Question

A speed reading course claims that it can boost reading speeds to 1050 words per minute. 

In a random sample of 49 people who took the course, the average was 1020 words per minute, with a standard deviation of 90 words per minute. What is the z-value rounded to the nearest hundredth?  Is there enough evidence to reject the claim?​

Answer 1

we get the Z-value of given data is
`-2.33`.

Yes there is enough evidence to reject the claim.

Explanation:

Given that,

Reading speed could be boost to 1050 words per minute.

total number of people is 49.

there average reading speed is 1020 words per minute.

Standard deviation is 90 words per minute.

So, for the Z-value Rounded to nearest Hundredth is

`Z-value = (xbar - u)/((\sigma)/(√(n) ) )`

`xbar = 1020`
`u = 1050`
`n=49`
`\sigma = 90` putting these values we get,

`z-value = (1020-1050)/((90)/(√(49) ) )`

=
`(-30* 7)/(90)`

=
`(-210)/(90) =-2.33`

Here, we get the Z-value of given data is
`-2.33`.

Now, for Evidence for Rejecting the claim we need to find P-value

P-value=
`P (Z<-2.33)`

=
`0.9903`

So, Yes there is enough evidence to reject the claim.