Question

Researchers doing a study comparing time spent on social media and time spent on studying randomly sampled 200 students at a major university. They found that students in the sample spent an average of 2.3 hours per day on social media and an average of 1.8 hours per day on studying. If all the students at the university in fact spent 2.2 hours per day on studying, with a standard deviation of 2 hours, the shape of the sampling distribution of the sample average time spent studying is: O Normal, centered at 1.8. ONormal, centered at 1.8 only if all samples have a sample average of 1.8 hours studying. O Normal, centered at 2.2. Normal, centered at 2.2 only if the studying times are Normally distributed.

Answer 1

1)shape of the sampling distribution:\

normal ; centered at 2.2

2)

as z score =(X-mean)/std errror and std error =standard deviaiton/sqrt(n)

P(Xbar<1.8)=P(Z<(1.8-2.2)/(2/sqrt(200))=P(Z<-2.83)=0.0023