At Least As Extreme A random sample of 860 births in New York State included 426 boys, and that sample is to be used for a test of the common belief that the proportion of male births in the population is equal to 0.512.


a. In testing the common belief that the proportion of male babies is equal to 0.512, identify the values of p^ and p.

A city government claims that no more than $25\%$ of households have solar panels. A researcher suspects the rate is actually higher and surveys $200$ households, finding that $62$ have solar panels. Test if there is evidence that more than $25\%$ of households have solar panels using $\alpha =0.01$.

A city claims that $30\%$ of households recycle regularly. A researcher surveys $200$ households to see if the true proportion is different and finds that $78$ recycle regularly. Use $\alpha =0.05$ to test the claim.

Finding P-Values

In Exercises 13–16, do the following:

i. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed.

ii. Find the P-value. (See Figure 8-3.)

iii. Using a significance level of α = 0.05 should we reject H0 or should we fail to reject H0?

The test statistic of z = -0.75 is obtained when testing the claim that p<1/3.

Finding P-Values

In Exercises 13–16, do the following:

i. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed.

ii. Find the P-value. (See Figure 8-3.)

iii. Using a significance level of α = 0.05 should we reject H0 or should we fail to reject H0?

The test statistic of z = -1.60 is obtained when testing the claim that p ≠ 0.455.

At Least As Extreme A random sample of 860 births in New York State included 426 boys, and that sample is to be used for a test of the common belief that the proportion of male births in the population is equal to 0.512.

b. For random samples of size 860, what sample proportions of male births are at least as extreme as the sample proportion of 426/860?

Discarded Plastic Find the test statistic used for the hypothesis test described in Exercise 1.

Perform a 2-tailed hypothesis test for the true proportion of successes using the given values:

$\alpha =0.01$, $n=40$, $x=28$, & claim is $p=0.75$

Perform a 2-tailed hypothesis test for the true proportion of successes using the given values:

$\alpha =0.10$, $n=100$, $x=42$, & claim is $p=0.25$