Name: HOMEWORK 5 Binomial Probability, Sign Test, Z-test, Single Sample T-test 1. (11 pts) A hockey team is convinced that the coin used to determine the order of play is weighted. The team captain steals this special coin and flips it 14 times to evaluate the hypothesis that the coin is weighted, and it shows up heads 12 times. Test this hypothesis (use alpha=.05). a. (2 pts) What is the appropriate test? b. (1 pt) State the null hypothesis: c. (1 pt) State the alternative hypothesis: d. (2 pts) Find the critical value: e. (1 pt) Calculate the obtained statistic: f. (2 pts) Make a decision: g. (2 pts) What does your decision mean? 2. (11 pts) A hockey team is convinced that the coin used to determine the order of play is weighted for heads. The team captain steals this special coin and flips it 14 times to evaluate the hypothesis that the coin is weighted for heads, and it shows up heads 12 times. Test this hypothesis (use alpha=.05). a. (2 pts) What is the appropriate test? b. (1 pt) State the null hypothesis: c. (1 pt) State the alternative hypothesis: d. (2 pts) Find the critical value: e. (1 pt) Calculate the obtained statistic: f. (2 pts) Make a decision: g. (2 pts) What does your decision mean? 3. (11 pts) A farmer would like to evaluate Miracle Grow when used on his potted daisy plants. He sets up 20 plants in a room all facing the same window, obtaining the same amount of sunlight, and waters them identically each day. For a month, he monitors how much each plant grows. Then, he adds Miracle Grow to every pot and monitors how much each plant grows during a month with Miracle Grow. At the end of two months, he discovers that 16 plants grew more with Miracle Grow. Test the hypothesis that Miracle Grow increases plant growth (using an alpha level of .01). a. (2 pts) What is the appropriate test? b. (1 pt) State the null hypothesis: c. (1 pt) State the alternative hypothesis: d. (2 pts) Find the critical value: e. (1 pt) Calculate the obtained statistic: 4. 5. f. (2 pts) Make a decision: g. (2 pts) What does your decision mean? (8 pts) What is a sampling distribution and why is it important for inferential statistics? (20 pts) I flip a fair coin 17 times. Answer the following questions: a. What is the probability of getting 9 heads? b. What is the probability of getting 2 heads? c.. What is the probability of getting 1 tail? d. What is the probability of getting 14 or more heads? e. What is the probability of getting 17 tails? 6. I toss an unfair coin 12 times. This coin is 65% likely to show up heads. Calculate the probability of the following. a. 11 heads: b. 2 or more heads: c. 7 heads: d. 9 tails: e. 8 or less heads: (6 pts) a. If the average American sleeps 8 hours a night, with a standard deviation of 1 hour, and I plan on gathering a sample of 12 college students to compare to this population, find the following: = = = x x = (6 pts) c. If Brooklyn College students have an IQ of 100, on average, with a standard deviation of 16 points, and I collect 48 BC Psychology students to see how Psych majors compare to all of BC, find the following: = = = x x 7. = 1. (11 pts) In the population, New Yorkers have an average of 2 pets in their homes, with a standard deviation of 1. I am interested in evaluating whether or not medical doctors differ from the population in regard to number of pets owned. Below is data from 9 doctors. Test this hypothesis using an alpha level of .01. # of pets 0 1 0 0 1 3 2 1 1 a. (2 pts) What is the appropriate test? b. (1 pt) State the null hypothesis: c. (1 pt) State the alternative hypothesis: d. (2 pts)Find the critical value: e. (2 pts)Calculate the obtained statistic: f. (2 pts)Make a decision: g. (1 pt) What does your decision mean? -------------------------------------------------(12 pts) A physiologist believes he has discovered a new steroid hormone that can control 8. the blood glucose in mammals. In an experiment he injects laboratory rats with a small amount of this steroid hormone and, after a suitable waiting period measures the blood glucose level of the rats. In his twelve experimental rats he obtains the following levels of blood glucose {35,36,37,33,34,35,33,35,37,36,34,35}. From previous studies of thousands of normal, un-manipulated rats he knows that the mean () blood glucose level in this species of rat (his laboratory population) is 31 and that the standard deviation () is 4.12. Evaluate the hypothesis that this new steroid hormone decreases blood glucose levels. Use an -level of 0.05 for this analysis. a. (2 pts) What is the appropriate test? b. (1 pt) State the null hypothesis: c. (1 pt) State the alternative hypothesis: d. (2 pts) Find the critical value: e. (3 pts) Calculate the obtained statistic: f. (2 pts) Make a decision:. g. (1 pt) What does your decision mean? 9. (12 pts) A physiologist believes he has discovered a new steroid hormone that can affect the blood glucose in reptiles. In an experiment he injects turtles with a small amount of this steroid hormone and, after a suitable waiting period measures the blood glucose level of the turtles. In his sixteen experimental turtles he obtains the following levels of blood glucose {2, 1, 3, 5, 2, 1, 1, 5, 3, 2, 1, 1, 2, 1, 1, 5}. From previous studies of thousands of normal, un-manipulated turtles he knows that the mean () blood glucose level in this species of turtle (his laboratory population) is 3. Evaluate the hypothesis that this new steroid hormone affects blood glucose levels. Use an -level of 0.01 for this analysis. a. (2 pts) What is the appropriate test? b. (1 pt) State the null hypothesis: c. (1 pt) State the alternative hypothesis: d. (2 pts) Find the critical value: e. (3pts) Calculate the obtained statistic: f. (2 pts) Make a decision: g. (1 pt) What does your decision mean