Write the formula of confidence interval for population mean

1) Answer following questions about confidence interval. 

1) Write the formula of confidence interval for population mean (5 points). 2) To construct CIs of annual gasoline expenditure of 3 million households living in Los Angeles county, you randomly choose 100 households. The sample mean was $2,000 and sample variance was $40,000. With the given information, calculate a 90%, 95% and 99% confidence interval for the annual gasoline expenditure (15 points).

2) A marketing research ?rm examines the relationship between wine consumption and whether a person likes to watch professional tennis on television. One hundred randomly selected people are asked whether they drink wine and whether they watch tennis. The following results are obtained:

1) What is the appropriate test for this problem (1 points)?

2) Set up the null and alternative hypotheses (2 points).

3) Write the formula of the test statistic (2 points).

4) Calculate the test statistic based on the formula (5 points).

5) Use Excel to calculate the p-value. Should we reject the null hypothesis at 5% significance level (5 points)?

6) Given the results of the test, does it make sense to advertise wine during a televised tennis match (assuming that the ratings for the tennis match are high enough)? Explain. (5 points)

In the book Business Research Methods (5th ed.), Donald R. Cooper and C. William Emory discuss a market researcher for an automaker who is studying consumer preferences for styling features of larger sedans. Buyers, who were classi?ed as “?rst-time” buyers or “repeat” buyers, were asked to express their preference for one of two types of styling—European styling or Japanese styling. Of 40 ?rst-time buyers, 8 preferred European styling and 32 preferred Japanese styling. Of 60 repeat buyers, 40 preferred European styling, and 20 preferred Japanese styling.

1) Create a cross-tabulation for the data (10 points)

2) Test the hypothesis that buyer status (repeat versus first-time) and styling preference are independent at the 0.05 level of significance. What is your conclusion? Show the procedure. (10 points)