Week 9 (02-02-26 to 06-02-26)

Prepare

📖 Read the syllabus

📖 Read the support resources

Participate

🖥️ Lecture 4

🖥️ Statistical Table - Statistical Table for probability estimations.

🖥️ Lecture 3 -Continuous Probability Distributions

🖥️ Lecture 2 - Discrete Probability Distributions

🖥️ Lecture 1 - Introduction to Probability

Practice

  1. 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.

  2. 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.

  3. A commonly prescribed drug for relieving nervous tension is believed to be only 60% effective. Experimental results with a new drug administered to a random sample of 100 adults who were suffering from nervous tension show that 70 received relief. Is this sufficient evidence to conclude that the new drug is superior to the one commonly prescribed? Use a 0.05 level of significance.

  4. A university organizes a movie night for students, expecting an average attendance of 12 students per hour based on past events. However, on the night before the MC3020 assignment exam, the organizers randomly sample 10 different hours and record the number of students attending:

    Attendance (students/hour): 12, 11, 13, 12, 11, 12, 13, 14, 10, 12

    Assume the attendance follows a normal distribution. Write all steps clearly to receive full marks.

    1. Test whether the mean attendance is still 12 students per hour, given that many students might skip the event to study for the MC3020 assignment exam. Use \(\alpha = 0.01\).
    2. Test whether the standard deviation has increased beyond 1 student/hour. Use a \(\alpha = 0.05\). (Increased variability may suggest erratic attendance due to exam stress.)

Exercise

  1. Past data indicate that the amount of money contributed by the working residents of a large city to a volunteer rescue squad is a normal random variable with a standard deviation of \(\$1.40\). It has been suggested that the contributions to the rescue squad from just the employees of the sanitation department are much more variable. If the contributions of a random sample of 12 employees from the sanitation department have a standard deviation of \(\$1.75\), can we conclude at the 0.01 level of significance that the variance of the contributions of all sanitation workers is greater than that of all workers living in the city?

    1. A factory produces 80,000 pistons daily. The acceptable defect rate is 0.8%. From a sample of 600 pistons, 1.2% were found defective.

    2. Estimate the proportion of defective pistons in the sample.

    3. Construct a 95% confidence interval for the true proportion of defective pistons.

    4. Test whether the defect rate is higher than 0.8% at a 5% significance level.

    5. Does the confidence interval support the hypothesis test conclusion?

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