Question

g A random sample of 100 students was taken. Eighty-five of the student in the sample experienced anxiety during the exam. We are interested in determining whether or not the proportion of the student who experience anxiety during the exam is significantly more than 80%. The test statistic is

Answer 1

The test statistic is
`z = 1.25`

Explanation:

We are interested in determining whether or not the proportion of the student who experience anxiety during the exam is significantly more than 80%.

At the null hypothesis, we test if the proportion is 80%, that is:

`H_0: p = 0.8`

At the alternate hypothesis, we test if the proportion is more than 80%, that is:

`H_a: p > 0.8`

The test statistic is:

`z = (X - \mu)/((\sigma)/(√(n)))`

In which X is the sample mean,
`\mu` is the value tested at the null hypothesis,
`\sigma` is the standard deviation and n is the size of the sample.

80% is tested at the null hypothesis:

This means that
`\mu = 0.8, \sigma = √(0.2*0.8) = 0.4`

A random sample of 100 students was taken. Eighty-five of the student in the sample experienced anxiety during the exam.

This means that
`n = 100, X = (85)/(100) = 0.85`

The test statistic is

`z = (X - \mu)/((\sigma)/(√(n)))`

`z = (0.85 - 0.8)/((0.4)/(√(10)))`

`z = 1.25`

The test statistic is
`z = 1.25`