Question

In: Statistics and Probability

1. P-value and confidence interval. A two-sided test of H0: μ = 0 yields a P-value...

1. P-value and confidence interval. A two-sided test of H0: μ = 0 yields a P-value of 0.03. Will the corresponding 95% confidence interval for μ include 0 in its midst? Will the 99% confidence interval for μ include 0? Explain your reasoning in each instance.

Solutions

Expert Solution

We reject null hypothesis if the p-value is less than the level of significance and accept null hypothesis if it is greater than .

[1- confidence interval = ]

95% confidence interval means 0.05 level of significance.

Here p-value is less than 0.05. [ 0.03<0.05]. Thus we reject our null hypothesis i.e we reject =0. Hence in this case the confidence interval won't have =0 in it.

99% confidence interval has a level of significance 0.01. Here the p-value (0.03) is greater than the level of significance thus we accept null hypothesis. (0.03>0.01) Hence here we accept =0 and accordingly we will have zero in the 99% confidence interval for .


Related Solutions

Question 1. a) The P-value for a two-sided test of the null hypothesis H0: mu =...
Question 1. a) The P-value for a two-sided test of the null hypothesis H0: mu = 30 is 0.08 i.) Does the 95% confidence interval include the value of 30? Explain. ii.) Does the 90% confidence interval include the value of 30? Explain. b) A 95% confidence for a population mean is (57,65) i.) Can you reject the null hypothesis that mu = 68 at the 5% significance level? Explain. ii.) Can you reject the null hypothesis that mu =...
Find the level of a two-sided confidence interval that is based on the given value of...
Find the level of a two-sided confidence interval that is based on the given value of t and the given sample size. 6. t = 1.943, sample size n = 7. (Multiple choice) Choices: 80%, 90%, 95%, 98% 7. t = 2.093, sample size n = 20. Choices: 90%, 98%, 95%, 99% 10. t = 1.753, n = 16 Choices: 80%, 90%, 95%, 99%
1.Construct the confidence interval for μ 1 − μ 2 for the level of confidence and...
1.Construct the confidence interval for μ 1 − μ 2 for the level of confidence and the data from independent samples given. 95% confidence: n 1 = 110, x - 1 = 77, s 1 = 15 n 2 = 85, x - 2 = 79, s 2 = 21 90% confidence: n 1 = 65, x - 1 = − 83, s 1 = 12 n 2 = 65, x - 2 = − 74, s 2 = 8...
What would be the p value of the test statistic .0006 for a two sided test...
What would be the p value of the test statistic .0006 for a two sided test and a degree of freedom of 8
Determine the t critical value for a two-sided confidence interval in each of the following situations.
 Determine the t critical value for a two-sided confidence interval in each of the following situations. (Round your answers to three decimal places.) (a) Confidence level = 95%, df = 5 (b) Confidence level = 95%, df = 10 (c) Confidence level = 99%, df = 10 (d) Confidence level = 99%, n = 10 (e) Confidence level = 98%, df = 22 (f) Confidence level = 99%, n = 36 You may need to use the appropriate table in the Appendix of Tables to answer this...
Consider a two-sided confidence interval for the mean μ when σ is known; X̄-Zα1 σ/√n ≤...
Consider a two-sided confidence interval for the mean μ when σ is known; X̄-Zα1 σ/√n ≤ μ ≤ X̄+Zα2 σ/√n where α1 + α2 = α. if α1= α2 = α/2, we have the usual 100(1-α)% confidence interval for μ. In the above, when α1 ≠ α2 , the interval is not symmetric about μ. Prove that the length of the interval L is minimized when α1= α2= α/2. Hint remember that Φ Zα = (1- α) , so Φ-1...
Solve the problem. A one-sided confidence interval for p can be written as p <  + E...
Solve the problem. A one-sided confidence interval for p can be written as p <  + E or p >  - E where the margin of error E is modified by replacing z/2 with z. If a teacher wants to report that the fail rate on a test is at most x with 90% confidence, construct the appropriate one-sided confidence interval. Assume that a simple random sample of 70 students results in 5 who fail the test. a) p < 0.032 b)...
2.Construct the confidence interval for μ 1 − μ 2 for the level of confidence and...
2.Construct the confidence interval for μ 1 − μ 2 for the level of confidence and the data from independent samples given. 90% confidence: n 1 = 28, x - 1 = 212, s 1 = 6 n 2 = 23, x - 2 = 198, s 2 = 5 99% confidence: n 1 = 14, x - 1 = 68, s 1 = 8 n 2 = 20, x - 2 = 43, s 2 = 3
Consider the following hypotheses: H0: μ ≤ 520 HA: μ > 520 Find the p-value for...
Consider the following hypotheses: H0: μ ≤ 520 HA: μ > 520 Find the p-value for this test based on the following sample information. a. x¯ = 533; s = 40; n = 19 p-value  0.10 0.05  p-value < 0.10 0.01  p-value < 0.025 0.025  p-value < 0.05 p-value < 0.01 b. x¯ = 533; s = 40; n = 38 0.05  p-value < 0.10 0.01  p-value < 0.025 p-value < 0.01 0.025  p-value < 0.05 p-value  0.10 c. x¯ = 533; s = 32; n = 30...
Consider the following hypotheses: H0: μ ≤ 330 HA: μ > 330 Find the p-value for...
Consider the following hypotheses: H0: μ ≤ 330 HA: μ > 330 Find the p-value for this test based on the following sample information. (You may find it useful to reference the appropriate table: z table or t table) a. x¯x¯ = 340; s = 44; n = 21 p-value  0.10 p-value < 0.01 0.05  p-value < 0.10 0.01  p-value < 0.025 0.025  p-value < 0.05 b. x¯x¯ = 340; s = 44; n = 42 0.01  p-value < 0.025 0.05  p-value < 0.10 0.025  p-value <...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT