Question

When the GSS most recently asked whether human beings developed from earlier species of animals, 53.8% of 1095 respondents answered that this was probably or definitely not true. Find a 99% confidence interval for the corresponding population proportion, and indicate whether you can conclude that a majoviny of Americans felt this way.

Answer 1

The true population proportion of Americans who believe that human beings developed from earlier species of animals is between 0.517 and 0.559.

We can conclude that a majority of Americans felt this way.

Step-by-step explanation:

We can find the 99% confidence interval for the population proportion by using the following formula:

`$$p \pm me$$`

where:

• p is the sample proportion (0.538)
• n is the sample size (1095)
• me is the margin of error, which is equal to
  `$z_(\alpha/2) \cdot √(p(1-p)/n)$`

For a 99% confidence interval,
`$\alpha` = 0.01, so
`$z_(\alpha/2)` = 2.575. Plugging in the values, we get:

`$$0.538 \pm 2.575 \cdot √(0.538(1-0.538)/1095) \approx (0.517, 0.559)$$`

Therefore, we can be 99% confident that the true population proportion of Americans who believe that human beings developed from earlier species of animals is between 0.517 and 0.559.

Since the lower bound of the confidence interval (0.517) is greater than 0.5, we can conclude that a majority of Americans felt this way.