing the type II error is ____.
Suppose you want to test H0 : µ = 4 against Ha : µ > 4. In addition, suppose that σ = 5, n = 36, and you will reject H0 if x > 5 and accept H0 otherwise. (a) (6 pts) Find the power of this test against the alternative µ = 5.6. (b) (2 pts) Find the probability of a Type II error in this situation (just use your answer from part (a) to help you do this).
In a test of H0: µ=150 against HA: µ<150, a sample of size 250 produces Z = -0.65 for the value of the test statistic. Thus the p-value is approximately equal to:
In testing H0: µ = 3 versus Ha: µ ¹ 3 when =3.5, s = 2.5, and n = 100, what is the p-value? a.0.0700 b.0.0228 c.0.0655 d.0.0456
You are conducting a significance test of H0: μ = 5 against Ha: μ > 5. After checking the conditions are met from a simple random sample of 30 observations, you obtain t = 2.35. Based on this result, describe the p-value. The p-value falls between 0.15 and 0.2. The p-value falls between 0.025 and 0.05. The p-value falls between 0.01 and 0.02. The p-value falls between 0.005 and 0.01. The p-value is less than 0.005.
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.