cribed. Consider the scenario ai from the previous question. Suppose you take an SRS of 50 avocados and find that the mean is 1.1 inches, which yields a p-value of 0.0542. Interpret the P-value in the context of the problem. What conclusion would you draw at the =0.05 level? At the =0.10 level?
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For each of the following settings, define the parameter of interest and write the appropriate null and alternative hypotheses for the test that is described.
- Consider the scenario ai from the previous question. Suppose you take an SRS of 50 avocados and find that the
mean is 1.1 inches, which yields a p-value of 0.0542. - Interpret the P-value in the context of the problem.
What conclusion would you draw at the =0.05 level? At the =0.10 level?
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- For each of the following settings, define the parameter of interest and write the appropriate null and alternative hypotheses for the test that is described. Scenario 2: According to the Galactic Empire’s study, 0.5% of the people in the galaxy are Jedi. You are interested in determining if the proportion of the Jedi on the planet Tatooine is different than the galaxy’s proportion.For the situation described below, state the null and alternative hypotheses to be tested. (Enter != for ≠ as needed.) A new variety of pearl millet is expected to provide an increased yield over the variety presently in use, which has a mean yield of about 55 bushels per acre.For each of the following settings, define the parameter of interest and write the appropriate null and alternative hypotheses for the test that is described. Scenario 1: In an avocado, the average seed diameter is 1 inch. However, you are an avocado expert and you believe that the average seed diameter is increasing recently.
- For the following setting, (a) describe the parameter of interest, and (b) state the appropriate hypotheses for a significance test. As part of its 2010 census marketing campaign, the U.S. Census Bureau advertised “10 questions, 10 minutes – that’s all it takes.” On the census form itself, we read, “The US Census Bureau estimates that, for the average household, this form will take about 10 minutes to complete, including the time for reviewing the instructions and answers.” We suspect that the actual time it takes to complete the form may be longer than advertised.For the following setting, (a) describe the parameter of interest, and (b) state the appropriate hypotheses for a significance test. According to the website sleepdeprivation.com, 85% of teens are getting less than eight hours of sleep a night. Jannie wonders whether this result holds in her large high school. She asks an SRS of 100 students at the school how much sleep they get on a typical night. In all, 75 of the responders said less than 8 hours.For each of the following situations, identify whether the appropriate test is a paired t-test (for parameter µd) or a two-sample t-test (for parameter µ1 - µ2). Briefly explain your answer. Sixty students were matched by initial pulse rate, with the two with the highest pulse forming a pair, and so on. Within each pair, one student was randomly chosen to drink a caffeinated beverage, while the other one drank an equivalent amount of water. Their pulse rates were measured 10 minutes later, to test whether caffeine consumption elevates pulse rates. To determine whether lack of sleep increases appetite, researchers recruited 50 volunteers and randomly assigned 25 of them to sleep at least 8 hours a night and the other 25 to sleep at most 5 hours a night, for 3 days. Calorie intake was recorded for all 50 volunteers for the 3-day period.
- Question 1 For the following scenarios provide the following: • the null and alternative hypotheses • explain whether the hypothesis test is left-tailed, right-tailed, or two-tailed, • explain how you should interpret a decision that rejects the null hypothesis, and • explain how you should interpret a decision that fails to reject the null hypothesis. a. A meal supplement provider claims that the average difference in calories between two brands is 55.If the test of H0: = 19 against Ha: ≠ 19 based on an SRS of 15 observations from a Normal populationproduces the statistic of t = –1.75. The P-value isFor each of the following scenarios, identify: the population of interest, the outcome variable being measured on each observational unit, whether the outcome variable being measured is categorical or quantitative/Continuous, the parameter of interest, define both in words and using the appropriate statistical symbol (π, π1 -π2, µ, µ1 - µ2, or µd), and the null and alternative hypotheses, written in correct statistical notation (not in words) (a) To examine the safety of working in a nuclear power plant, we assess deaths due to cancer among all deaths at a particular power plant. Based on vital statistics, about 20% of all deaths can be attributed to some form of cancer. (b) A randomized trial study is performed to compare survival (time to death in months) two chemotherapy drugs (A vs B) among cancer patients. A sample of cancer patients are randomly assigned to treatment A or B.
- a. Which of the two excel outputs above is the correct result of the data?b. What is the appropriate set of hypotheses for this test?c. From the given results above, which test is appropriate to test the significant difference between the heat-producing capacities of the coal from the mines?d. What is the t- critical value?e. What is the p-value?f. At α=0.05, what is the correct decision?If you were constructing a 99% confidence interval of the population mean based on a sample ofn = 41 where the standard deviation of the sample is S = 15, the critical value of t will beFor parts a and b, use technology to estimate the following. a) The critical value of t for a 98% confidence interval with df=4. b) The critical value of t for a 90% confidence interval with df=111.