Discuss the following:
Q1. In 2002, approximately 177,000 tax returns were sampled to obtain estimates of various parameters. The mean income tax per return for the returns sampled was $9401. If, in reality, the population mean income tax per return in 2001 was $9489, 88 sampling error was made in estimating that parameter by the sample mean of $9401. Is this true? Explain.
Q2. In the previous problem, if the IRS had sampled 250,000 returns instead of 177,000 the sampling error would have been necessarily smaller. Is this true? Explain.
Q3. The published data on sales of new motor vehicles in the US shows that in the year 2001, American spent an average of $21,605 for a new car. Assume a standard deviation of $10,200. For samples of 50 new car sales in 2001, the mean and standard deviation of all possible sample mean prices are $21,605 and $1442.50. Is this true? Explain.