1) A random sample of 100 observations is obtained from a normally distributed population with a standard deviation of 10. What is a 95% confidence interval for the mean of the population if the sample mean is 40?
2) The mean monthly expenditure on gasoline per household in Slippery Rock is determined by selecting a random sample of 36 households. The sample mean is $68, with a sample standard deviation of $17. What is a 90% confidence interval for the mean monthly expenditure on gasoline per household in Slippery Rock?
3) The Federal Reserve Board made eight interest rate cuts on its benchmark short term rates in a particular year. Credit cards, however, averaged around 14% with the lowest credit cards charging around 8%. A financial analyst believes that the average rate on credit cards that charge monthly fees is lower than the national average of all credit cards. A random sample of 49 different credit cards that charged monthly fees revealed a sample mean of 13.5%. Assume a population standard deviation of 1.4%. Test the financial analyst's belief that the average rate charged by credit cards with monthly fees is less than 14%. Use a 5% significance level.
4) A retail federation conducted a nationwide survey of 1000 adults last October and found that approximately 55% of the respondents planned to do some type of Halloween decorating. The federation claims that households spend an average of $45 on Halloween candy, costumes, and decorations; the total Halloween market is estimated to generate about $7 billion in sales. Suppose that a retail manager in Pembroke wished to determine if the average household in the Pembroke area planned to spend more than $45. A random sample of 25 households yielded a mean of $52 with a standard deviation of $18. Do the data support the belief that the average household in the Pembroke area spends more than $45 in preparation for Halloween; use a significance level of .01.