Questions are in attached file
1. The time (in days) until maturity of a certain variety of tomato plant is normally distributed with mean μ and standard deviation = 2.1. I select a simple random sample of 6 plants of this variety and measure the time until maturity. The sample yields sample mean x ̄ = 63. You read on the package of seeds that these tomatoes reach maturity, on average, in 61 days. Use significance test to see if your seeds are reaching maturity later than expected, which might indicate that your package of seeds is too old. Use α = 0.05. A. (2Pts) What is your hypotheses? B. (2Pts) What is the test statistic? C. (2Pts) Compute the P-value. D. (2Pts) What is your conclusion? 2. (6Pts) The Framingham Heart Study examined the systolic blood pressure of 3534 participants. They found the average systolic blood pressure to be 127.3 mmHg. The population standard deviation is known to be 19 mmHg. Construct a 95% confidence interval for the population mean systolic blood pressure 3. Goodyear Tire guarantees that their tires last 15,000 miles. To test this claim, you sample 12 tires. The sample average for miles lasted is 14,680 with a sample standard deviation of 3,500. Perform a one tailed t-test for the population mean to see whether Goodyear Tires claim is plausible, or if in fact the tires actually don’t last that long. A. (2Pts) What are the null and alternative hypotheses? B. (2Pts) Calculate the test statistic. C. (2Pts) Suppose the critical t-value (for 11 degrees of freedom) that leaves 5% in the left tail is t∗ = −1.796. Do you reject the null hypothesis or not? D. (2Pts) What is your conclusion? 4. HP produces toner cartridges for laser printers and claims that each cartridge can print 3500 pages in black ink before needing to be replaced. It is important that this estimate be accurate for two reasons. If the estimate is too low, then they are losing money because they could be charging more. If the estimate is too high, then they are cheating their customers, which could lead to lower sales. With lower budgets, public schools are always looking for ways to reduce costs. During the school year, one school keeps track of the number of pages each cartridge is able to print before needing to be replaced. Use the data in Minitab to determine if HP is presenting an accurate estimate for the mean number of pages that can be printed for a single black cartridge. Assume the population standard deviation is 150 pages and use a 5% level of significance. a. (1Pt) State the null and alternative hypotheses. b. (1Pt) Verify that the conditions for performing a Z-test for a single population mean hold. Copy and paste any Minitab outputs or graphs used to aid in your decision onto your answer sheet. c. (2Pts) Perform the Z-test for a single population mean using Minitab. Copy and paste the output that contains the test statistic and p-value onto your answer sheet. d. (1Pt) What is/are the critical value(s)? e. (1Pt) Using the level of significance and the p-value from part (c), should you reject or fail to reject the null hypothesis? Briefly explain your reasoning. f. (1Pt) Write a conclusion in the context of the problem. g. (1Pt) Based on your decision in part (e), would a 95% confidence interval contain the hypothesized mean of 3500? Briefly explain your reasoning. h. (1Pt) Suppose the true population mean is actually 3450. Did you make the correct decision, a Type I error, or a Type II error in part (e)? 5. Census at School is an international classroom project where students from 4th through 12th grades complete an online survey and compare the results of their class with random samples of students from around the world. The goal of this project is to get students involved in doing statistics at an early age. In 2019, 26 high school seniors in Pennsylvania completed the survey. One question asked students to report how much sleep they got on a typical school night. Use the data in conjunction with Minitab to determine if high school seniors in Pennsylvania are getting significantly less than the recommended 8 hours of sleep each night. A. (2Pts) What is the appropriate type of inference to use? Briefly explain why using the variable situation and parameter of interest. B. (1Pt) State the null and alternative hypotheses. C. (1Pt) Verify that the conditions for performing the test specified in part (a) hold. Copy and paste any Minitab outputs or graphs used to aid in your decision onto your answer sheet. D. (2Pts) Perform the test specified in part (a) in Minitab. Copy and paste the part of the output that contains the test statistic and p-value onto your answer sheet. E. (1Pt) Calculate and report the effect size. F. (1Pt) Use Minitab to calculate a 95% confidence interval for the true average number of hours that Pennsylvania high school seniors get each school night. Copy and paste the appropriate part of the output onto your answer sheet. G. (1Pt) Write a conclusion in the context of the problem. Be sure to use the p-value, the effect size, and the confidence interval to aid in your conclusion. Suppose we had known that the true population standard deviation was 1.60. H. (1Pt) What would have been different about the hypothesis test? I. (1Pt) What would have been different about the confidence interval calculated in part (f)? 6. John Kerrich was a mathematician who was held in an internment camp in Denmark during World War II. During this time, he and fellow prisoner Eric Christensen flipped a coin 10,000 times to try and demonstrate Jacob Bernoulli’s Law of Large Numbers. The first 2,000 coin flips are contained in the Minitab dataset. Use the data in Minitab to determine if the coin that Kerrich was flipping was fair. Use heads as the success outcome and tails as the failure outcome. A. (2Pts) What is the appropriate type of inference to use? Briefly explain why using the variable situation and parameter of interest. B. (1Pt) State the null and alternative hypotheses. C. (1Pt) Verify that the conditions for performing the test specified in part (a) hold. Copy and paste any Minitab outputs or graphs used to aid in your decision onto your answer sheet. D. (2Pts) Perform the test specified in part (a) in Minitab. Copy and paste the part of the output that contains the test statistic and p-value onto your answer sheet. · Minitab has two options for the test. Click on “Options” and select “Normal approximation” from the dropdown menu for “Method”. This is the method that matches the method we discussed in class. E. (1Pt) Use Minitab to calculate a 95% confidence interval for the true proportion of heads flipped with this coin. Copy and paste the appropriate part of the output onto your answer sheet. F. (1Pt) Write a conclusion in the context of the problem. Be sure to use the p-value, the effect size, and the confidence interval to aid in your conclusion.