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Answer:
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.
<u>Assumptions:</u>
The sample size (<em>n</em>) 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 <em>p</em> and standard deviation .
Since the sampling distribution of sample proportions follows a normal distribution use the <em>z</em>-test for one proportion to perform the test.
<u>The hypothesis is:</u>
: 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.
<u>Decision Rule:</u>
At the level of significance α = 0.05 the critical region for a one-tailed <em>z</em>-test is:
**Use the <em>z</em> table for the critical values.
So, if the null hypothesis will be rejected.
<u>Test statistic value:</u>
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.
<u>Conclusion:</u>
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%.
