An urn contains red balls and blue balls. Let p represent the proportion of red ball We would like to test Ho: p = 0.5 We choose 10 balls at random with replacement and we reject the null hypothesis there are less than 2 or more than 8 red balls in the sample. What is the probabilit of a Type II error if in fact p=0.3? pbinom(7,10,0.3)-pbinom (2,10,0.3) pbinom(8,10,0.3)-pbinom (1,10,0.3) pbinom(8,10,0.3)-pbinom (2,10,0.3)
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- Test the claim about the difference between two population means H, and u2 at the level of significance a. Assume the samples are random and independent, and the populations are normally distributed. Claim: 41 SH2; a = 0.10. Assume o, #o, Sample statistics: X, = 2417, s, = 179, n, = 12 and X2 = 2296, s2 = 53, n2 = 10 Identify the null and alternative hypotheses. Choose the correct answer below. 대= 내 : "H OF. Ho: H1 2H2 Find the standardized test statistic t. (Round to two decimal places as needed.) Find the P-value. (Round to three decimal places as needed.) Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim. V Ho. There V enough evidence at the 10% level of significance to reject the claim.K In a random sample of males, it was found that 23 write with their left hands and 212 do not. In a random sample of females, it was found that 58 write with their left hands and 442 do not. Use a 0.05 significance level to test the claim that the rate of left-handedness among males is less than that among females. Complete parts (a) through (c) below. a. Test the claim using a hypothesis test. Consider the first sample to be the sample of males and the second sample to be the sample of females. What are the null and alternative hypotheses for the hypothesis test? O A. Ho: P₁ P2 H₁: P₁ P2 O D. Ho: P₁ P2 H₁: P₁ P2 Z= OB. Ho: P1 P2 H₁: P₁ P2 Identify the test statistic. -0 (Round to two decimal places as needed.) Identify the P-value. OE Ho: P1 H₁: P₁ The P-value is hypothesis. There P-value= (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? P₂ P₂ OC. Ho: P₁ SP2 H₁: P₁ P₂ OF. Ho: P1 P2 H₁: P₁ P2 the significance level of a = 0.05, so Because…Test the claim about the differences between two population variances a and o at the given level of significance a using the given sample statistics. Assume that the sample statistics are from independent samples that are randomly selected and each population has a normal distribution. Claim: o so, a = 0.05 Sample statistics: s, = 705, n, =3, s = 368, n, = 9 Find the null and alternative hypotheses. OA Hoio> Hạ: o so3 OC. Hoi o z0 H,: oHi could fill out the blanks for me2. We wish to test the hypothesis Ho: = 0.20 against the alternative hypothesis Ha: #0.20 using the following region of rejection: y in (0,1,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25}. a. What is the probability of a Type I error for this experiment? b. What is the probability of a Type II error for this experiment for a= 0.25? c. What is the power for this experiment for a = 0.25? d. The experiment was performed and y obs was equal to 6. What statistical conclusion would you draw based on this observed number of successes?In a random sample of 320 cars driven at low altitude, 40 of them exceeded the standard 10 grams of particulate pollution per gallon of fuel consumed. In another independent random sample of 80 cars driven at high altitude, 20 of them exceeded the standard. Let P 1be the true proportion of cars that exceed the standard in low altitudes and P 2be the true proportion of cars that exceed the standard in high altitudes. What is the test statistic for testing this hypothesis.Only C and DSuppose there is a claim that a certain population has a mean, µ, that is different than 7. You want to test this claim. To do so, you collect a large random sample from the population and perform a hypothesis test at the 0.05 level of significance. To start this test, you write the null hypothesis H, and the alternative hypothesis H, as follows. Hoi u= 7 H: u =7 Suppose you also know the following information. The critical values are - 1.960 and 1.960 (rounded to 3 decimal places). The value of the test statistic is 2.477 (rounded to 3 decimal places). (a) Complete the steps below to show the rejection region(s) and the value of the test statistic for this test. Standard Normal Distribution Step 1: Select one-tailed or two-tailed. One-tailed 0.3 Two-tailed Step 2: Enter the critical value(s). (Round to 3 decimal places.) 0.2+ 0.1+ Step 3: Enter the test statistic. (Round to 3 decimal places.) 2 (b) Based on your answer to part (a), choose the correct statement. O The value of the test…A police office claims that the proportion of people wearing seat belts is less than 65%. To test this claim, a random sample of 200 drivers is taken and its determined that 126 people are wearing seat belts. The following is the setup for this hypothesis test: Ho :p-0.65 Ha : p < 0.65 In this example, the p-value was determined to be 0.277 come to a conclusion and interpret the results for this hypothesis test for a proportion (use a significance level of 5%) Select the correct answer below: O The decision is to reject the Null Hypothesis. The conclusion is that there is enough evidence to support the claim The decision is to fail to reject the Null Hypothesis. The conclusion is that there is not enough evidence to support the claimSEE MORE QUESTIONS