Business Statistics Assignment

Assignment for Midterm Break
1. Most of the information technology developers claim that wireless connection would give a speed of at least 11 Mbps compared to a 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 wireless usage should be implemented? (Test at a 7% significance level).
b) Repeat the test by using a 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 is raised by a jack is more than 100kg. a random sample of 125 jacks with a mean of 102. 2kg and a standard deviation of 15. 17kg is taken.
a) Do you agree that a jack can raise more than a 100 kg vehicle? (use α = 0. 03)
b) Repeat the test by using a 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 α = 0. 05)
b) Repeat the test by using a p-value approach.
4. A researcher needs on average, 1. 2 years to complete his short-term research. A random sample of 12 researchers 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 α =0. 05)
b) Repeat the test by using a 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 a p-value approach.
6. In a labor-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 an average of 33.0 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 a 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 kilograms. 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 a p-value approach.

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