We have seen that two different tests for Ho B₁ = 0 versus H₁: B₁0, a t-test and a F-test. : Please show that the F-test statistic is equal to the t-test statistic squared. Hint: F-test statistic = t-test statistic MSreg MSres B₁ s.e.(B₁) " where MSreg = ²1(Y₁ - Y)², MSres = Σi-1(Y₁ - Ŷ₁)²/(n − 2). - =1
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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.The following table provides values of the function f(x,y). However, because of potential; errors in measurement, the functional values may be slightly inaccurately. Using the statistical package included with a graphical calculator or spreadsheet and critical thinking skills, find the function f(x,y)=a+bx+cy that best estimate the table where a, b and c are integers. Hint: Do a linear regression on each column with the value of y fixed and then use these four regression equations to determine the coefficient c. x y 0 1 2 3 0 4.02 7.04 9.98 13.00 1 6.01 9.06 11.98 14.96 2 7.99 10.95 14.02 17.09 3 9.99 13.01 16.01 19.02Unfortunately, arsenic occurs naturally in some ground water.t A mean arsenic level of u = 8.0 parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 36 tests gave a sample mean of x = 7.1 ppb arsenic, with s = 2.2 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use a = 0.01. A USE SALT (a) What is the level of significance? State the null and alternate hypotheses. O Ho: H= 8 ppb; H,: H > 8 ppb O Ho: H 8 ppb; H: H = 8 ppb (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The standard normal, since the sample size is large and a is unknown. O The Student's t, since the sample size is large and a is known. O The standard normal, since the sample size is large and a is known. O The Student's t, since the sample size is large and a is unknown. What is…
- Unfortunately, arsenic occurs naturally in some ground water.t A mean arsenic level of u = 8.0 parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 36 tests gave a sample mean of x = 7.1 ppb arsenic, with s = 2.2 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use a = 0.01. A USE SALT (a) What is the level of significance? State the null and alternate hypotheses. O Họ: u = 8 ppb; H,: u > 8 ppb O Ho: H 8 ppb; H,: u = 8 ppb (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since the sample size is large and a is unknown. O The Student's t, since the sample size is large and a is known. O The standard normal, since the sample size is large and a is known. The Student's t, since the sample size is large and a is unknown. What is the…Unfortunately, arsenic occurs naturally in some ground water.t A mean arsenic level of u = 8.0 parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 36 tests gave a sample mean of x = 6.7 ppb arsenic, with s = 3.0 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use a = 0.01. n USE SALT (a) What is the level of significance? State the null and alternate hypotheses. O Ho: H = 8 ppb; H,: u > 8 ppb O Ho: H = 8 ppb; H,: H + 8 ppb O Ho: H 8 ppb; H,: u = 8 ppb O Ho: H = 8 ppb; H,: µ 0.100 O 0.050 < P-value < 0.100 O 0.010 < P-value < 0.050 O 0.005 < P-value < 0.010 P-value < 0.005 Sketch the sampling distribution and show the area corresponding to the P-value. MacBook Pro escResearchers wanted to measure the effect of alcohol on the development of the hippocampal region in adolescents. The researchers randomly selected 13 adolescents with alcohol use disorders. They wanted to determine whether the hippocampal volumes in the alcoholic adolescents were less than the normal volume of 9.02 cm. An analysis of the sample data revealed that the hippocampal volume is approximately normal with x= 8.17 ands=0.6. Conduct an appropriate test at the a= 0.05 level of significance. Choose the correct hypotheses. Ho 9.02 V9.02 Find the test statistic. to =D (Round to two decimal places as needed.) Find the P-value The P-value is (Round to three decimal places as needed.) What conclusion can be drawn? O A. Reject Hn. There is sufficient evidence to conclude that the hippocampal volumes in the alcoholic adolescents are less than the normal volume of 9.02 cm".
- The mean weight of loaves of bread produced at the bakery where you work is supposed to be 1 pound. You are the supervisor of quality control at the bakery, and you are concerned that new employees are producing loaves that are too light. Suppose you weigh an SRS of bread loaves and find that the mean weight is 0.975 pound. We want to test Ho = 1 H a = 0.01, we reject Họ. We do not have convincing evidence that the true mean weight for all loaves of bread produced at the bakery is less than one pound. Because the P-value of 0.0806 > a = 0.01, we fail to reject Ho. We do not have convincing evidence that the true mean weight for all loaves of bread produced at the bakery is less than one pound. Peceuse the P-value of 0.0806 > a = 0.01, we reject Ho. We have convincing evidence that the true mean weight for all loaves of bread produced at the bakery is less than one pound. Because the P-value of O.0806 > a = 0.01, we accept Ho. We have convincing evidence that the true mean weight for…The following scatterplot shows the mean annual carbon dioxide (CO,) in parts (CO2) per million (ppm) measured at the top of a mountain and the mean annual air temperature over both land and sea across the globe, in degrees Celsius (C). Complete parts a through h on the right. f) View the accompanying scatterplot of the residuals vs. CO2. Does the scatterplot of the residuals vs. CO, show evidence of the violation of any assumptions behind the regression? 16.800 A. Yes, the outlier condition is violated. 16.725 O B. Yes, the linearity and equal variance assumptions are violated. 16.650 C. Yes, the equal variance assumption is violated. 16.575 O D. No, all assumptioris are okay. 16.500 O E. Yes, all the assumptions are violated. 325.0 337.5 350.0 362.5 CO2 (ppm) OF Yes, the linearity assumption is violated. his vear, What mean temperature doesGestation For women, pregnancy lasts about 9 months.In other species of animals, the length of time fromconception to birth varies. Is there any evidence thatthe gestation period is related to the animal’s lifespan?The first scatterplot shows Gestation Period (indays) vs. Life Expectancy (in years) for 18 speciesof mammals. The highlighted point at the far rightrepresents humans. a) For these data, r = 0.54, not a very strong relation-ship. Do you think the association would be stronger or weaker if humans were removed?Explain.b) Is there reasonable justification for removing humansfrom the data set? Explain.c) Here are the scatterplot and regression analysis for the17 nonhuman species. Comment on the strength of theassociation.d) Interpret the slope of the line.e) Some species of monkeys have a life expectancy ofabout 20 years. Estimate the expected gestation periodof one of these monkeys.
- What is a covariate?A diet center wanted to test three different methods for losing weight to determine if the average weight loss (reported in pounds/week) for each method is the same. The results for the three methods are tabulated below. Given that there is a significant difference between the three methods, use the Tukey test to determine if there is a significant difference between each pair of methods. Let a=0.05. (picture attached)Consider a function R(r, y) = /y. Assuming r and y are correlated, what is the standard deviation of R as a function of r, y, and their standard deviations? IHR = 1/y were an eficiency for a detector, with y representing the total number of events in which a particle passed through and ar the subset of events in which the detector activated, would the calculation above apply? Why or why not? Write down the equation for the binomial error on an efficiency measurement, explaining in