Concept explainers
An image is partitioned into two regions, one white and the other black. A reading taken from a randomly chosen point in the white section will be
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EBK FIRST COURSE IN PROBABILITY, A
- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.arrow_forwardIn an effort to link cold environments with hypertension in humans, a preliminary experiment was conducted to investigate the effect of cold on hypertension in rats. Two random samples of 6 rats each were exposed to different environments. One sample of rats was held in a normal environment at 26°C. The other sample was held in a cold 5°C environment. Blood pressures and heart rates were measured for rats for both groups. The blood pressures for the 12 rats are shown in the table below. a. Provide a 95% confidence interval on the difference in the two population meansb. Do the data provide sufficient evidence that rats exposed to a 5°C environment have a higher mean blood pressure than rats exposed to a 26°C environment? Use α = 0.05arrow_forwardThe molecular weight of a particular polymer should fall between 750 and 1,035. Thirty samples of this material were analyzed with the results X-bar = 902 and s = 90. Assume that molecular weight is normally distributed.arrow_forward
- The concentration of carbon dioxide (COy) in the atmosphere is increasing rapidly due to our use of fossil fuels. Because plants use COz to fuel photosynthesis, more COz may cause trees and other plants to grow faster. An elaborate apparatus allows researchers to pipe extra CO, to a 30-meter circle of forest. They selected two nearby circles in each of three parts of a pine forest and randomly chose one of each pair to receive extra COz. The response variable is the mean increase in base area for 30 to 40 trees in a circle during a growing season. We measure this in percentage increase per year. Here are one year's data Pair 1 2 3 Control Plot 9.752 7.263 5.742 Treated Plot 10.587 9.244 8.675 Treated - Control 0.835 1.981 2.933 State the null and alternative hypotheses. Explain clearly why the investigators used a onesided alternative. Use at procedure to carry out a test and report your conclusion in simple language. The investigators used the test you just carried out.Any use of the…arrow_forwardsuppose you and a friend each take different random samples of data pairs (x,y) from the same popuation. Assumethe samples are the same size. Based on your samples, you compute r=0.83. Based on her sample, your friend computes r=0.79. Is your friends value for r wrong?arrow_forwardThe authors of a paper compared two different methods for measuring body fat percentage. One method uses ultrasound, and the other method uses X-ray technology. The table gives body fat percentages for 16 athletes using each of these methods (a subset of the data given in a graph that appeared in the paper). For purposes of this exercise, you can assume that the 16 athletes who participated in this study are representative of the population of athletes. Athlete 0 Ho: Md = Ha: Md 0 < 0 5 6 7 8 9 10 11 12 13 14 15 16 X-ray 4.75 7.00 9.25 12.00 17.25 29.50 5.50 6.00 8.00 8.50 9.25 11.00 12.00 14.00 17.00 18.00 USE SALT Ultrasound 4.75 4.00 9.00 11.75 17.00 27.75 6.50 6.75 8.75 9.75 9.50 12.00 12.25 15.75 18.00 18.50 X Find the test statistic and P-value. (Use a table or SALT. Round your test statistic to one decimal place and your P-value to three decimal places.) t = P-value = 0.000 Mx-ray ultrasound.)arrow_forward
- The concentration of carbon dioxide (CO2) in the atmosphere is increasing rapidly due to our use of fossil fuels. Because plants use CO2 to fuel photosynthesis, more CO, may cause trees and other plants to grow faster. An elaborate apparatus allows researchers to pipe extra CO, to a 30-meter circle of forest. They selected two nearby circles in each of three parts of a pine forest and randomly chose one of each pair to receive extra CO,. The response variable is the mean increase in base area for 30 to 40 trees in a circle during a growing season. We measure this in percent increase per year. Here are one year's data. Control plot - Control Treated plot 10.547 Pair Treated 9.732 0.815 7.273 9.244 1.971 5.762 8.675 2.913 (a) State the null and alternative hypotheses. (Where u is the mean difference, treated minus control.) Но: и На: и Explain clearly why the investigators used a one-sided alternative. The researchers have no preconceived idea what extra CO, will do to the growth rate.…arrow_forwardThe authors of a paper compared two different methods for measuring body fat percentage. One method uses ultrasound, and the other method uses X-ray technology. The table gives body fat percentages for 16 athletes using each of these methods (a subset of the data given in a graph that appeared in the paper). For purposes of this exercise, you can assume that the 16 athletes who participated in this study are representative of the population of athletes. Athlete Ho: Md = 0 Ha: Ha 0 = 0 Ho: Md < 0 Ha: Md P-value = X-ray 4.75 7.00 9.25 12.00 5 17.25 6 29.50 7 5.50 8 6.00 9 8.00 10 8.50 11 9.25 12 11.00 13 12.00 14 14.00 15 17.00 16 18.00 = 0 1 2 3 4 USE SALT Ultrasound 4.75 4.00 9.00 11.75 17.00 27.75 6.50 6.75 8.75 9.75 9.50 12.00 12.25 15.75 18.00 18.50 Find the test statistic and P-value. (Use a table or SALT. Round your test statistic to one decimal place and your P-value to three decimal places.) t = 0.534 0.000 X X State the conclusion in the problem context. We fail to reiect H.…arrow_forwardUse the figure to the right, which shows the percentages of adults from several countries who favor building new nuclear power plants in their country. The survey included random samples of 1115adults from Country A, 1021 adults from Country B,1038 adults from Country C, and 1067 adults from Country D. At α=0.04, can you reject the claim that the proportion of adults in Country C who favor building new nuclear power plants in their country is greater than the proportion of adults from Country D who favor building new nuclear power plants in their country? Assume the random samples are independent. Country A: 54%. Country B: 51%. Country C: 48%. Country D:37%. Part A: Choose the correct answer. A. H0:p1>p2 Ha:p1≤p2 B. H0:p1≤p2 Ha:p1>p2 C. H0:p1<p2 Ha:p1≥p2 D. H0:p1=p2 Ha:p1≠p2 E. H0:p1≠p2 Ha:p1=p2 F. H0:p1≥p2 Ha:p1<p2 Find the standardized test statistic. Use technology to calculate the P-value. Decide whether to reject or fail to reject the…arrow_forward
- A researcher does a study looking at whether the distribution of people’s favorite form of media (radio, television, internet, podcasts, or video games) has changed since previous research on this topic from the year 1995. Notice there are c = 5 categories on this variable. Additionally, the study was done by surveying n=100 people. The researcher does the calculations and gets χ2Obtained of 8.74, and a χ2Critical of 9.49 (using alpha = .05). What is the correct H0 decision and APA sentence? Group of answer choices Reject H0 APA sentence: χ2(99, n=100) = 8.74, p < .05 Fail to Reject H0 APA sentence: χ2(4, n=100) = 8.74, p > .05 Fail to Reject H0 APA sentence: χ2(5, n=100) = 8.74, p < .05 Reject H0 APA sentence: χ2(4, n=100) = 9.49, p < .05arrow_forwardAssume that IQ scores are normally distributed with μ = 100 and σ = 15 What IQ score would be needed to score in the top 2% of IQ scores?arrow_forwardThe shelf life of a particular dairy product is normally distributed with a μ of 12 days and a σ of 3 days. What percent of the products last 15 or more days?arrow_forward
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