A 95% confidence interval for the proportion of sea fans infected on the Las Redes Reef was calculated to be (0.423, 0.615)Based on this confidence interval, which one of the following statements is necessarily TRUE?Group of answer choices51.9% of all sea fans on the Las Redes Reef are infectedIf the study was repeated many times over, and the sample proportion of infected sea fans (p-hat) was recorded each time, then we would expect approximately 95% of the resulting estimates (the p_hat's) to be between (0.423 0.615).51.9% of all sea fans are infected.We don't know exactly what proportion of sea fans on the Las Redes Reef are infected but we know that it is definitely between 0.423 and 0.615.We can be 95% sure that the proportion of sea fans infected on the Las Redes Reef is between 0.423 and 0.615.

Given a 95% Confidence Interval for a population proportion: (0.54, 0.86) which of the following are plausible values for the true population proportion?There may be one or more correct answer. See Section 3.2 if you're not sure what is meant by 'plausible value'.0.320.570.780.680.210.390.51

Suppose (35,40) is a 95% confidence interval estimate for a population mean 𝜇. Which of the following are true statements?I. There is a .95 probability that 𝜇 is between 35 and 40.II. If 100 random samples of the given size are picked and a 95% confidence interval is calculated from each, then 𝜇 will be in 95 of the resulting intervals.III. If 95% confidence intervals are calculated from all possible samples of the given size, 𝜇 will be in 95% of these intervals.I and III and IIIII and IIII, II, and IIINone of the above gives the complete set of true responses.

Use the given data to construct a 99.5% confidence interval for the population proportion p.=x52,  =n71Round the answer to at least three decimal places.Theconfidenceintervalis, .

The overall research question for this task is “How does the proportion of all litter on beach one that is plastic compare to the proportion of all litter on beach two that is plastic?” The confidence interval is (0.277,0.451) the sample proportion for plastic litter from first beach is 0.386, sample size of first beach is 448 and the the sample proportion for plastic litter from second beach is 0.75，sample size of second beach is 132 Write one sentence that interprets the confidence interval for difference in proportions in terms of a comparison.

Determine the 99% confidence interval for the population mean. (Round your answers to 3 decimal places.)