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- Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.[4-5] CONSIDER that the data is UNCORRELATED use alpha .05. Provide the following: CI of the F value Statistical InterpretationThe average American gets a haircut every 34 days. Is the average smaller for college students? The data below shows the results of a survey of 15 college students asking them how many days elapse between haircuts. Assume that the distribution of the population is normal. 32, 21, 34, 22, 33, 40, 27, 27, 26, 35, 36, 28, 20, 33, 29 What can be concluded at the the αα = 0.10 level of significance level of significance? For this study, we should use Select an answer t-test for a population mean z-test for a population proportion The null and alternative hypotheses would be: H0:H0: ? p μ Select an answer > = < ≠ H1:H1: ? μ p Select an answer < = > ≠ The test statistic ? t z = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 3 decimal places.) The p-value is ? > ≤ αα Based on this, we should Select an answer fail to reject accept reject the null hypothesis. Thus, the final conclusion is that ... The data…
- Let X∼Uniform(0,1) distribution. Find the PDF of Y= 3√X and derive the expected value and the variance of Y.Suppose a sample Y1, ..., Yn is selected from an exponential distribution with E (Yi) = θ and V (Yi) = θ2. Let θˆ be an estimator of the mean, θ.1. Explain what a parameter is. What is the parameter of interest in this case?2. Name the properties of a good estimator and explain, shortly, what is meant by each. (a)(b) (c)3. Given the properties you discussed in (2) and the parameter of interest identified in (1), what estimator would you propose?4. What would the sampling distribution of this estimator be? Why?The critical value for t for n = 9 for a one tail test at a = 5% LOS is %3D t table link: https://drive.google.com/drive/folders/10Vh9s) usp=sharing a. 1.860 b. 2.896 C. 1.833 d. 2.821
- Let X1, . . . , Xn be iid from Exp(β). Find the distribution of the sample maximum Y = X(n). Is this an exponential distribution? (This question was rejected this morning. I did double check and there is no missing info with this question.)Let X ~N(0, e2). Find the CRLB for variances of the unbiased estimator of T(0) = 0². %3DThe proportion of rats that successfully complete a designed experiment (e.g., running through a maze) is of interest for psychologists. Denote by Y the proportion of rats that complete the experiment, and suppose that the experiment is replicated in 10 different rooms. Assume that Y₁, Y2,..., Y10 are i.i.d. Beta random variables with a = 2 and B = 1. Recall that for this Beta model, the pdf is fy(y)= J2y if 0 0.9).
