Quantitative Methods Assignment - TSTA602

This assignment explores key topics in quantitative methods, including probability distributions, hypothesis testing, and regression analysis.

<h3 style="text-align: left;">Rewritten Instructions:</h3>
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Group Formation: This is a group assignment. Each group should consist of no more than 3 students. Students are responsible for forming their groups.
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Submission: Each group must submit a single assignment copy with a cover sheet, signed by all group members.
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Turnitin Submission: The assignment must be submitted via Turnitin before the due date.
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<h3 style="text-align: left;">Rewritten Questions:</h3>
<h4 style="text-align: left;">Question 1: Probability Analysis (5 marks)</h4>
Part a (2 marks): Use the z-table to find the following probabilities: i) P(-1.5 < Z < 0.7) ii) P(1.15 < Z < 2.45) iii) Z at 0.35
Part b (3 marks): An alkaline battery lasts an average of 26 hours in a toy car with a standard deviation of 2.5 hours. i) What’s the probability the battery lasts between 25 and 29 hours? ii) What’s the probability it lasts longer than 29 hours? iii) What’s the probability it lasts less than 25 hours?
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<h4 style="text-align: left;">Question 2: Sampling and Normal Distribution (5 marks)</h4>
Part a (2 marks): From a sample of 25, where μ=100 and σ=20, calculate: i) P( X < 96) ii) P(96 < X < 105)
Part b (3 marks): University professors work an average of 52 hours per week with a standard deviation of 6 hours. i) What’s the probability a professor works more than 60 hours per week? ii) Calculate the probability that the mean work week of three randomly selected professors exceeds 60 hours.
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<h4 style="text-align: left;">Question 3: Hypothesis Testing (5 marks)</h4>
Part a (2 marks): Conduct a hypothesis test where H0: μ = 20, H1: μ ≠ 20, with σ = 5, n = 25, X̄ = 21, and α = 0.05. i) Calculate the test statistic and determine whether to reject H0.
Part b (3 marks): A sample of 200 has X̄ = 175 and s = 22. i) Test if there’s enough evidence at the 5% significance level to conclude that the population mean differs from 180. ii) Repeat with the population standard deviation = 22.
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<h4 style="text-align: left;">Question 4: Confidence Intervals (4 marks)</h4>
Part a (2 marks): From a sample of 25 with a mean of 500 and σ = 15: i) Estimate the population mean with 99% confidence. ii) Repeat with σ = 30.
Part b (2 marks): A sample of 5 has X̄ = 175 and s = 30. i) Estimate the population mean with 90% confidence. ii) Repeat with σ = 30.
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<h4 style="text-align: left;">Question 5: Regression Analysis (6 marks)</h4>
Interpret the regression results of a study on the relationship between household utility bills and house size. Part a (4 marks): i) Interpret the slope of the regression line. ii) Write the estimated regression line. iii) Calculate and interpret the coefficient of determination. iv) Calculate and interpret the coefficient of correlation.
Part b (2 marks): Conclude what can be inferred about the relationship between utility bills and house size.
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<h3 style="text-align: left;">Expert Assistance:</h3>
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Quantitative Methods Assignment - TSTA602

This assignment explores key topics in quantitative methods, including probability distributions, hypothesis testing, and regression analysis.

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