Suppose that job applicants applying for positions at a large corporation are required to complete a questionnaire to determine employment eligibility. Though many applicants do give acceptable responses to all 13 questions on the questionnaire, the human resources director suspects that recent job applicants are less likely to meet the minimum hiring requirements than past applicants. To assess the recent pool of applicants, the director selects a simple random sample of 451 questionnaires and records the number of acceptable responses. She finds that this sample contains an average of 11.800 acceptable responses, with a standard deviation of 0.442 responses. Furthermore, records from all applications over the last several years give the standard deviation for the number of acceptable responses as 0.309. The director uses this information to construct a 95% z-confidence interval for the mean number of acceptable responses per questionnaire. Does this situation meet the requirements for a z-confidence interval? No, because the sample standard deviation is different from the standard deviation for all applicants. No, because the number of acceptable answers on the pre-employment questionnaires is discrete and therefore cannot possibly be normally distributed in the population. Yes, because the data come from a random sample. Yes, because the data come from a simple random sample, the population standard deviation is known, and the sample size is large.

A auto shop wants to examine the proportion of customers that have to return after an appointment. Last year, an examination of 264 customers found that 30.1% had to return after an appointment. You instituted some changes at the auto shop this year, and found from a sample of 326 customers that 22.4% had to return after an appointment. You want to conduct an analysis to determine if there has been an increase in the proportion of customers that need to return after an appointment since the past year, with a = 0. 10. Using this information, what is the critical value of your analysis? Round your final answer to two decimal places. 2.11 1.96 2.33 1.28 1.64

From the U.S. Census Bureau’s American Community Survey in 2019 it was found that 33.13%of United States residents over the age of 25 had an educational attainment of a bachelor’sdegree or higher. In the District of Columbia, the percentage of residents over the age of 25 whohad attained a bachelor’s degree or higher was 59.67%. An investigator for the U.S. CensusBureau took a random sample of seven residents from the District of Columbia and asked themtheir highest educational degree they had obtained. a) Verify that the sample from the District of Columbia satisfies the conditions of thebinomial experiment. Write one sentence to check each requirement in context of theinvestigation.b) Assuming the sample from the District of Columbia is a binomial experiment, build theprobability distribution in a single table and include the table in your solutions. You maypresent this table horizontally or vertically and leave the probabilities unrounded. Thereare two possible ways to do this:  To…

A researcher is interested in exploring the relationship between calcium intake and weight loss. Two different groups, each with 2626 dieters, are chosen for the study. Group A is required to follow a specific diet and exercise regimen, and also take a 500-mg supplement of calcium each day. Group B is required to follow the same diet and exercise regimen, but with no supplemental calcium. After six months on the program, the members of Group A had lost a mean of 10.4 pounds with a standard deviation of 2.6 pounds. The members of Group B had lost a mean of 11.7pounds with a standard deviation of 2.8 pounds during the same time period. Assume that the population variances are not the same. Construct a 99% confidence interval to estimate the true difference between the mean amounts of weight lost by dieters who supplement with calcium and those who do not. Let Population 1 be the amount of weight lost by Group A, who took a 500-mg supplement of calcium each day, and let Population 2 be…