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Unfortunately, arsenic occurs naturally in some ground watert. A mean arsenic le

ID: 2947391 • Letter: U

Question

Unfortunately, arsenic occurs naturally in some ground watert. 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 36 tests gave a sample mean of x = 7.2 ppb arsenic, with s = 2.8 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use a 0.05. (a) What is the level of significance? State the null and alternate hypotheses. (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The standard normal, since the sample size is large and ? is known. The standard normal, since the sample size is large and ? is unknown. The Student's t, since the sample size is large and ? is unknown. O The Student's t, since the sample size is large and ? is known. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Find the P-value. (Round your answer to four decimal places.)

Explanation / Answer

Solution :

Given that x-bar = 7.2 , s = 2.8 , n = 36 , ? = 8

(b) => ? = 0.05 then c = 1-? = 0.95

=> df = n-1 = 35

For 95% confidence interval , t = 1.69

=> test statistic t = (x-bar - ?)/(s/sqrt(n))

= (7.2 - 8)/(2.8/sqrt(36))

= -1.714

(c) P-value = 0.0477