Question

Claim: Most adults believe that it is important to vote on Election Day. A software firm survey of 544 randomly selected adults showed that 62% of them believe that it is important to vote on Election Day.

(Round to two decimal places as needed.)

Answer 1

To two decimal places, the value of the test statistic is 4.47.

The value of the test statistic can be calculated using the formula for a test statistic in the context of a hypothesis test for a proportion. The test statistic is given by:

`[ z = \frac{p - P}{\sqrt{(P(1-P))/(n)}} ]`

Where:

( p ) is the sample proportion

( P ) is the hypothesized population proportion

( n ) is the sample size

In this case, the sample proportion is ( p = 0.62 ) (which corresponds to 62% as a decimal), the hypothesized population proportion is ( P = 0.50 ) (which corresponds to 50% as a decimal, representing no difference from the null hypothesis), and the sample size is ( n = 544 ).

Substituting these values into the formula, we get:

`[ z = \frac{0.62 - 0.50}{\sqrt{(0.50(1-0.50))/(544)}} ]`

Solving for ( z ), we find:

`[ z \approx 4.47 ]`

Rounding to two decimal places, the value of the test statistic is 4.47.

Complete question:

Claim: Most adults believe that it is important to vote on Election Day. A software firm survey of 544 randomly selected adults showed that 62% of them believe that it is important to vote on Election Day. The value of the test statistic is (Round to two decimal places as needed.)