Final answer:
The analysis rejects the null hypothesis, indicating a significant increase in the proportion of US homes watching at least one live American football game since 2012.
Step-by-step explanation:
To test the claim that the proportion of US homes watching at least one live American football game has changed, we can use a one-proportion hypothesis test. The null hypothesis (H0) would be that the proportion remains the same as in 2012, while the alternative hypothesis (H1) would be that the proportion has changed.
The criteria for a one-proportion hypothesis test are as follows:
The data is categorical, with only two possible outcomes: watched at least one live American football game or did not.
The sample is random and representative of the population of interest.
The expected number of successes and failures in the sample should be at least 10.
Calculating the Test Statistic
The test statistic for a one-proportion hypothesis test is calculated using the formula:
z=p-P/√p(1-p)/n
Where:
p is the sample proportion
P is the hypothesized population proportion under the null hypothesis
n is the sample size
In this case, p = 288/450 = 0.64, P = 0.59, and n = 450.
Using a significance level of 0.05, we can calculate the critical z-value from a standard normal distribution table. With a one-tailed test (since we are testing if the proportion has increased), the critical z-value is approximately 1.645.
Next, we calculate the test statistic:
z=0.64-0.59/√0.64(1-0.64)/450
z=2.16
Since the calculated z-value (2.16) is greater than the critical z-value (1.645), we reject the null hypothesis.
Based on the results of the one-proportion hypothesis test, there is sufficient evidence to conclude that the proportion of US homes watching at least one live American football game has increased since 2012.