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 |
| 13 | |
| 10 | |
| 7 | |
| 3 |
- 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 Size | 12 | 15 |
| 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 |
| Depression | 8 |
| Hyperactive | 6 |
| Anxiety | 18 |
| Paranoia | 4 |
| Insomnia | 4 |
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.
SUMMARY OUTPUT
| Regression Statistics | |
| R Square | 0.9861 |
| Observations | 8 |
ANOVA
| Sources | SS | DF | MS | F |
| Factor | 6.72 | 424.4211 | ||
| Error | ||||
| Total |
| Coefficients | b | t | p |
| Intercept | 14.075 | 52.9403 | 0.0000 |
| Time (minutes) | −0.2 | −20.6015 | 0.0000 |
- 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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