f a random sample of size n = 20 from a normal population with the variance = 25 has the mean ī = 64.3, construct a 95% confidence interval for the population mean µ. %3D
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- For a hypothesis test H0:μ=6H0:μ=6 versus H1:μ≠6H1:μ≠6 and variance known, calculate the p-value for the test statistics: (4 d.p.) i) zc=2.05 ii) zc = -1.84 iii) zc = 2.86Find the error margin for a 98% confidence interval for the average value of Y when X is 9.In a large design class, the scores on the "PDI" project were normally distributed with u = 100. The professor examined a sample of n= 56 students who used extra resources instead of only one resource like the other students in the class He found that the mean for students who used extra resources was M= 104.125. He used a one-sample t test to analyze the results, and part of the SPSS output is shown below. %3D One-Sample Statistics Std Error Mean N. Mean Std Deviation pdi 56 104.1250 12.58435 1 68165 One-Sample Test Test Value 100 95% Confidence Interval of the Difference Mean Difference df Sig (2-tailed) 55 Lower Upper 7.4951 pdi 2453 017 4.12500 7549 A. What are the professor's null and altemative hypotheses? B. 2. reject H, b. do not reject H, What is the professor's decision? C. resources. Identify this inform2tion and explain how you used it. You can use certain information from the table to answer Part B without referring to any other
- The mean measured verbal IQ (IQV) score of a random sample of 20 children was 86.9 with a standard deviation of 18.5. The mean measured performance IQ score (IQP) of a random sample of 20 children was 101.8 with a standard deviation of 20.0. Using the Critical Value method and alpha = 0.005 to test the claim that the mean IQV is less than the mean IQP. Assume the population variances are not equal (so use unpooled). Step 4a: Find the test statistic. Round to 2 decimal places.Spray drift is a constant concern for pesticide applicators and agricultural producers. The inverse relationship between droplet size and drift potential is well known. The paper "Effects of 2,4-D Formulation and Quinclorac on Spray Droplet Size and Deposition"+ investigated the effects of herbicide formulation on spray atomization. A figure in a paper suggested the normal distribution with mean 1050 µm and standard deviation 150 µm was a reasonable model for droplet size for water (the "control treatment") sprayed through a 760 ml/min nozzle. USE SALT (a) What is the probability that the size of a single droplet is less than 1380 µm? At least 950 µm? (Round your answers to four decimal places.) less than 1380 μm at least 950 μm (b) What is the probability that the size of a single droplet is between 950 and 1380 µm? (Round your answer to four decimal places.) (c) How would you characterize the smallest 2% of all droplets? (Round your answer to two decimal places.) The smallest 2% of…The ............. is/are used to construct confidence intervals around OLS parameters. A. population regression function B. confidence limits C. standardized normal distribution D. standard errors of β1 and β2 E. β^1−β1/se(β^1) and β^2−β2/se(β^2)
- In a trivariate distribution, it 112= 0.7, 113 = 0.61 and 223 = 0.4 find all the multiple correlation coefficients. Also obtain the standard of estimates 01.23 61:23, 02:13 and 53:12 given that: 52= 1:06, 62 = 2.15 and 3= 3.46.5 c.)3) For a sample of 306 students in a basic business communications course, the sample regression line y = 58.813 + 0.2875x was obtained. Here y = final student score at the end of the course x = score on a diagnostic writing skills test given at the beginning of the course The coefficient of determination was 0.1158 and the estimated standard deviation of the estimator of the slope of population regression line was 0.04566. a) Define and interpret the estimates of the regression equation. b) Interpret the coefficient of determination. c) What will happen to the final student score if his diagnostic writing test score increases by 2? d) How can you inmprove this model?
- The table below shows the number of hours per day 11 patients suffered from headaches before and after 7 weeks of soft tissue therapy. At x = 0.01, is there enough evidence to conclude that soft tissue therapy helps to reduce the length of time patients suffer from headaches? Assume the samples are random and dependent, and the population is normally distributed. Complete parts (a) through (f). Patient 8 9 10 11 Q 1 Daily headache hours (before) 2.3 3.4 3.3 2.6 1.8 Daily headache hours (after) 1.8 2.7 1.8 1.6 1.9 1.9 1.2 2.5 2.2 2.0 1.1 2 3 4 5 6 7 4.1 3.2 3.5 2.4 3.7 2.6 C (a) Identify the claim and state Ho and Ha The claim is "The therapy the length of time patients suffer from headaches." Let μd be the hypothesized mean of the patients' daily headache hours before therapy minus their daily headache hours after it. State Ho and H₂. Choose the correct answer below. OA. Ho: Hd=d O C. Ho: Hd ≤0 OB. Ho. Họ sở Ha: Hd >d Ha: Hdd Ha: Hd>0 OD. Ho: Hd #d Ha:Hd=d O E. Ho: Hd zd Ha: Hd 3.169…Which of the following would compute a CRITICAL VALUE for a 96% level of confidence to estimate the population mean when sigma is known and the sample size is 25. =T.INV(0.02,25) =T.INV.2T(0.04,24) =T.INV.2T(0.04,25) =NORMSINV(0.02) =NORMSINV(0.04) =T.INV(0.04,24) =NORMSINV(0.96)