Extracted text: 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="" o="" ho:="" h="8" ppb;="" h,:="" u="">< 8="" ppb="" o="" ho:="" h="8" ppb;="" h:="" u+="" 8="" ppb="" hoih=""> 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 value of the sample test statistic? (Round your answer to three decimal places.) (c) Estimate the P-value. O P-value > 0.100 O 0.050 < p-value="">< 0.100="" o="" 0.010="">< p-value="">< 0.050="" o="" 0.005="">< p-value="">< 0.010="" o="" p-value="">< 0.005 sketch the sampling distribution and show the area corresponding to the p-value. -4 -2 a plot of the student's t-probability curve has a horizontal axis with values from -4 to 4. the curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately o on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. the area under the curve between do-2.45 and 4 is shaded. (d) based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? are the data statistically significant at level a? o at the a = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. o at the a = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. o at the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. o at the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (e) interpret your conclusion in the context of the application. o there is sufficient evidence at the 0.01 level to conclude that the mean level of arsenic in the well is less than 8 ppb. o there is insufficient evidence at the 0.01 level to conclude that the mean level of arsenic in the well is less than 8 ppb. 0.005="" sketch="" the="" sampling="" distribution="" and="" show="" the="" area="" corresponding="" to="" the="" p-value.="" -4="" -2="" a="" plot="" of="" the="" student's="" t-probability="" curve="" has="" a="" horizontal="" axis="" with="" values="" from="" -4="" to="" 4.="" the="" curve="" enters="" the="" window="" from="" the="" left,="" just="" above="" the="" horizontal="" axis,="" goes="" up="" and="" to="" the="" right,="" changes="" direction="" over="" approximately="" o="" on="" the="" horizontal="" axis,="" and="" then="" goes="" down="" and="" to="" the="" right="" before="" exiting="" the="" window="" just="" above="" the="" horizontal="" axis.="" the="" area="" under="" the="" curve="" between="" do-2.45="" and="" 4="" is="" shaded.="" (d)="" based="" on="" your="" answers="" in="" parts="" (a)="" to="" (c),="" will="" you="" reject="" or="" fail="" to="" reject="" the="" null="" hypothesis?="" are="" the="" data="" statistically="" significant="" at="" level="" a?="" o="" at="" the="" a="0.01" level,="" we="" reject="" the="" null="" hypothesis="" and="" conclude="" the="" data="" are="" statistically="" significant.="" o="" at="" the="" a="0.01" level,="" we="" reject="" the="" null="" hypothesis="" and="" conclude="" the="" data="" are="" not="" statistically="" significant.="" o="" at="" the="" a="0.01" level,="" we="" fail="" to="" reject="" the="" null="" hypothesis="" and="" conclude="" the="" data="" are="" statistically="" significant.="" o="" at="" the="" a="0.01" level,="" we="" fail="" to="" reject="" the="" null="" hypothesis="" and="" conclude="" the="" data="" are="" not="" statistically="" significant.="" (e)="" interpret="" your="" conclusion="" in="" the="" context="" of="" the="" application.="" o="" there="" is="" sufficient="" evidence="" at="" the="" 0.01="" level="" to="" conclude="" that="" the="" mean="" level="" of="" arsenic="" in="" the="" well="" is="" less="" than="" 8="" ppb.="" o="" there="" is="" insufficient="" evidence="" at="" the="" 0.01="" level="" to="" conclude="" that="" the="" mean="" level="" of="" arsenic="" in="" the="" well="" is="" less="" than="" 8="">