### Business Statistics

QMT2033 BUSINESS STATISTICS Assignment for mid -term break 1. Most of the information technology developers claim that wireless connection would give speed of at least 11 Mbps compared to wired connection. A sample of 105 computers using wireless connection shows it gives a mean of 11. 7 Mbps and a standard deviation of 2. 3 Mbps. a) Do you think that the wireless usage should be implemented? Test at 7% significance level). b) Repeat the test by using p-value approach. 2. A jack is usually used for raising the axle of a motor so that a wheel may be changed.

It is known that the weight of the vehicle that be raised by a jack is more than 100kg. a random sample of 125 jacks with a mean of 102. 2kg and standard deviation of 15. 17kg is taken. a) Do you agree that a jack can raise more than a 100 kg vehicle? (use ? = 0. 03) b) Repeat the test by using p-value approach. 3. In a normal situation, on average, a song needs a duration of at most 3. 5 minutes to be played. The duration of a random sample of 11 songs is taken, and the data are as follows: 5. 32 6. 53 4. 52 3. 20 3. 39 4. 00 4. 10 3. 15 3. 47 4. 01 2. 3 a) By using the data, do you agree with the statement that a song needs a duration of at most 3. 5 minutes to be played? (use ? = 0. 05) b) Repeat the test by using p-value approach. 4. A researcher needs on average, 1. 2 years to complete his short-term research. A random sample of 12 researcher are taken, and the duration (in years) to complete their research are recorded as below: 4. 3 1. 0 1. 5 1. 6 1. 2 0. 8 2. 1 2. 4 0. 7 1. 3 0. 4 a) Do these data support the stamen that a researcher needs exactly 1. 2 years to complete his research? (use ? =0. 05) b) Repeat the test by using p-value approach. 5.

Newly purchased automobile tyres of a certain type are supposed to be filled with a pressure of at most 34 psi. A random sample of 36 such tyres was selected and it gives a sample mean of 34. 66 psi and a standard deviation of 2. 14 psi. a) Does this sample prove that such tyres fill with a pressure of at most 34 psi? (Use 7% significance level). b) Repeat the test by using p-value approach. QMT2033 BUSINESS STATISTICS 6. In a labour-management discussion it was brought up that workers at a certain large plant, take on average at least 32. 6 minutes to get to work. If a random sample of 60 workers took on the average of 33. minutes with a standard deviation of 6. 1 minutes, what can you conclude based on the sample taken? (Use 0. 017 level of significance). Repeat the test by using p-value approach. 7. A manufacturer has developed a new fishing line, which he claims has a mean breaking strength of 15 kilograms with a standard deviation of 0. 5 kilogram. To test the eligibility of the claim, a random sample of 50 lines has been tested and it gave a mean of 14. 9 kilograms. Can you help the manufacturer to test his claim? (Use a significance level of 0. 08). Repeat the test by using p-value approach.