Question

To check whether the popularity of a political candidate is down from 60%, a random sample of 1000 voters is surveyed. K out of 1000 favor the candidate.

If K=580 test the 60% popularity hypothesis at significance level α = .05.

Find the minimal number K that does not reject the 60% popularity hypothesis.

Using Ti-34 calculator

Equations/answer written out using

binomcdf(x,x,x)

Binompdf(x,x,x)

Invnorm

InvT

tcdf

If possible/needed to solve the equation

Answer 1

HYPOTHESIS TEST-

We have to perform one sample proportion test.

We have to test for null hypothesis

against the alternative hypothesis

Our test statistic is given by

Here,

Number of observations

[Using code 'normalcdf(-10,-1.290994,0,1)']

Level of significance

We reject our null hypothesis if

Here, we observe that

So, we cannot reject our null hypothesis.

Hence, based on the given data we can conclude that there is no significant evidence that the popularity of a political candidate is down from 60%.

MINIMAL NUMBER K-

Suppose, minimal number be k.

Then we have as follows.

Number of observations

Level of significance

So, critical value is given by [Using code 'invNormal(0.05,0,1)']

Thus we need,

Hence, the minimal number K that does not reject the 60% popularity hypothesis is 575.