With the performed hypothesis test, the data supports the statement that the percentage of TV sets owned in the US is about 80%.
The approximate number of television sets for every 1,000 people in the United States = 806
The percentage of TV sets owned in the United States = 80%
Significance level, a = 0.05
To perform a hypothesis test is as follows:
Null hypothesis (H₀): The percentage of TV sets owned in the US is 80%
Alternative hypothesis (H₁): The percentage of TV sets owned in the US is not 80%
Using the z-test for proportions to test this hypothesis with the formula for the z-test for proportions as:
z = (p - P) / √(P(1-P) / n)
Where: p = sample proportion
P = population proportion under the null hypothesis
n = sample size
The sample proportion (p) is 806/1000 = 0.806.
The population proportion under the null hypothesis (P) is 0.80.
We can calculate the standard error as √(P(1-P) / n)
= √(0.80 * 0.20 / 1000)
= 0.0126.
Then, we can calculate the z-score as (0.806 - 0.80) / 0.0126
= 0.006 / 0.0126
= 0.4762.
Using a standard normal distribution table, at a significance level of 0.05, the critical z-value is approximately ±1.96.
The calculated z-score of 0.4762 is within the range of -1.96 to 1.96. We fail to reject the null hypothesis because there is insufficient evidence to conclude that the percentage of TV sets owned in the US is not 80%.
Thus, the data supports the statement that the percentage of TV sets owned in the US is about 80%.