The Linguistics Department at the University of Massachusetts at Amherst recently studied the relationship between external facial movements and the acoustics of speech sounds. Facial motions were...

The Linguistics Department at the University of Massachusetts at Amherst recently studied the relationship between external facial movements and the acoustics of speech sounds. Facial motions were captured using infrared markers and summarized using a unitless measure (x). A special unidirectional microphone was used for acoustic recording and to measure the sound level of speech (y, in dB). A random sample of individuals was selected, and each was asked to read a certain word. The facial expression and sound level were recorded for each person, and the summary statistics are given below.

a. Find an estimate of the true mean decibel level for a facial expression value of x = 0.40.

b. Find a 95% confidence interval for the true mean decibel level for a facial expression value of x = 0.40.

c. Suppose the facial-expression value is 0.55. Conduct a hypothesis test to determine whether there is any evidence that the true mean decibel level is greater than 30. Use a significance level of 0.01.