Unfortunately, arsenic occurs naturally in some ground water.t A mean arsenic level of u = 8.0 parts per billion (ppb) isconsidered 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 thatthe 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 ppbO Ho: H< 8 ppb; H: u = 8 ppbO Ho: H = 8 ppb; H,: u < 8 ppbO Ho: H= 8 ppb; H: u+ 8 ppbHoiH> 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 > 0.100O 0.050 < P-value < 0.100O 0.010 < P-value < 0.050O 0.005 < P-value < 0.010OP-value < 0.005Sketch the sampling distribution and show the area corresponding to the P-value.-4-2A plot of the Student's t-probability curve has a horizontal axiswith values from -4 to 4. The curve enters the window from theleft, just above the horizontal axis, goes up and to the right,changes direction over approximately o on the horizontal axis, andthen goes down and to the right before exiting the window justabove the horizontal axis. The area under the curve betweenDO-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 statisticallysignificant 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.OThere is insufficient evidence at the 0.01 level to conclude that the mean level of arsenic in the well is less than8 ppb.

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Description: Unfortunately, arsenic occurs naturally in some ground water.t A mean arsenic level of u = 8.0 parts per billion (ppb) isconsidered safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested on a regular basis for

We have given that Sample size n=36 ,xbar = 7.1 ,mu=8bbp ,s=2.2 and level of significance =0.01

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Statistics

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 Ho: H= 8 ppb; H,:> 8 ppb O Ho: u< 8 ppb; H,: - 8 ppb O Ho: H= 8 ppb; H,:H < 8 ppb HoiH = 8 ppb; H,: u + 8 ppb O Ho: H > 8 ppb; H,: = 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. 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 -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. 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.

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 Ho: H= 8 ppb; H,:> 8 ppb O Ho: u< 8 ppb; H,: - 8 ppb O Ho: H= 8 ppb; H,:H < 8 ppb HoiH = 8 ppb; H,: u + 8 ppb O Ho: H > 8 ppb; H,: = 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. 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 -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. 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.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 13PPS

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