Question

a) Use the Student's t-distribution to find the t-value for each of the given scenarios. Round t-values to four decimal places.

• Find the value of t such that the area in the right tail of the t-distribution is 0.01, if the sample size is 89.
  
  t=
  
• Find the value of t such that the area in the left tail of the t-distribution is 0.0005, if the sample size is 134.
  
  t=
  
• Find the value of t such that the area in the right tail of the t-distribution is 0.005, if the sample size is 142.
  
  t=
  
• Find the two values of t such that 95% of the area under the t-distribution is centered around the mean, if the sample size is 71. Enter the solutions using a comma-separated list.
  
  t=

b) A forester with the National Park Service was tasked with estimating the average age of the bald cypress trees (Taxodium distichum) in Big Cypress Swamp - a region in Everglades National Park. The forester extracted core samples from 32 randomly selected bald cypress trees in Big Cypress Swamp. The mean age of the sample was 253.5 years with a standard deviation of 13.2 years.

Using a 95% confidence level, determine the margin of error, E, and a confidence interval for the average age of all bald cypress trees in Big Cypress Swamp. Report the confidence interval using interval notation. Round solutions to two decimal places, if necessary.

The margin of error is given by E=.

A 95% confidence interval is given by ____

c) Each year, researchers at the U.S. Bureau of Labor Statistics (BLS) administer the American Time Use Survey (ATUS). Researchers estimate the average amount of time Americans spend on daily activities, such as working, housework, and leisure activities. In particular, one activity that is of interest is the average amount of time Americans spend watching television each day.

A researcher complied a random sample of 16 Americans and asked each person how much time they spent watching television each day. The results are given below.

2	0.5	1.5	3.4	4.7	2.5	0.5	2
4.5	3.6	3.6	1.3	1.8	3.6	1	0.6

Determine the point estimate, x¯ and the sample standard deviation, s. Round the solutions to four decimal places, if necessary.

x¯=

s=

Using a 98% confidence level, determine the margin of error, E, and a confidence interval for the average time Americans spend watching television each day. Report the confidence interval using interval notation. Round solutions to two decimal places, if necessary.

The margin of error is given by E=.

A 98% confidence interval is given by . ____

d) An epidemiologist needs to estimate the proportion of residents of St. Lucie county that have been infected with COVID-19. Determine the most conservative estimate of the sample size required to limit the margin of error to within 0.075 of the population proportion for a 98% confidence interval.

Round the solution up to the nearest whole number.

n=

Answer 1