What is the null hypothesis in the Wilcoxon Signed-Ranks Test?
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- An article in the Washington Post on March 16, 1993 stated that nearly 45 percent of all Americans have brown eyes. A random sample of n=84 C of I students found 31 with brown eyes.We test H0:p=.45Ha:p≠.45 (a) What is the z-statistic for this test? (b) What is the P-value of the test?A researcher wants to test if the average performance of a new teaching method is different from the traditional teaching method in a sample of 25 students. The researcher used the Wilcoxon Signed-Ranks Test and obtained a T-value of 43. What can be concluded from the test result?In an early home game, an NBA team made 66 of their 100 free throw attempts. In one of theirlast home games, the team made 68 of 90 attempts. At α = .10, did the team significantlyimprove its free throw percentage (left-tailed test)?
- Imagine you are doing a Related-Samples t-test, and you are on Step Two of the hypothesis test. The sample of difference scores that you calculated is -1, -1, -3, +2, 0, -4. If you are doing the test with α = .01, and two tails, what would he correct t-critical be?note for drop downs in last question: performed > (worse than, similarly to, better than) random guesses , so they > (do not appear, appear) effective.When should the Wilcoxon Signed-Rank test be used instead of a paired t-test?
- A sociologist wishes to study whether the rank attained by officers in the New York City Police Department (NYPD) is related to gender. Data have been collected for both male and female officers in NYPD. The summary data and test for independence results from StatCrunch are given below. At a= 0.05 level of significance, draw a conclusion about whether these data indicate that the rank of the officer is independent of gender.(a) Is this an observational study or experiment?(b) What are the explanatory and response variables, respectively?Explanatory variable:Response variable:(c) Write down the null and alternative hypotheses of the test for independence.Contingency table results:Rows: RANKColumns: GENDER male female total officer 21900 4281 26181 detective 4058 806 4864 sergeant 3898 415 4313 lieutenant 1333 89 1422 captain 359 12 371 higher ranks 218 10 228 total 31766 5613 37379A major oil company has developed a new gasoline additive that is supposed to increase mileage. To test this hypothesis, ten cars are randomly selected. The cars are driven both with and without the additive. The results are displayed in the following table. Can it be concluded, from the data, that the gasoline additive does significantly increase mileage? Let d=(gas mileage with additive)−(gas mileage without additive)�=(gas mileage with additive)−(gas mileage without additive). Use a significance level of α=0.05�=0.05 for the test. Assume that the gas mileages are normally distributed for the population of all cars both with and without the additive. Car 1 2 3 4 5 6 7 8 9 10 Without additive 27.2 13.7 12.5 13.4 14.7 25.5 10.3 13.9 14.5 25 With additive 29.7 15.7 14.1 16.4 17.8 27.8 12.1 15 17.3 28 Copy Data Step 1 of 5: State the null and alternative hypotheses for the test.Bocellie rejected a null hypothesis. The reason for doing this is that the hypothesis required a right-tailed test and the t value was 2.5 whereas the t critical value was 2. Which of the following are we certain about: Both Type I and Type II error were made A Type II error was not made Neither Type I nor Type II error was made A Type I error was not made
- Foofy obtained a significant Fobt from an experiment with five levels. She therefore concludes that changing every condition of the independent variable results in a significant change in the dependent variable. (a) Is she correct? Why or why not? (b) What must she now do?Does training in stress reduction make a difference for student success? 15 students received training (M1= 88, SS1= 400) and 15 students did not (M2= 82, SS2= 440). Test using α = .05 Which is the null hypothesis, H0?700 doctors went through extra training compared to 1200 doctors who did not. Of the doctors who went through extra training, 125 of them majored in psychology. Of the 1200 doctors who did not do extra training, 174 of them majored in psychology. Perform a hypothesis test to see if there is a statistically significant evidence that the proportion of doctors who went through extra training is significantly greater than the proportion of doctors who did not. Perform the test at the alpha = .5 level. What is the p value and conclusion of this test?