Question

1. A Telecommunications company recently installed a new speech recognition system for its repair calls. In their old system, operators had to press keys on the numeric keypad to answer questions, which led to longer time on service calls.

The company is conducting a study to determine the effectiveness of the new system and to do so they want to estimate the average duration of service calls with the new system.

They analyzed a random sample of 15 service calls and obtained an average duration of service calls of 30.45 minutes and a standard deviation of 4.72 minutes.

What is the margin of error for a 90% confidence interval for the mean duration of service calls ? (USE 3 Decimals)

2. A bank officer wants to determine the amount of the average total monthly deposits per customer at the bank. He believes an estimate of this average amount using a confidence interval is sufficient. He assumes the standard deviation of total monthly deposits for all customers is about $9.11. How large a sample should he take to be within $3 of the actual average with 95% confidence?

3. A study will be conducted to construct a 90% confidence interval for a population proportion. An error of 0.15 is desired. There is no knowledge as to what the population proportion will be. What sample size is required ?

4.

A manufacturing company is considering the acquisition of a TR-LX61, a new robotic machine that is supposed to reduce the variable cost or unit cost of production.   Since the acquisition of the TR-LX61 will involve some expenditures, management is willing to buy the machine only if they can be conviced that production costs will be less than $6.83 per unit produced.

Based on examination of 25 randomly selected units, they obtained an average variable cost of $6.15 and a standard deviation of $0.92.

What is the value of the test statistic to determine if production costs per unit are less than $6.83 ? (Use 3 DECIMALS)

5.

A Telecommunications company recently installed a new speech recognition system for its repair calls. In their old system, operators had to press keys on the numeric keypad to answer questions, which led to longer time on service calls. on service calls. The company is conducting a study to examine the impact of the new system on the average duration of service calls.   Average duration of service calls was 31.4 minutes prior to the installation of the new system. They analyzed a random sample of 25 service calls and obtained an average duration of service calls of 28.2 minutes. Based on historical data, the standard deviation of duration of service calls is known to be σ =7.2 minutes.

What is the P value of the the hypothesis test to determine if the system has changed the average duration of service calls ? (Use 4 DECIMALS)

Answer 1