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Part A: Hypothesis testing 1. The National Sleep Foundation recommends that teenagers aged 14 to 17 years old get at least 8 hours of sleep per night for proper health and wellness. A statistics class at a large high school suspects that students at their school are getting less than 8 hours of sleep on average. To test their theory, they randomly sample 42 of lhese students and ask them how many hours of sleep they get per night and the standard deviation 2.1. The mean from the sample x'=7.5. Proof that the statement of null hypothesis is acceptable at the level of condence 95%. [5 marks] 2. A fast-food company advertises that the pre-cooked weight for its burgers is. on average, 0.2 kg. The company runs a regular quality control test that involves weighing a sample of 25 burgers to see if the burgers are too light or too heavy. If the sample of 25 mean weight is signicantly different than 0.2 kg, then they recycle the entire batch. Does the company need to recycle the entire batch if the mean sample = 0.21kg with standard deviation = 0.05 when p value = 0.01? [5 marks] 3. A city had an unemployment rate of 7%. The mayor pledged to lower this gure and supported programs to decrease unemployment. A group of citizens wanted to test if the unemployment rate had actually decreased, so they obtained a random sample of 300 citizens to see what proportion of the sample was unemployed. With the sample mean = 6.8% and standard deviation of 0.88, proof that the claim of null hypothesis is correct at the p value = 0.05. [5 marks] 4. A newspaper report claims that more than 30%, percent of all tea-drinkers prefer green tea to black tea. Leo is the ofce manager at a company with thousands of employees. He wonders if the newspaper's claim holds true at his company. To nd out, Leo asks a simple random sample of 125 tea-drinking employees which they prefer: green tea or black tea. The mean sample = 23%, with the standard deviation = 12, and p value = 0.05. [5 marks] Part B: Probability 1. A bag contains 4 white balls, 6 blue balls, 2 red balls and 3 green balls. Fund the probability that a ball chosen from the bag is a. a white ball. b. a green ball. c. red and white ball. d. not a black ball. [10 marks] 2. Tree diagram a. The probability of getting a red ball from a bag is 4}9 and the probability of getting a blue ball 519 if the independent method is applied. By using the tree diagram method, nd the probability of getting the red ball at the rst pick and blue ball at second pick. [19 marks] b. by using the dependent method, that the rst ball picks out without replacement, now shows the calculalion by using a tree diagram. What is the probability of getting the red ball at the rst pink and blue ball second pick? [10 marks]