In a random sample of 21 ​people, the mean commute time to work was 34.1 minutes and the standard deviation was 7.2 minutes. Assume the population is normally distributed and use a​ t-distribution to construct a 80​% confidence interval for the population mean μ. What is the margin of error of μ​?     Interpret the results. The confidence interval for the population mean μ is=(     ,      ) ​(Round to one decimal place as​ needed.)     The margin of error of μ is= ​(Round to one decimal place as​ needed.)     Interpret the results.   A.If a large sample of people are taken approximately 80​% of them will have commute times between the bounds of the confidence interval.   B.With 80​% ​confidence, it can be said that the population mean commute time is between the bounds of the confidence interval.   C.With 80​% confidence, it can be said that the commute time is between the bounds of the confidence interval.   D.It can be said that 80​% of people have a commute time between the bounds of the confidence interval.

From generation to generation, the average age when smokers first start to smoke varies. However, the standard deviation of that age remains constant at around 2.1 years. A survey of 37 smokers of this generation was done to see if the average starting age is at least 19. The sample average was 18.1 with a sample standard deviation of 1.3. Do the data support the claim at the 5% level? Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) O Part (a) O Part (b) O Part (c) O Part (d) State the distribution to use for the test. (Round your standard deviation to four decimal places.) O Part (e) What is the test statistic? (Round your answer to two decimal places.) --Select--- v = O Part (f) What is the p-value? (Round your answer to four decimal places.) Explain what the p-value means for this problem. O If H, is false, then there is a chance equal…

The operations manager at a light emitting diode (LED) light bulb factory needs to estimatethe mean life of a large shipment of LEDs. The manufacturer’s specifications are that thestandard deviation is 1,500 hours. A random sample of 64 LEDs indicated a sample mean lifeof 49,875 hours.Construct a 95% confidence interval estimate for the population mean life of LED light bulbsin this shipment.Ans: CI = ______________________ Paste your working here:

The researcher took a random sample of 50 residents and found that the mean height of men is 175cm. Suppose that the team is made aware of the fact that the distribution of heights is distributed normally.  1, The sample median is an unbiased estimate of the mean height of men. Is the following statement about the estimator true?    2, Determine whether or not the median or mean is an efficient estimator of the population median.