A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 19.6, and the sample standard deviation, s, is found to be 5.6. (a) Construct a 98% confidence interval about u if the sample size, n, is 32. (b) Construct a 98% confidence interval about µ if the sample size, n, is 58. How does increasing the sample size affect the margin of error, E? (c) Construct a 99% confidence interval about u if the sample size, n, is 32. How does increasing the level of confidence affect the size of the margin of error, E? (d) If the sample size is 21, what conditions must be satisfied to compute the confidence interval? (a) Construct a 98% confidence interval about u if the sample size, n, is 32. Lower bound:; Upper bound: (Round to two decimal places as needed.) CHE

The law of large numbers states that as the number of observations drawn at random from a population with finite mean  increases, the mean  of the observed values:   a. tends to get closer and closer to the population mean .   b. gets smaller and smaller.   c. gets larger and larger.   d. fluctuates steadily between 1 standard deviation above and 1 standard deviation below the mean.   I collect a random sample of size n from a population and compute a 95% confidence interval for the proportion I observe from the population. What could I do to produce a new confidence interval with a larger width (larger margin of error) based on these same data?   a. I could use the same confidence level but compute the interval n times; approximately 5% of these intervals will be larger.   b. Nothing can guarantee absolutely that I will get a larger interval; I can only say the chance of obtaining a larger interval is 0.05.   c. I could use a smaller confidence…

A simple random sample of size n is drawn from a population that is normally distributed. The sample​ mean, x​, is found to be 115​, and the sample standard​ deviation, s, is found to be 10. ​(a) Construct an 80​% confidence interval about μ if the sample​ size, n, is 25. ​(b) Construct an 80​% confidence interval about μ if the sample​ size, n, is 12. ​(c) Construct a 70​% confidence interval about μ if the sample​ size, n, is 25. ​(d) Could we have computed the confidence intervals in parts​ (a)-(c) if the population had not been normally​ distributed?

The distribution of study times for first year students follows a Normal distribution with standard deviation σσ = 54 minutes. Suppose a sample of 487 students found that the mean study time for these students was x¯x¯= 173 minutes per week. Use this to find a 88.28% confidence interval to estimate the mean study time for all students. We are 88.28% confident that the mean study time for first year students is between minutes_____ and ____  minutes.   What is the margin of error for your confidence interval?