According to nielsen media research. of all the u. s. households that owned at least one television set, 83% had two or more sets. a local cable company canvassing the town to promote a new cable service found that of the 300 households visited, 240 had tow or more television sets. at  α= .05 proportion is less than the one in the report. 

The proportion of U.S. households that owned two or more televisions is 83%.

Step-by-step explanation:

To determine whether the proportions of U.S. households that owned two or more televisions is less than 83% or not let us perform a hypothesis test for single proportion.

Assumptions:

The sample size (n) selected by the local cable company is 300 which is quite large. Then according to the Central limit theorem the sampling distribution of sample proportion follows a normal distribution with mean p and standard deviation .

Since the sampling distribution of sample proportions follows a normal distribution use the z-test for one proportion to perform the test.

The hypothesis is:

: The proportion of U.S. households that owned two or more televisions is 83%, i.e.

:The proportion of U.S. households that owned two or more televisions is less than 83%, i.e.

Decision Rule:

At the level of significance α = 0.05 the critical region for a one-tailed z-test is:

**Use the z table for the critical values.

So, if the null hypothesis will be rejected.

Test statistic value:

Here is the sample proportion.

Compute the value of as follows:

Now compute the value of the test statistic as follows:

The test statistic is -1.383 which is more than -1.645.

Thus, the test statistic lies in the acceptance region.

Hence we fail to reject the null hypothesis.

Conclusion:

At 0.05 level of significance we fail to reject the null hypothesis stating that the proportion of U.S. households that owned two or more televisions is  83%.