Suppose that a random sample of 75 Republicans had a mean income of $60,000 with a standard deviation of $5,100, whereas among a random sample of 41 Democrats the mean income was $50,000 with a standard deviation of $4,100 (a) What is the difference of the sample means? (b) What is the standard error of the difference of sample means (to the nearest dollar)? (c) How many degrees of freedom (df) are there?
Suppose that a random sample of 75 Republicans had a mean income of $60,000 with a standard deviation of $5,100, whereas among a random sample of 41 Democrats the mean income was $50,000 with a standard deviation of $4,100
(a) What is the difference of the sample means?
(b) What is the standard error of the difference of sample means (to the nearest dollar)?
(c) How many degrees of freedom (df) are there?
(d) What is the critical t at the 95% confidence level (to 3 decimal places)?
(e) The question of interest is whether the two population mean incomes are different. State the null hypothesis in words.
(f) Please give a 95% confidence interval for the difference in mean incomes of the two groups (to the nearest dollar).
(g) Based solely on your calculations, according to this confidence interval, can we say the two groups’ mean incomes differ significantly (i.e., that the mean incomes of the corresponding two groups in the population, rather than the sample)? How do you know?
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