Question

In a certain university, 12 out of 250 first year students like to listen to classical music. We want to test if the percentage of the first year students who like to listen to classical music is less than 10%. Construct the randomization distribution and find the p-value

Answer 1

Therefor it is clear that the percentage of first year student like to listen classical music is less than 10 %

Explanation:

Given as ;

The total number of first year students in an university = 250

The number of student who like to listen classical music = 12 out of 250

Let x % of student like to listen classical music

So, x% of 250 = 12

or,
`(x)/(100)` × 250 = 12

or, x × 250 = 12 × 100

Or, x =
`(1200)/(250)`

∴ x = 4.8

I.e the percentage of first year student like to listen classical music is 4.8%

Now, Again

The 10% of the total number of student is

I.e 10% of 250

or,
`(10)/(100)` × 250

Or ,
`(2500)/(100)`

I.e The 10% of the total number of student = 25

Since 4.8 % of total number of students is 12 and 10% of total number of students is 25

Therefor it is clear that the percentage of first year student like to listen classical music is less than 10 % . answer