The assignment due date is February  22nd. Please read the instructions carefully. 

1- The Fillmore Institute has established a service designed to help charities increase the amount of money they collect from their direct-mail solicitations. Its consulting is aimed at increasing the mean dollar amount returned from each giver and also at reducing the variation in amount contributed from giver to giver. The Badke Foundation collects money for heart disease research. Over the last eight years, records show that the average contribution per returned envelope is $14.25 with a standard deviation of $6.44. The Badke Foundation directors decided to try the Fillmore services on a test basis. They used the recommended letters and other request materials and sent out 1,000 requests. From these, 166 were returned. The data showing the dollars returned per giver are in the file called Badke.

Based on the sample data, what conclusions should the Badke Foundation reach regarding the Fillmore consulting services? Use appropriate hypothesis tests with a significance level = 0.05 to reach your conclusions.

2- Maher Saddles, Inc., produces bicycle seats. Maher’s operations manager has recently made a change in the production process for the company’s high-end seat. After waiting for the process to become stable, he took a random sample of 25 assembly times and found a standard deviation of 47 seconds. He recognizes this is only a point estimate of the variation in completion times and so wants to report both a 90% and a 95% confidence interval estimate for the population variance.

3- Soft drink bottling companies such as Coca-Cola use quality-control techniques to assure that the average amount of cola in the cans is 12 ounces. Suppose that a small standard deviation of 0.05 ounce is acceptable. Any significant difference from this standard deviation would reflect badly on the quality-control measures concerning the average amount of cola in the 12-ounce cans. A sample of size 20 indicated that the standard deviation was 0.070.

a. Determine if the standard deviation of the amount of cola in the cans differs from the standard deviation specified by the quality control division. Use a significance level of 0.10.

b. The quality-control sampling occurs several times
a day. In one day, seven samples were taken, and three indicated that the standard deviation was not 0.05. If the seven samples were taken at a time in which the standard deviation met specifications, determine the probability of having at least three out of seven samples indicate the specification was not being met.