Question

Benzene is a toxic chemical used in the manufacturing of medicinal chemicals, dyes, artificial leather, and linoleum. A manufacturer claims that its exit water meets the federal regulation with a mean of less than 7980 ppm of benzene. To assess the benzene content of the exit water, 10 independent water samples were collected and found to have an average of 7900 ppm of benzene. Assume a known population standard deviation of 80 ppm and use a significance level of 0.01. Test the manufacturer’s claim.(a) State the Null and Alternative hypothesis. (b) calculate the test statistics. (c) Find the P-value and draw your conclusion. Round your answer to 5 decimal places. (d) Find a 99% two-sided confidence bound on the true mean. Round your answer to 2 decimal places.

Answer 1

Answer:

a:  H0: µ = 7980, Ha:  µ < 7980 (claim)

b:  -3.162

c:  P-value is 0.00576

d: 7821.61 < µ < 7978.39

Step-by-step explanation:

The given data for the situation is:

µ = 7980, σ = 80, x = 7900, n = 10

The hypothesis are

H0: µ = 7980

Ha:  µ < 7980 (claim)

This is a left tailed test, with a significance level of 0.01,  so the critical value for the situation is: t < -2.821

See the attached photo 1 for the calculation of the test statistic...

Use a chart, software or online calculator to find the p-value of the test statistic

See attached photo 2 for the construction of the confidence interval