1-6 please

1) In preparing a report on the economy, we need to estimate the percentage of businesses that plan to hire additional employees in the next 90 days. How many randomly selected employers must we contact in order to create an estimate in which we are 98% confident with a margin of error of 3%? 2) During routine screening, a doctor notices that 22% of her adult patients show higher than normal levels of glucose in their blood - a possible warning sign for diabetes. Hearing this, some medical researchers decide to conduct a large-scale study, hoping to estimate the proportion to within 2.5% with 95% confidence. How many randomly selected adults must they test? 3) Describe how the critical value of t for a 95% confidence interval changes as the numbers of degrees of freedom increases. Bjork Larsen was trying to decide whether to use a new racing wax for cross-country skis. He decided that the wax would be worth the price if he could average less than 55 seconds on a course he knew well, so he planned to study the wax by racing on the course 8 times. His 8 race times were 56.3, 65.9, 50.5, 52.4, 46.5, 57.8.52.2, and 43.2 seconds. 4) Determine if a confidence interval is appropriate by checking the necessary assumptions and conditions. 5) Should he buy the wax? Justify your answer using a confidence interval. 6) A nutrition lab tested 40 hot dogs to see if their mean sodium content was less than the 325-mg upper limit set by regulations for "reduced sodium" franks. A 90% confidence interval estimated the mean sodium content for this kind of hot dog at 317.2 to 326.8 mg. Given this, what would you tell the lab about whether the hot dogs satisfy the regulation