The U.S. Bureau of Labor Statistics reports that 11.3% of U.S. workers belong to unions (BLS website, January 2014). Suppose a sample of 400 U.S. workers is collected in 2014 to determine whether union efforts to organize have increased union membership. a. Formulate the hypotheses that can be used to determine whether union membership increased in 2014. Ho: p Select Select b. If the sample results show that 52 of the workers belonged to unions, what is the p-value for your hypothesis test (to 4 decimals)? c. Ata- 05, what is your conclusion? Select
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- The National Institute of Mental Health published an article stating that in any two-year period, approximately 10.5percent of American adults suffer from depression or a depressive illness. Suppose that in a survey of 150 people in a certain town, eight of them suffered from depression or a depressive illness. If you were conducting 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, what would the null and alternative hypotheses be?A low-level CDC bureaucrat wants to please his boss by gathering evidence thatthe current government-mandated shutdown of society is not causing people’s mentalhealth to deteriorate, so that it can safely be continued for several years if anyexpert says it’s necessary.He polls a random sample of 1600 citizens, gathering data on such items asincome loss, weight gain, access to toilet paper, hours spent binge-watchingNetflix, and number of injuries caused by household fights, and compiles all thisinto a scientifically-weighted “misery index”.The mean misery index from the sample is 99.2; it seems reasonable to use apopulation standard deviation σ = 19.1.a) Does this information provide significant evidence (at the 5% level) that thenationwide mean misery index is less than 100? Set up appropriate null andalternative hypotheses, calculate the appropriate test statistic, find the P-value,and state your conclusion. (10)b) A CDC press release publishing the results of this study claims that…A low-level CDC bureaucrat wants to please his boss by gathering evidence thatthe current government-mandated shutdown of society is not causing people’s mentalhealth to deteriorate, so that it can safely be continued for several years if anyexpert says it’s necessary.He polls a random sample of 1600 citizens, gathering data on such items asincome loss, weight gain, access to toilet paper, hours spent binge-watchingNetflix, and number of injuries caused by household fights, and compiles all thisinto a scientifically-weighted “misery index”.The mean misery index from the sample is 99.2; it seems reasonable to use apopulation standard deviation σ = 19.1.a) Does this information provide significant evidence (at the 5% level) that thenationwide mean misery index is less than 100? Set up appropriate null andalternative hypotheses, calculate the appropriate test statistic, find the P-value,and state your conclusion. b) A CDC press release publishing the results of this study claims that…
- In analyzing the consumption of cottage cheese by members of various occupational groups, the United Dairy Industry Association found that 326 of 837 professionals seldom or never ate cottage cheese, versus 220 of 489 white-collar workers and 522 of 1243 blue-collar workers (Sheet 53). Assuming independent samples, use the 0.03 level in testing the null hypothesis that the population proportions could be the same for the three occupational groups. Sheet 53 Group 1 Group 2 Group 3 Total seldom or never 326 220 522 1068 often 511 269 721 1501 Total 837 489 1243 2569 Select one: a) chi-square stat = 4.81, crit. value = 7.01, fail to reject H0, population proportions are not different b) p-value = 0.09, reject H0, population proportions are not different c) chi-square stat = 4.81, crit. value = 9.2, fail to reject H0, population proportions are not different d) p-value = 0.029, reject H0, population proportions differentA 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 notUtilizing 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?
- 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. find the p value31% of all pygmy softshell toises have stripes on their shells. A herpetologist in Cititon collects a sample of 28 pygmy softshell tortoises and finds that 8 of them have stripes on their shells. Is there enough evidence to conclude, at a significance of alpha=0.05, that the proportion of pygmy softshell tortoises in Cititon with stripes on their shells is less than 31%? What is the claim? What is the null hypothesis? What is the alternative hypothesis? What is the test statistic? What is/are the critical value(s)? Do we reject the null hypothesis? What conclusion do we draw? What is the P-value for the problem above?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 random sample of 50 suspension helmets used by motorcycle riders and automobile race-car drivers was subjected to an impact test, and on 18 of these helmets some damage was observed.The Stanford University Heart Transplant Study was conducted to determine whether an experimental heart transplant program increased lifespan. Each patient entering the program was officially designated a heart transplant candidate, meaning that he was gravely ill and might benefit from a new heart. Patients were randomly assigned into treatment and control groups. Patients in the treatment group received a transplant, and those in the control group did not. The table below displays how many patients survived and died in each group ___ control______treatment___ alive 4 | 24 dead 30 | 45 A hypothesis test would reject the conclusion that the survival rate is the same in each group, and so we might like to calculate a confidence interval. Explain why we cannot construct such an interval using the normal approximation. What might go wrong if we constructed the confidence interval despite this problem?31% of all pygmy softshell tortoises have stripes on their shells. A herpetologist in Cititon collects a sample of 28 pygmy softshell tortoises and finds that 8 of them have stripes on their shells. Is there enough evidence to conclude, at a significance of alpha = 0.05, that the proportion of pygmy softshell tortoises in Cititon with stripes on their shells is less than 31%? What is the claim? What is the null hypothesis? What is the alternative hypothesis? What is the test statistic? What is/are the critical value(s)? Do we reject the null hypothesis? What conclusion do we draw? What is the P-value for the problem above?