Question

in a sample of 500 voters, 400 indicated they favour the incumbent governor.The 95% confidence interval of voters not favouring the incumbent is ​

Answer 1

Answer:

Step-by-step explanation:

Our question is: in a sample of 500 voters, 400 indicated they favour the incumbent governor.The 95% confidence interval of voters not favouring the incumbent is ..

Lets consider the fact that we have that our population is 500 voters and 400 of them indicated favour to the governor.

Now we need to consider (1 - x) * 100 = 95, where x is a constant to use n order to help us finding our interval with a distribution table.

Hence x = 0.05.

We also know that 400/500 are the percentage of voters who indicated they favour the incumbent governor.

Thus 400/500 will be our mean value.

Hence, our 95% confidence interval will be of the form of the interval of the picture bellow.

Where s is our standard deviation and with the table bellow we can easil check that t_499,0.025 = 1.965.

Then we just need to substitute the values and get the valid interval of 95% confidence.

I hope this helped you.

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