A random sample of 100 observations is obtained from a normally distributed population with a

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?

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?

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.

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.