Q1. (a) A research has been conducted to study the reaction time of students toward some stimuli. With a sample size of 50 students, the data recorded as the following. Reaction Time (s) Frequency 0.1 – 0.2 6 0.2 – 0.3 11 13 10 7 3 Complete the frequency distribution with the classes, midpoints, and …
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Q1. (a) A research has been conducted to study the reaction time of students toward some stimuli. With a sample size of 50 students, the data recorded as the following.
|Reaction Time (s)||Frequency|
|0.1 – 0.2||6|
|0.2 – 0.3||11|
- Complete the frequency distribution with the classes, midpoints, and cumulative frequencies.
- Calculate the standard deviation of the reaction time.
(b) Dave’s daily carbohydrate intake follows a normal distribution with a mean of 300 g and a standard deviation of 10 g.
- Express the distribution notation of Dave’s daily carbohydrate intake.
- Determine the probability for Dave’s carbohydrate intake is less than 300 g in a particular day.
- Determine the probability for the carbohydrate intake of Dave falls between 285 g and 320 g in a particular day.
Q2. (a) It is believed that students with a high level of stress would spend more time in-game compared to the students at the low-stress level. A researcher has collected some data.
|Low-Stress Students||High-Stress Students|
|Sample Mean||3 hours||5 hours|
|Sample Variance||4 hours2||2 hours2|
Test at 10% significance level, whether the common belief stated above is a valid statement.
(b). The data of clients’ symptoms and a number of clients have been collected from different counselling centres and organized in the frequency table below. A hypothesis test of equality in proportions to be conducted at a 5% significance level.
|Symptoms||Number of Clients|
Conduct the test of hypothesis about the equality in proportions of different symptoms.
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Q3. A sample of 60 employees has been selected for a survey. Based on the survey, the mean working hours per week of the employees is 41.2 hours. Assume the population standard deviation of weekly working hours is 3 hours.
- State the sampling distribution should be considered.
- Construct the 95% confidence interval for the population mean working time.
- Describe the consequences: if the sample size is increased without affecting other values; the population standard deviation is increased while other values remain constant.
- State whether it is reasonable to conclude that the mean working hours per week is 40 hours at a 5% significance level. Explain.
- State the probability to commit type I error in (3).
- State whether the conclusion in (3) would change if the significance level increases to 10%? Justify the answer.
- State a positive and a negative consequence if the significance level in (3) reduce to 1%.
- Explain the commit of type II error in (3).
Q4. A manufacturing factory is trying to reduce production waste (in kg). The manager has collected some data from several production sessions. By regression, the following Microsoft Excel output is produced.
- Complete the ANOVA table. Hence, state the range of the p-value for the ANOVA table.
- State the number of production sessions taken by the manager.
- Determine the determination coefficient. Hence, interpret the answer.
- Determine the Pearson’s correlation coefficient. Hence, comment on the correlation between production waste and operation time.
- Develop the regression equation of production waste dependent on the operation time.
- Predict the production waste amount if the operation time is 1 hour.
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