A film alliance used a random sample of 50 U.S. citizens to estimate that the typical American spent 78 hours watching videos and DVDs last year. The standard deviation of this sample was 9 hours.
What is your question?
To estimate the typical number of hours Americans spent watching videos and DVDs last year, a film alliance used a random sample of 50 U.S. citizens. The sample mean was found to be 78 hours, with a sample standard deviation of 9 hours.
The sample mean, in this case, is the estimated average number of hours spent watching videos and DVDs by the U.S. population. It represents the "typical" American's behavior in this particular context. However, since the sample mean is based on a random sample rather than the entire population, there is always some degree of uncertainty associated with it.
The sample standard deviation, on the other hand, indicates the variability or spread of the data points in the sample. In this case, the standard deviation of the sample is 9 hours, suggesting that the average number of hours spent watching videos and DVDs may vary within a range of plus or minus 9 hours from the estimated mean.
It's important to note that while this sample provides an estimate, it may or may not accurately represent the entire U.S. population. To get a better understanding of the population's behavior, a larger and more representative sample or complete population data would be needed.
To calculate the sample mean, the film alliance likely added up the number of hours spent watching videos and DVDs for all 50 individuals in the sample, then divided it by the total number of individuals. In this case, it resulted in an average of 78 hours.
To calculate the sample standard deviation, the film alliance likely calculated the variance first by finding the squared difference between each individual's number of hours and the sample mean, then dividing the sum of these squared differences by the number of individuals minus one (49 in this case). Finally, they took the square root of the variance to obtain the standard deviation of 9 hours.
By using a random sample and calculating the sample mean and standard deviation, the film alliance was able to estimate the typical number of hours Americans spent watching videos and DVDs last year while accounting for the variability in the data.