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Unfortunately, arsenic occurs naturally in some groundwater.† A mean arsenic level of ???? = 8.0 partsper billion (ppb) is considered safe for agricultural use. A...

Question

Unfortunately, arsenic occurs naturally in some groundwater.† A mean arsenic level of ???? = 8.0 partsper billion (ppb) is considered safe for agricultural use. A wellin Texas is used to water cotton crops. This well is tested on aregular basis for arsenic. A random sample of 31 testsgave a sample mean of x = 6.9 ppbarsenic, with s = 2.4 ppb. Does thisinformation indicate that the mean level of arsenic in this well isless than 8 ppb? Use ???? = 0.01.(a)What is the level of significance?(b)What i

Unfortunately, arsenic occurs naturally in some ground water.† A mean arsenic level of ???? = 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 31 tests gave a sample mean of x = 6.9 ppb arsenic, with s = 2.4 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use ???? = 0.01. (a) What is the level of significance? (b) What is the value of the sample test statistic? (Round your answer to three decimal places.)



Answers

Unfortunately, arsenic occurs naturally in some ground water (Reference: Union Carbide Technical Report $K / U R-1$ ). A mean arsenic level of $\mu=8.0$ 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 37 tests gave a sample mean of $\bar{x}=7.2 \mathrm{ppb}$ arsenic, with $s=1.9 \mathrm{ppb} .$ Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use $\alpha=0.01.$

In this exercise, we are given the following information. For example, it's of size five. It has an average of 24.3 and a sample standard deviation of 4.1. And in part a. We were asked to find and interpret a 95% confidence interval for the population mean for 95% confidence interval. We can also assume, based on the question that the population is approximately normally distributed, so therefore for a 95% confidence interval are critical. Value is 2.776 The CIA itself is given by this formula and this gives an interval from 19.21 to 29.4. So we can say that we are 95% confident that the true population mean lies between these two numbers. Now, for part B, we are asked to predict the value for another sample from this population in a way that predicts the precision and reliability. What we are talking about is a precision interval which we found in exercise 49 to be equal to the following Mhm. And so if we plug in our numbers, we will do this at the 95% confidence level as well. And we get this interval so we can say that we are 95% confident that the value of a future specimen, um drawn from this population will be between 11.83 and 36.77


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