Question

The claim is that the proportion of peas with yellow pods is equal to 0.25%E2%80%8B (or 25%). The sample statistics from one experiment include 540 peas with 104 of them having yellow pods. Find the value of the test statistic.

Answer 1

The value of the test statistic is -0.4.

Explanation:

The null hypothesis is:

`H_(0) = 0.25`

The alternate hypotesis is:

`H_(1) \\eq 0.25`

We have to find the standard deviation
`\sigma`, which is

`\sigma = \sqrt{(p(1-p))/(n)}`

In which p is the proportion estimated at the null hypothesis.

Sample of 540. So

`\sigma = \sqrt{(0.25*0.75)/(540)} = 0.0186`

Our test statistic is:

`t = (X - p)/(\sigma)`

In which X is the mean calculated.

So

`X = (104)/(540) = 0.1926`

`t = (X - p)/(\sigma)`

`t = (0.1926 - 0.2)/(0.0186)`

`t = -0.4`

The value of the test statistic is -0.4.