A sample of two observatiors x₁, x2 has been drawn from a normal population. It is required to test the hypothesis that the population mean is 0. Prove that on the basis of t-test with equal test at 20% level of significance, the hypothesis will be rejected if: 1x₁ + x₂121x₁ - x₂ I tan 72°
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- A standardized IQ test is known to be normally distributed and has μ=100 and σ=10. there is a common belief that students in wealthier school districts tend to have higher IQ scores. A researcher randomly selects a sample of 25 students from wealthy school districts. The average IQ of the sample is x̅=103. Conduct a test if the average score for students from wealthy districts is higher than 100, assuming α=0.05The calibration of a scale is to be checked by weighing a 11 kg test specimen 25 times. Suppose that the results of different weighings are independent of one another and that the weight on each trial is normally distributed with o = 0.200 kg. Let u denote the true average weight reading on the scale. (a) What hypotheses should be tested? Ho: H = 11 Ha: u + 11 Ho: H + 11 H3i H 11 a (b) With the sample mean itself as the test statistic, what is the P-value when x = 10.83? (Round your answer to four decimal places.) What would you conclude at significance level 0.01? Conclude that the true mean measured weight differs from 11 kg. Conclude that the true mean measured weight is the same as 11 kg. (c) For a test with a = 0.01, what is the probability that recalibration is judged unnecessary when in fact u = 11.2? (Round your answer to four decimal places.) For a test with a = 0.01, what is the probability that recalibration is judged unnecessary when in fact u = 10.9? (Round your answer to…Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 139 to 194 cm and weights of 39 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x= 167.63 cm, y = 81.47 kg, r=0.106, P-value = 0.294, and y = - 108 + 1.04x. Find the best predicted value of y (weight) given an adult male who is 172 cm tall. Use a 0.05 significance level. The best predicted value of y for an adult male who is 172 cm tall is kg. (Round to two decimal places as needed.)
- 60% of students entering four-year colleges receive a degree within six years. Is this percent larger than for students who play intramural sports? 172 of the 249 students who played intramural sports received a degree within six years. What can be concluded at the level of significance of αα = 0.10? For this study, we should use (t-test, z-test) The null and alternative hypotheses would be: Ho: (symbol) (symbol) _____ (please enter a decimal) H1: (symbol) (symbol) _____ (Please enter a decimal) The test statistic (symbol) = _____ (please show your answer to 3 decimal places.) The p-value = _______ (Please show your answer to 4 decimal places.) The p-value is (symbol) αα Based on this, we should the null hypothesis. Thus, the final conclusion is that ... The data suggest the population proportion is not significantly larger than 60% at αα = 0.10, so there is sufficient evidence to conclude that the population proportion of students who…Questions are added as a picture from another file since there didn't seem to be a way to type some characteristics into this text field. A classmate is interested in estimating the variance of the error term in Yi = β0 + β1Xi + ui. a.) found on atta b.) found on attachmentPast research has indicated that the average age of death row inmates is 41 years old. researcher would like to determine if the average age has changed. She randomly selects 50 death row inma s and ds their average age to be 37 years old. The hypothesis the statistician wants to test is: a. Ho: µ=37 vs_ Ha: µ ± 41. b. Ho: µ=41 vs Ha: µ< 41. Ho: u = 41 vs. H: u 41 d. Ho: µ=37 vs_Ha: µ< 41. C. 2. If a player at a casino is playing roulette and betting on red, there is a 18 / 38 or 0.474 chance that he will win on any spin of the roulette wheel. If we take a random sample of 300 players betting on red, then p is the proportion of times that the player wins. What is the mean of the sampling distribution of p? t' a. b. What is the standard deviation (os) of the sampling distribution of p? c. If repeated samples of 300 players are taken, what would be the range of the sample proportion of players victories according to the 95 part of the 68-95-99.7 rule" pts) 3. The z statistic for a…
- In a certain article, laser therapy was discussed as a useful alternative to drugs in pain management of chronically ill patients. To measure pain threshold, a machine was used that delivered low-voltage direct current to different parts of the body (wrist, neck, and back). The machine measured current in milliamperes (mA). The pretreatment experimental group in the study had an average threshold of pain (pain was first detectable) at u = 3.30 mA with standard deviation o = 1.23 mA. Assume that the distribution of threshold pain, measured in milliamperes, is symmetric and more or less mound-shaped. (Round your answers to two decimal places.) (a) Use the empirical rule to estimate a range of milliamperes centered about the mean in which about 68% of the experimental group will have a threshold of pain from mA to (b) Use the empirical rule to estimate a range of milliamperes centered about the mean in which about 95% of the experimental group will have a threshold of pain from mA to mAA random sample of 500 adult residents of Maricopa County found that 361 were in favor of increasing the highway speed limit to 75 mph, while another sample of 400 adult residents of Pima County found that 292 were in favor of the increased speed limit. Do these data indicate that there is a difference in the support for in increasing the speed limit between the residents of the two counties? Use a = 0.05. (a) Test the hypothesis Ho: P₁ = P2 versus H₁: P₁ P2. What is zo? Round your answer to two decimal places (e.g. 98.76). Zo = (b) Is it reasonable to conclude that there is a difference in the support for increasing the speed limit between the residents of the two counties?Estimate ff e+y“ dA with R = [0, 3] × [0, 3] using m = n = 2 and midpoints as your R sample points.
- Solve with R, pleasendependent random samples are selected from two populations and are used to test the hypothesis Hn: (H, - H2) = 0 against the alternative H,: (4, - H2) #0. An analysis of 232 observations from population 1 and 311 from population 2 yielded p-value of 0.113. Complete parts a and b below. a. Interpret the results of the computer analysis. Use as0.10. A. Since this p-value exceeds the given value of a, there is insufficient evidence to indicate that the population means are different. O B. Since the given a value exceeds this p-value, there is insufficient evidence to indicate that the population means are different. OC. Since the given a value exceeds this p-value, there sufficient evidence to indicate that the population means are different. O D. Since this p-value exceeds the given value of , there is sufficient evidence to indicate that the population means are different. b. If the alternative hypothesis had been Ha: (H1 - H2) <0, how would the p-value change? Interpret the p-value…there is a claim that people living near major roads have higher blood levels of lead. 30 women living near the main road were randomly selected and the mean blood lead level was calculated as x̄1=15 and s1=5.0. in addition, 25 more women who did not live around the main road were sampled and calculated as x̄2=8.9 and s2=3.9. does this data obtained support the above claim? (test at α=0.05 significance level.)