Dottie Kleman is the "Cookie Lady." She bakes and sells cookies at 50 different locations. Ms. Kleman is concerned about absenteeism among her workers. The information below reports the number of days absent for a sample of 10 workers during the last two-week pay period. The sample mean is calculated to be 1.8 and sample standard deviation is 1.1353. Develop a 95% confidence interval for the population mean. Assume that the population distribution is normal. Is it reasonable to conclude that the typical worker misses 1 day during a pay period?
A) [0.99, 2.61] It is unreasonable to conclude that the mean number of days of work missed is1per employee.
B) [0.99, 2.61] It is reasonable to conclude that the mean number of days of work missed is 1 per employee.
C) [-0.99, -2.61] It is unreasonable to conclude that the mean number of days of work missed is 1 per employee.
D) [-0.99, -2.61] It is reasonable to conclude that the mean number of days of work missed is 1 per employee.

Question

Dottie Kleman is the "Cookie Lady." She bakes and sells cookies at 50 different locations. Ms. Kleman is concerned about absenteeism among her workers. The information below reports the number of days absent for a sample of 10 workers during the last two-week pay period.  The sample mean is calculated to be 1.8 and sample standard deviation is 1.1353. Develop a 95% confidence interval for the population mean. Assume that the population distribution is normal. Is it reasonable to conclude that the typical worker misses 1 day during a pay period?
A) [0.99, 2.61] It is unreasonable to conclude that the mean number of days of work missed is1per employee. 
B) [0.99, 2.61] It is reasonable to conclude that the mean number of days of work missed is 1 per employee. 
C) [-0.99, -2.61] It is unreasonable to conclude that the mean number of days of work missed is 1 per employee. 
D) [-0.99, -2.61] It is reasonable to conclude that the mean number of days of work missed is 1 per employee.

Quizplus · Accepted Answer

Using a t-distribution with 9 degrees of freedom and a level of significance of 0.05, the critical value is 2.306.

The formula for a confidence interval for the population mean is:

CI = sample mean ± (t-critical value) * (sample standard deviation / sqrt(sample size))

CI = 1.8 ± 2.306 * (1.1353 / sqrt(10))

CI = [0.99, 2.61]

Since the confidence interval includes the value of 1, it is reasonable to conclude that the typical worker misses 1 day during a pay period.

Dottie Kleman Is the "Cookie Lady