Final answer:
To determine if the sample supports the claim that Americans watch, on average, 12 hours of sports programs in a month with a standard deviation of 4 hours, we can use a hypothesis test.
Step-by-step explanation:
To determine if the sample supports the claim that Americans watch, on average, 12 hours of sports programs in a month with a standard deviation of 4 hours, we can use a hypothesis test.
1. Null hypothesis (H0): The population mean is equal to 12 hours.
2. Alternative hypothesis (Ha): The population mean is not equal to 12 hours.
3. Test statistic: Using the sample mean of 9.9, the population mean of 12, the standard deviation of 4, and a sample size of 55, we can calculate the test statistic using the formula: (sample mean - population mean) / (standard deviation / sqrt(sample size)).
4. Critical value: Since the confidence level is 99%, we can use a Z-score table to find the critical value at a significance level of 0.01 (1 - 0.99).
5. Conclusion: If the test statistic falls within the critical region (outside the critical value), we reject the null hypothesis and conclude that the sample supports the claim. Otherwise, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim.