Week 11 (30-06-25 to 04-07-25)

Prepare

📖 Read the syllabus

📖 Read the support resources

Participate

🖥️Lecture 4 - Statistical Inferences

🖥️ Statistical Table - Statistical Table for probability estimations.

🖥️Lecture 3 - Continuous Probability Distributions

🖥️ Lecture 2 - Discrete Probability Distributions

🖥️ Lecture 1 - Introduction to Probability

Practice

  1. An efficiency expert wishes to determine the average time that it takes to drill three holes in a certain metal clamp. How large a sample will she need to be \(95\%\) confident that her sample mean will be within 15 seconds of the true mean? Assume that it is known from previous studies that \(\sigma = 40\) seconds.

  2. A machine is used to manufacture cylindrical metal pieces. To evaluate the precision of the machine, a sample of metal pieces was collected, and their diameters were measured. The recorded diameters (in centimetres) are as follows: 1.01, 0.97, 1.03, 1.04, 0.99, 0.98, 0.99, 1.01, and 1.03. (Assuming the diameters are approximately normally distributed.)

    1. Compute the sample mean and standard deviation of the diameters.
    2. Construct a 99% confidence interval for the true mean diameter of all metal pieces produced by the machine.
    3. Construct a 99% confidence interval for the population variance \(\sigma^2\) of the diameters of all cylindrical metal pieces produced by the machine.
    4. By using the results from part(c), construct a 99% confidence interval for the standard deviation of the diameters of all cylindrical metal pieces produced by the machine.

  3. The Edison Electric Institute has published figures on the number of kilowatt hours used annually by various home appliances. It is claimed that a vacuum cleaner uses an average of 46 kilowatt hours per year. If a random sample of 12 homes included in a planned study indicates that vacuum cleaners use an average of 42 kilowatt hours per year with a standard deviation of 11.9 kilowatt hours, does this suggest at the 0.05 level of significance that vacuum cleaners use, on average, less than 46 kilowatt hours annually? Assume the population of kilowatt hours to be normal.

  4. A manufacturer of sports equipment has developed a new synthetic fishing line that the company claims has a mean breaking strength of 8 kilograms with a standard deviation of 0.5 kilograms. Test the hypothesis that \(\mu = 8\) kilograms against the alternative that \(\mu = 8\) kilograms if a random sample of 50 lines is tested and found to have a mean breaking strength of 7.8 kilograms. Use a 0.01 level of significance.

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