1. Suppose we are supervising a research project in which depressed patients are randomly assigned to receive one of 6 different common treatments for depression. After receiving the treatment for 4 weeks, patients' depressive symptoms are reassessed, and their symptom level is quantified and analyzed. (a) If we use one-way ANOVA to compare the six group means, what is the null hypothesis (in symbolic form – i.e., Ho:..)? (b) Why can't we express the alternative hypothesis as
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- What is meant by the sample space of an experiment?Suppose, when conducting a 2-way ANOVA, you find significant main effects for both of your factors of interest (i.e. gender and educational attainment, categorized as high school graduate or less vs. more than a high school education), but no significant interaction between the 2 factors. Which of the following statements, if any, are reasonable conclusions? Question 22 options: A) Since there is no significant interaction between gender and educational attainment, we can conclude that the outcome does not differ between groups. B) Since there is a significant main effect for gender, then the outcome must be significantly different between males and females. C) Since there is a significant main effect for educational attainment, then the outcome must be significantly different between the 2 educational attainment groups. D) All of the above are reasonable conclusions. E) Answers B and C are reasonable…10. The research department at the home office of Superior Insurance conducts ongoing research on the causes of automobile accidents, the characteristics of the drivers, and so on. A random sample of 400 policies written on single persons revealed 120 had at least one accident in the previous three- year period. Similarly, a sample of 600 policies written on married persons revealed that 150 had been in at least one accident. At the 0.05 significance level, is there a significant difference in the proportions of single and married persons having an accident during a three-year period? Determine and interpret the p- value.
- A researcher designs an experiment in which the single independent variable has five levels. If the researcher performed an ANOVA and rejected the null hypothesis, how many post hoc comparisons would he make (assuming he was making all possible comparisons)?The National Institute of Mental Health published an article stating that in any one-year period, approximately 8.8% of American adults suffer from depression or a depressive illness. Suppose that in a survey of 2000 people in a certain city, 11.3% of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that city suffering from depression or a depressive illness is more than the 8.8% in the general adult American population. Test the relevant hypotheses using a 5% level of significance. Give answer to at least 4 decimal places. a. What are the correct hypotheses? (Select the correct symbols and use decimal values not percentages.) H0: H1: b. Based on the hypotheses, find the following: c. Test Statistic = d. p-value = e. Based on the above we choose to:_____________ f. The correct summary would be: ____________ that the true proportion of people in that city suffering from depression or a…The National Institute of Mental Health published an article stating that in any one-year period, approximately 8.8% of American adults suffer from depression or a depressive illness. Suppose that in a survey of 2000 people in a certain city, 11.3% of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that city suffering from depression or a depressive illness is more than the 8.8% in the general adult American population. Test the relevant hypotheses using a 5% level of significance. Give answer to at least 4 decimal places. a. What are the correct hypotheses? H0: H1: b.) Based on the hypotheses, find the following: c.) Test Statistic = d.) p-value = e.) Based on the above we choose to________________ f.) The correct summary would be:____________ that the true proportion of people in that city suffering from depression or a depressive illness is more than the percent in the general…
- In ANOVA, what will be the conclusion when the means of the between groups vary from within groups? a.Accept the null hypothesis b.Reject the null hypothesis c.Conduct main effects d.Conduct interaction effectsThe research department at the home office of New Hampshire Insurance conducts on-going research on the causes of automobile accidents, the characteristics of the drivers, and so on. A random sample of 400 policies written on single persons revealed 120 had at least one accident in the previous three-year period. Similarly, a sample of 600 policies written on married persons revealed that 150 had been in at least one accident. At the .05 significance level, is there a significant difference in the proportions of single and married persons having an accident during a three year period? Determine the p-value.4. The National Institute of Mental Health published an article stating that in any one-year period, approximately 9.5 percent of American adults suffer from depression or a depressive illness. Suppose that in a survey of 100 people in a certain town, seven of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult American population.
- A machine in a factory must be repaired if it produces more than 10% defectives in a day. A random sample of 100 produced items contains 15 defectives, and the supervisor says that the machine must be repaired. Given the aforementioned information and the hypotheses H0: p ≤ 0.1 and H1: p > 0.1, does the sample support the supervisor's decision at the 0.01 significance level?Utilizing the previous table: A sample of 25 cities have been classified as high or low on their homicide rates and on the number of handguns sold within the city limits. Was the null hypothesis rejected or accepted?A study, which randomly surveyed 3,700 households and drew on this information from the IRS, found that 79% of households have conducted at least one IRA rollover from an employer-sponsored retirement plan. Suppose a recent random sample of 90 households in a certain county was taken and respondents were asked whether they had ever funded an IRA account with a rollover from an employer-sponsored retirement plan. Based on the sample data below, can you conclude at the 0.10 level of significance that the proportion of households in the county that have funded an IRA with a rollover is different from the proportion for all households reported in the study? 77 respondents said they had funded an account; 13 respondents said they had not