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In constructing a confidence interval for the population mean using the t-distn'bution, we often need the degrees of freedom (df), confidence level, and the critical value. Use the Student t-distribution to determine the missing values in the table below. Report the positive it critical value accurate to 3 decimal places. Sample Degrees of Confidence Critical size freedom level value (t) Check Answer If n = 12, i = 34, and s = 3, find the margin of error E at a 90% confidence level. Give your answer to at least two decimal places. .5 (Hint: Use the formula E = t - ; where S is the sample standard deviation, and n is the sample size .) w: :J The Chartered Financial Analyst (CFA) designation is fast becoming a requirement for serious investment professionals. Although it requires a successful completion of three levels of grueling exams, it also entails promising careers with lucrative salaries. A student of finance is curious about the average salary of CFA charterholders in Toronto. He takes a random sample of 56 charterholders and computes a mean salary of $86,200 with a standard deviation of $5,050. Use this sample information to find a 99% confidence interval for the average salary of CFA charterholders in Toronto. Assume that the values are approximately normally distributed. Use t-distribution. Round to the nearest dollar. (a) What is the best point estimate of the population mean? :] dollars For part (b) round your answer to 3 decimal places. (b) What is the critical t-value that will need to be used to calculate the confidence interval? For parts (b),(c), round your answer to the nearest dollar. (d) What is the 99% confidence interval? A student of journalism is curious about the average rates paid to freelancers by online magazines. She takes a random sample of 101 online publications and computes a mean rate per word of 13.5 cents, with a sample standard deviation of 5.1 cents. The student wants to use this sample information to find a 90% confidence interval for the average pay rate per word. Round all final answers to 3 decimal places. (a) What is the critical t-value that will need to be used to calculate the confidence interval? (b) What is the 90% confidence interval? A criminal justice researcher wants to construct a 95 % confidence interval with a sample size of 20. The sample mean and standard deviation are calculated as a: = 18 and s = 9. What is the t-value from the student t-table? O 2.861 O 2.086 O 2.093 O 2.539 0 None of the above. A Health and Safety student at Humber is curious about the average salaries paid to City of Toronto Environmental Health and Safety managers. She takes a random sample of 61 managers and computes a mean salary of $96,000, with a sample standard deviation of $800. The student wants to use this sample information to find a 90% confidence interval for the average pay. Round your t-value to 3 decimal places and the confidence interval values to 2 decimals. (a) What is the critical t-value that will need to be used to calculate the confidence interval? (b) What is the 90% confidence interval? In constructing a confidence interval for a population mean, which of the following are true? Select four (4} true statements from the list below: C . A point estimate is a single population parameter that is used to a estimate a sample statistic. C . If a particular 94% confidence interval captures the population mean, then for the same sample data, the population mean will also be captured at the 98% confidence level. C . A confidence interval that fails to capture the population mean will also fail to capture the sample mean. C . If a confidence interval for the population mean is constructed from a sample of size n = 30, that interval must contain the population mean. C . If the point estimate and lower limit for a confidence interval are 175.5 and 156.5 respectively, then the upper limit must be 370. C - If a confidence interval does not contain the point estimate, then an error has been made in the calculation. C - The width of the confidence interval depends on the size of the sample. C - Increasing the sample size will not change the width of the confidence interval. C . Increasing the confidence level will not change the width of the confidence interval. C . For a confidence level of 96%, the left-tail area a/ 2 = 0.08. C . A 96% confidence interval must capture 96% of the population values. C - For the same sample data, a 95% confidence interval will be narrower than a 99% confidence interval. For a confidence level of 90% with a sample size of 31, find the critical t value