This assignment can be done manually using the statistic tables, formulas, and calculator

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Assignment #4 (5%)

•This assignment can be done manually using the statistic tables, formulas, and calculator. Work must be shown for marks to be given. Round the confidence interval limits to 2 decimal places.

•This is an individual assignment. You can discuss it with your friends but you have to write up the assignment on your own. Please submit your assignment solution through the Blackboard-Course Message or my Humber email: tan.le@humber.ca

1. A statistics professor is in the process of investigating how many classes postsecondary students miss each semester. To help answer this question, he took a random sample of 64 Humber College students and asked each to report the number of classes he/she had missed in the previous semester. The average number of classes missed is x = 10 classes. Assume that the population standard deviation of classes missed σ is 4 classes. Construct a 98% confidence interval for the population mean number of classes missed by all students at Humber. (Hint: Using the Z-distribution)(5 marks)

2.A policing researcher would like to estimate a population means μ to within 5 units. The confidence level has been set at 95% and the population standard deviation σ is 12. Determine the sample size n. (Hint: Using the Z-distribution)(3 marks)

3.Domestic violence in the United States is a serious problem. Once arrested, offenders are very likely to re-offend. Domestic violence counseling programs define success when an offender completes a counseling program and goes six or more months (180 days) without re-offending. Construct a 98% confidence interval number of days to re-offend for men who repeat domestic violence: 17 17 14 31 33 35 45 65 20 58 (Hint: Using the t-distribution) (Note: Sample size n = 10, x = 33.50 days and s = 17.77 days.)(5 marks)

4.The average length of stay of inmates at a provincial correctional facility is believed to be at least 23 months. To test this belief, a sample of 25 inmates were randomly selected at the facility. Their mean length of stay was found to be 𝗑� = 20 months with a standard deviation of S = 6.5 months. Is there enough evidence (at significance level α = 1% = 0.01) to conclude that inmates spend less than an average of 23 months at the facility? (Hint: Using the student t-distribution)(7 marks)

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