Week 10 (09-02-26 to 13-02-26)

Prepare

📖 Read the syllabus

📖 Read the support resources

Participate

🖥️Lecture 5 - Statistical Inferences II

🖥️ Statistical Table - Statistical Table for probability estimations.

🖥️Lecture 4 - Statistical Inferences I

🖥️ Lecture 3 -Continuous Probability Distributions

🖥️ Lecture 2 - Discrete Probability Distributions

🖥️ Lecture 1 - Introduction to Probability

Practice

  1. The average height of females in the freshman class of a certain college has historically been 162.5 centimeters with a standard deviation of 6.9 centimeters. Is there reason to believe that there has been a change in the average height if a random sample of 50 females in the present freshman class has an average height of 165.2 centimeters? Use a 5% level of significance and the P-value method to determine the outcome.

  2. As a part of the evaluation of Colombo municipal council employees, the city manager audits the parking tickets issued by city parking officers to determine the number of tickets that were contested by the car owner and found to be improperly issued. In past years, the number of improperly issued tickets per officer had a normal distribution with mean μ =380. Because there has recently been a change in the city’s parking regulations, the city manager suspects that the mean number of improperly issued tickets has increased. An audit of 12 randomly selected officers is conducted to test whether there has been an increase in improper tickets. Use the sample data given here which is audit collected from each officers:

    390, 380, 369, 392, 398, 393, 392, 396, 399, 391, 387, 393

    1. Give a point estimate of the mean number of improperly issued tickets. Construct a 95% confidence interval on the mean number of improperly issued tickets. Interpret this interval.

    2. Is there sufficient evidence that the mean number of improperly issued tickets is greater than 380? Use a α = 0.01.

    3. Is there sufficient evidence that the variance number of improperly issued tickets is greater than 35? Use a α= 0.05.

  3. An educational researcher designs a study to compare the effectiveness of teaching English to non-English speaking people by a computer software program and by the traditional classroom system. The researcher randomly assigns 125 students from a class of 300 to instruction using the computer. The remaining 175 students are instructed using the traditional method. At the end of a 6-month instructional period, all 300 students are given an examination with the results reported in given table

    Computer Instruction Traditional Instruction
    Pass 94 113
    Fail 31 62
    Total 125 175

    1. Form 95% confidence interval for the difference in proportions of students passing the examination between instruction using the computer software program and the traditional method

    2. Does instruction using the computer software program appear to increase the proportion of students passing the examination in comparison to the pass rate using the traditional method of instruction? Use a α = 0.01.

Exercise

  1. Investigating Student Engagement in MC3020 Lectures:  The MC3020 course coordinator at the University of Jaffna is evaluating two teaching methods to address low student engagement during lectures. Method A employs interactive quizzes, while Method B utilizes group discussions. A random sample of seven students was assigned to Method A, and another seven students were assigned to Method B. The active participation time (minutes per lecture) for each student was recorded as follows:

    Method A (Interactive Quizzes): 8, 12, 13, 9, 3, 10, 8

    Method B (Group Discussions): 10, 8, 12, 15, 6, 8, 11

    Assuming active participation times follow normal distributions in the population and using a 0.05 significance level, address the following:

    1. Estimate the population mean difference in engagement time (Method A – Method B).

    2. Test whether the population variances of engagement times are equal.

    3. Construct a 95% confidence interval for the population mean difference (Method A – Method B).

    4. Test whether the two methods differ significantly in their effect on student engagement.

    5. Compare your results from Part (c) (confidence interval) and Part (d) (hypothesis test). Explain how these results are consistent or inconsistent with each other in light of the conclusion about mean differences.

  2. A study was conducted in which two types of engines, A and B, were compared. Gas mileage, in miles per gallon, was measured. Fifty experiments were conducted using engine type A and 75 experiments were done with engine type B. The gasoline used and other conditions were held constant. The average gas mileage was 36 miles per gallon for engine A and 42 miles per gallon for engine B. Find a 96% confidence interval on \(\mu_B −\mu_A\), where \(\mu_A\) and \(\mu_B\) are population mean gas mileages for engines A and B respectively. Assume that the population standard deviations are 6 and 8 for engines A and B, respectively.

  3. A study was conducted by the Department of Zoology at the Virginia Tech to estimate the difference in the amounts of the chemical orthophosphorus measured at two different stations on the James River. Orthophosphorus was measured in milligrams per liter. Fifteen samples were collected from station 1, and 12 samples were obtained from station 2. The 15 samples from station 1 had an average orthophosphorus content of 3.84 milligrams per liter and a standard deviation of 3.07 milligrams per liter, while the 12 samples from station 2 had an average content of 1.49 milligrams per liter and a standard deviation of 0.80 milligram per liter. Find a 95% confidence interval for the difference in the true average orthophosphorus contents at these two stations, assuming that the observations came from normal populations with different variances.

  4. An experiment was performed to compare the abrasive wear of two different laminated materials. Twelve pieces of material 1 were tested by exposing each piece to a machine measuring wear. Ten pieces of material 2 were similarly tested. In each case, the depth of wear was observed. The samples of material 1 gave an average (coded) wear of 85 units with a sample standard deviation of 4, while the samples of material 2 gave an average of 81 with a sample standard deviation of 5. Assume that the populations to be approximately normal with equal variances.

    1. Construct a 95% confidence interval for the difference in mean wear between Material 1 and Material 2.
    2. Test, at the 0.05 level of significance, whether the mean wear of Material 1 exceeds that of Material 2 by more than 2 units.

  5. The following data represent the running times of films produced by two motion-picture companies.

    Company Time (minutes)
    I 103 94 110 87 98
    II 97 82 123 92 175 88 118

    Assume that the running-time differences are approximately normally distributed with unequal variances.

    1. Compute a 90% confidence interval for the difference between the average running times of films produced by the two companies.
    2. Test, at the 0.10 level of significance, the hypothesis that the average running time of Company 2 exceeds that of Company 1 by 10 minutes, against the alternative that the difference is less than 10 minutes.

Perform

Mid Semester Examination scheduled on February 11, 2026 (Wednesday). To ensure that the exam runs smoothly, we have arranged the exam halls as follows: 

  • Group 1 (Registration numbers 2024/E/001 to 2024/E/101) will be in Exam Hall 1 (First floor, Computer Engineering Department)  

  • Group 2 (Registration numbers 2024/E/102 to 2024/E/198and re-attempt students) will be in Exam Hall 2 (Drawing Hall 2nd floor, Admin Building).

Make sure to review all sections thoroughly to ensure you’re prepared for the exam! I hope everyone follows the exam policies and cooperates with the exam administration to make the exam run smoothly. Moreover, you can access class materials by checking out the course webpage.

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