Question

Ariana Grande released her well anticipated “thank u, next” album on February 8th , 2019. A researcher wants to know how Clemson college students feel about her new album. Fifteen Clemson college students were randomly sampled to listen to the album and rate the album on a scale from 0 -100.The following ratings were collected:

100, 91, 85, 89, 94, 72, 79, 81, 85, 95, 89, 85, 97, 81, 90. Using this data, answer the following questions:

a) Calculate a point estimate that separates the lowest 50% of ratings from the highest 50% of ratings.

b) Calculate a point estimate of the mean rating for the population

c) Calculate the standard error of the point estimate from part (b)

d) Calculate a point estimate of the proportion of all ratings greater than or equal to 90.

.

Answer 1

Solution:-
a)
=> Median : The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

72 79 81 81 85 85 85 89 89 90 91 94 95 97 100   

So, the median is 89 .

b) Mean : 1313/15 = 87.53

c) standard error = s/sqrt(n) = 7.4820/sqrt(15) = 1.9318

d) The number of observations that are greater than equal to 90 is (6)

P = number of values in the sample that are greater than or equal 90/total number of values in the sample

P = 6/15 = 0.4