Quantitative analysis

Problem 1
The amount of fluid in a half-liter bottle of diet cola is normally distributed, and from past experience, the standard deviation is known to be 1.20 milliliters. A sample of 50 bottles reveals a mean weight of 502.1 ml. Construct and interpret a 90% confidence interval for the mean. Be sure to interpret the meaning of this interval.

Problem 2
A marketing firm recently studied the number of times men and women who live alone buy take-out dinners in a month. Two independent samples were taken, one with 35 men and another with 40 women. The mean number of take-out dinners for men is 24.51 with a known population standard deviation of 4.48, and the mean number of take-outs for women is 22.69 with a known population standard deviation of 3.86. Conduct a two-tailed hypothesis test to determine if the two means are different, with a .10 level of significance.

Problem 3: Conduct a one-tailed hypothesis test given the following information.
A test was conducted to determine whether gender of a spokesperson affected the likelihood that consumers would prefer a new product. A survey of consumers at a trade show employing a female spokesperson determined that 70 out of the 150 customers preferred the product, while 62 out of 180 customers preferred the product when a male spokesperson was employed. At the .01 level of significance, do the samples provide sufficient evidence to indicate that on the average, more consumers prefer a new product when the spokesperson is female?

Problem 4: Conduct a two-tailed hypothesis test given the following information.
The director of human resources at a large firm is comparing the distance traveled to work by employees in their office in downtown Atlanta with the distance for those in the downtown Jacksonville office. A sample of 17 Atlanta employees showed they travel a mean of 369 miles per month, with a sample standard deviation of 29 miles. A sample of 14 Jacksonville employees showed they travel a mean of 381 miles per month, with a sample standard deviation of 25 miles. At the .01 level of significance, is there a difference in the mean number of miles traveled between the two groups?

Problem 5: Define autocorrelation in the following terms
a. In which type of regression is it likely to occur?
b. What is the negative impact of autocorrelation in a regression?
c. Which method is used to determine if it exists?
d. If found in a regression, how is autocorrelation eliminated?

Problem 6: Define multicollinearity in the following terms
a. In which type of regression is it likely to occur?
b. What is the negative impact of multicollinearity in a regression?
c. Which method is used to determine if it exists?
d. If multicollinearity is found in a regression, how is it eliminated?