The hypothesis is given as H0 : p = 0.5 and Ha : p != 0.5,...
The hypothesis is given as H0 : p = 0.5 and Ha : p != 0.5, where p is the probability of “head”. Then, test statistic is given as T, the number of head in 10 flips. Then, it is reasonable to assume T follows a binomial distribution with parameters, n = 10 and p, i.e. Bin(10, p). Now, I claim two R.R.s as: R.R.1 = {7, 8, 9, 10} and R.R.2 = {9, 10}.
1. Calculate α and β with respect to R.R.1.
2. Calcualte α and β with respect to R.R.2.
3. Compare the change of α and β and draw the conclusion of trade-off between α and β.
4. We want to minimize both α and β, which means we have to find a balance point between them. Explain the standard stratege we use here in language.
Homework Answers
A hypothesis testing: H0: p=0.49 HA: p<0.49.
A hypothesis testing: H0: p=0.49 HA: p<0.49. We conduct a survey with sample size n=171 and have pˆ=0.39. With α=0.05, do you reject or fail to reject the Null hypothesis? Enter 1 if you "reject the Null hypothesis" and 0 if you "fail to reject the null hypothesis".Note:1- Enter either 0 or 1 in the box. The box does not accept text as an answer. Your answer should be either 0 or 1 and no other answers will be accepted.
onsider the hypothesis test below. H0: p 1 - p 2 ≤ 0 Ha: p 1...
onsider the hypothesis test below. H0: p 1 - p 2 ≤ 0 Ha: p 1 - p 2 > 0 The following results are for independent samples taken from the two populations. Sample 1 Sample 2 n1 = 200 n2 = 400 p1 = 0.23 p2 = 0.16 What is the value of the test statistic (to 2 decimals)? What is the p-value (to 4 decimals)? With α = .05, what is your hypothesis testing conclusion?
Suppose we to test H0: η = 4.5 vs. Ha: η< 4.5, where η is the...
Suppose we to test H0: η = 4.5 vs. Ha: η< 4.5, where η is the population median. Among n= 10 observations, let S be the number of the measurements which are larger than 4.5. Under H0, S follows a binomial(n= 10,p = 0.5). 1) Which of the following sample results gives the strongest evidence to support Ha? a. S=4 b. S=5 c. S=6 d. They are all the same 2) Following the problem, suppose S = 1, what is...
2) Use critical values and p-values to test the null hypothesis H0: μ1 − μ2 ≤...
2) Use critical values and p-values to test the null hypothesis H0: μ1 − μ2 ≤ 20 versus the alternative hypothesis Ha: μ1 − μ2 > 20 by setting α equal to .10. How much evidence is there that the difference between μ1 and μ2 exceeds 20?
Consider the following hypothesis test: H0: μ = 18 Ha: μ ≠ 18 A sample of...
Consider the following hypothesis test: H0: μ = 18 Ha: μ ≠ 18 A sample of 48 provided a sample mean x = 17 and a sample standard deviation s = 4.9. a. Compute the value of the test statistic (to three decimal places.) b. Use the t distribution table (Table 2 in Appendix B) to compute a range for the p-value. (to two decimal places) p-value is between is c. At α = .05, what is your conclusion? p-value...
Exercise 9-39 Algo Consider the following hypotheses: H0: μ = 20 HA: μ ≠ 20 The...
Exercise 9-39 Algo Consider the following hypotheses: H0: μ = 20 HA: μ ≠ 20 The population is normally distributed. A sample produces the following observations: (You may find it useful to reference the appropriate table: z table or t table) 24 20 24 21 21 24 19 Click here for the Excel Data File a. Find the mean and the standard deviation. (Round your answers to 2 decimal places.) b. Calculate the value of the test statistic. (Round...
Consider the following hypothesis test. H0: μ ≥ 10 Ha: μ < 10 The sample size...
Consider the following hypothesis test. H0: μ ≥ 10 Ha: μ < 10 The sample size is 155 and the population standard deviation is assumed known with σ = 5. Use α = 0.05. (a) If the population mean is 9, what is the probability that the sample mean leads to the conclusion do not reject H0? (Round your answer to four decimal places.) (b) What type of error would be made if the actual population mean is 9 and...
Consider the following hypothesis test: H0: μ = 18 Ha: μ ≠ 18 A sample of...
Consider the following hypothesis test: H0: μ = 18 Ha: μ ≠ 18 A sample of 48 provided a sample mean x = 17 and a sample standard deviation s = 4.7. a. Compute the value of the test statistic (to three decimal places.) b. Use the t distribution table (Table 2 in Appendix B) to compute a range for the p-value. (to two decimal places) p-value is between ___________ is __________ c. At α = .05, what is your...
Consider the following hypotheses: H0: μ = 19 HA: μ ≠ 19 The population is normally...
Consider the following hypotheses: H0: μ = 19 HA: μ ≠ 19 The population is normally distributed. A sample produces the following observations: (You may find it useful to reference the appropriate table: z table or t table) 20 23 17 21 21 24 23 Click here for the Excel Data File a. Find the mean and the standard deviation. (Round your answers to 2 decimal places.) b. Calculate the value of the test statistic. (Round intermediate calculations to...
Two samples are drawn to test the hypothesis, H0: p = 0.5 vs HA: p ≠0.5{"version":"1.1","math":"<math...
Two samples are drawn to test the hypothesis, H0: p = 0.5 vs HA: p ≠0.5{"version":"1.1","math":"<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>H</mi><mn>0</mn></msub><mo>:</mo><mo> </mo><mi>p</mi><mo> </mo><mo>=</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>5</mn><mo> </mo><mi>v</mi><mi>s</mi><mo> </mo><msub><mi>H</mi><mi>A</mi></msub><mo>:</mo><mo> </mo><mi>p</mi><mo> </mo><mo>≠</mo><mn>0</mn><mo>.</mo><mn>5</mn></math>"}. One sample has size n1=250{"version":"1.1","math":"<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mn>1</mn></msub><mo>=</mo><mn>250</mn></math>"} and the other has size n2=125{"version":"1.1","math":"<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mn>2</mn></msub><mo>=</mo><mn>125</mn></math>"}. Both samples yield the same sample proportion of 0.4. Consider the statement: Both samples will produce the same p-value for the hypothesis test above. Is this statement always true, sometimes true or never true? Question 12 options: Always true Sometimes true Never true Previous PageNext Page
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