Question

Plastic microparticles are contaminating the world’s shorelines and studies have shown that most of these come from washing polyester clothes, especially fleece. A recent study of 110 samples from shorelines at various locations around the world found that the mean number of polyester fibers discharged into wastewater from washing fleece is 280 fibers per liter of wastewater, with a standard deviation of 848

a. Explain why this meets the conditions to use a theoretical distribution to form the confidence interval.

b. Find and interpret a 99% confidence interval for the mean number of polyester fibers discharged into wastewater.

Answer 1

a)

since our sample size is greater than 30, the Central Limit Theorem tells that the sampling distribution will approximately a normal distribution so we use normal distribution to estimate critical z values

b)