A field experiment plan on irrigation quota and organic fertilization on rice is as follows: (1) irrigation quota: 5000 (IQ1), 7500 (IQ2), 10000 (IQ3) m³/hm², (2) organic fertilizer: 0.5 (OF1), 0.75 (OF2), 1.0 (OF3), 1.5 (OF4) t/hm², (3) replication: 3 times. You are required: Design and arrange the PLOTS into the experimental field by methods of random blocks and split-plot (the fertility gradient is assumed from north to south).
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- We consider the problem of improving lithium car batteries. A research group is makıng great advances using a new type anode and they claim that the mean life is greater than 1600 recharge cycles. To support this claim, they create 36 new batteries and subject them to recharge cycles until they fail. The claim will be established if the sample mean lifetime is greater than 1640 cycles. Otherwise, the claim will not be established and further improvements are needed. Assume that the population standard deviation o = 192 cycles is known. (a) Find the probability of a Type I error. (b) Find the probability of a Type II error when u = 1680 cycles.MDM Farms grows normally distributed potatoes and is testing a new crop. After 4 months, 20 plants produce potatoes with the following weights (in kg): 0.7, 1.4, 1.4, 1.3, 0.3, 1.4, 0.6, 1.3, 1.3, 1.1, 0.9, 1.5, 1.1, 1.5, 0.6, 1.4, 1.1, 0.5, 0.6, 0.8 a. Find the mean and standard deviation of the sample. b. What percent of potatoes grown from this crop will be over 2 kg?Reducing scrap of 4-foot planks of hardwood is an important factor in reducing cost at a wood-flooring manufacturing company. Accordingly, engineers at Lumberworks are investigating a potential new cutting method involving lateral sawing that may reduce the scrap rate. To examine its viability, samples of 600 and 500 planks, respectively, were examined under the old and new methods. Sixty-two of the 600 planks were scrapped under the old method, whereas 34 of the 500 planks were scrapped under the new method. (You may find it useful to reference the appropriate table: z table or t table) a. Construct the 90% confidence interval for the difference between the population scrap rates between the old and new methods, respectively. (Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.) Confidence interval is I to %. 論
- Determine your independent and dependent variables, which type of ANOVA would you choose, and how much replication would be needed. Farmer Joe has eight different plots of land. He applies two different nitrogen levels randomly to each of the 8 plots, low and high. In addition, four different strawberry varieties are randomized within the plots. He is measuring mass of fruit for his outcome. I would like to see if there is a difference in birth weight among cat breeds. I will measure 5 different cat breeds.Reducing scrap of 4-foot planks of hardwood is an important factor in reducing cost at a wood-flooring manufacturing company. Accordingly, engineers at Lumberworks are investigating a potential new cutting method involving lateral sawing that may reduce the scrap rate. To examine its viability, samples of 600 and 500 planks, respectively, were examined under the old and new methods. Sıxty-two of the 600 planks were scrapped under the old method, whereas 34 of the 500 planks were scrapped under the new method. (You may find It useful to reference the approprlate table: z table or t table) a. Construct the 90% confidence Interval for the difference between the population scrap rates between the old and new methods, respectively. (Negative values should be Indicated by a minus sign. Round Intermedlate calculatlons to at least 4 decimal places and final answers to 2 decimal places.) Confidence interval is % to b. Select the null and alternative hypotheses to test for differences in the…An experiment to test the effectiveness of regular treatments with fluoride varnish to reduce tooth decay involved 36 volunteers who had half of their teeth (the right side or left side, determined by a coin flip) painted with a fluoride varnish every six month for 5 years. At the end of the treatments, the number of new cavities during the treatment period was compared on treatment (fluoride varnish) side versus the control (no fluoride varnish) side. The appropriate statistical test for analyzing the results of this experiment is O Paired t test for a mean difference O One sample z test for a population mean O Two sample t test for a difference in means O One sample z test for a population proportion O Two sample z test for a difference in proportions
- According to a certain government agency for a large country, the proportion of fatal traffic accidents in the country in which the driver had a positive blood alcohol concentration (BAC) is 0.34. Suppose a random sample of 109 traffic fatalities in a certain region results in 50 that involved a positive BAC. Does the sample evidence suggest that the region has a higher proportion of traffic fatalities involving a positive BAC than the country at the x = 0.01 level of significance? Because npo (1-Po) = 24.5 > 10, the sample size is (Round to one decimal place as needed.) What are the null and alternative hypotheses? p = 0.34 versus H₁: p > 0.34 Ho: p (Type integers or decimals. Do not round.) Find the test statistic, Zo. Zo = 2.62 (Round to two decimal places as needed.) Find the P-value. P-value = (Round to three decimal places as needed.) less than 5% of the population size, and the sample is given to be random, the requirements for testing the hypothesis are satisfied.A two-way ANOVA experiment with interaction was conducted. Factor A had three levels (columns), factor B had five levels (rows), and six observations were obtained for each combination. Assume normality in the underlying populations. The results include the following sum of squares terms: SST=1542 SSA= 1042 SSB = 358 SSAB = 39 a. Construct an ANOVA table. (Round "MS" to 4 decimal places and "F" to 3 decimal places.) ANOVA Source of Variation Rows Columns Interaction Error Total SS 0 df Answer is not complete. 0 MS F p- value 0.000 0.000 0.002A selected, inbred rat strain had a tail measuring an average of 5.4 cm. An inbred, wild caught strain had 6.2 cm long tails. The selected and wild caught strains were crossed producing the F1 and F2 below. Generation Progeny Phenotype F1 20 5.8 cm F2 250 5 to 6.6 cm a) Assume that 4 genes control tail length. What is the average contribution per allele in the F2 generation? b) What proportion of the F2 would have tails 6 cm in length? c) Which of the following best describes the PARENTAL rat strains? AAbbCCDD x aaBBccdd AABBCCDD x aabbccdd AABBccdd x aabbCCDD d) How many offspring (approximately) in the F2 would have 5 cm long tails?
- Seedlings of understory trees in mature tropical rainforests must survive and grow using inter- mittent flecks of sunlight. How does the length of exposure to these flecks of sunlight (fleck duration) affect growth? Leakey et al. (2005) experimentally irradiated seedlings of the Southeast Asian rainforest tree Shorea leprosula with flecks of light of varying duration while maintaining the same total irradiance to all the seedlings. Their data for 21 seedlings are listed in the following table. i. What is the rate of change in relative growth rate per minute of fleck duration? provide a standard error for your estimate. ii. using these data, test the hypothesis that fleck duration affects seedling growth rate. iii. Calculate a 99% confidence interval for the slope of the population regression.Calcium is the most abundant mineral in the human body and has several important functions. Most of the body calcium is stored in the bones and teeth, where it functions to support their structure. Recommendations for calcium are provided in Dietary Reference Intakes, developed by the Institute of Medicine of the National Academy of Sciences. The recommended adequate intake (RAI) for calcium for adults (ages 19-50) is 1000 mg per day. A random sample of 18 adults with incomes below the poverty level gave the following calcium intakes:886 633 943 847 934 8411193 820 774 834 1050 10581192 975 1313 872 1079 809Assume the population standard deviation for daily calcium intake for adults with incomes below the poverty level is 188mg.At the 0.05 level of significance, does the data provided above provide evidence to suggest that the mean calcium intake of all adults with incomes below the poverty level is less than the RAI pf 1000mg per day? Step 1: Define the parameter & setup the…