Question

Let x be a random variable that represents micrograms of lead per liter of water (µg/L)....

Let x be a random variable that represents micrograms of lead per liter of water (µg/L). An industrial plant discharges water into a creek. The Environmental Protection Agency (EPA) has studied the discharged water and found x to have a normal distribution, with

σ = 0.7 µg/L.

Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount and thereby produce a slightly more "conservative" answer.

(a) The industrial plant says that the population mean value of x is

μ = 2.0 µg/L.

However, a random sample of

n = 10

water samples showed that

x = 2.53 µg/L.

Does this indicate that the lead concentration population mean is higher than the industrial plant claims? Use

a = 1%.

(i) What is the level of significance?

What is the value of the sample test statistic? (Round your answer to two decimal places.)

(b) Find a 95% confidence interval for μ using the sample data and the EPA value for σ. (Round your answers to two decimal places.)

lower limit     µg/L
upper limit     µg/L


(c) How large a sample should be taken to be 95% confident that the sample mean

x

is within a margin of error

E = 0.4 µg/L

of the population mean? (Round your answer up to the nearest whole number.)
water samples

Homework Answers

Answer #1

The statistical software output for this problem is:

One sample Z summary hypothesis test:
μ : Mean of population
H0 : μ = 2
HA : μ > 2
Standard deviation = 0.7

Hypothesis test results:

Mean n Sample Mean Std. Err. Z-Stat P-value
μ 10 2.53 0.22135944 2.3942959 0.0083

95% confidence interval results:

Mean n Sample Mean Std. Err. L. Limit U. Limit
μ 10 2.53 0.22135944 2.0961435 2.9638565

Hence,

a) i) Level of significance = 0.01

Sample test statistic = 2.39

b) 95% confidence interval:

Lower limit = 2.10 mg/L

Upper limit = 2.96 mg/L

c) Sample size

n = 12

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters...
Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of whole blood. Then x has a distribution that is approximately normal, with population mean of about 14 for healthy adult women. Suppose that a female patient has taken 10 laboratory blood tests during the past year. The HC data sent to the patient's doctor are as follows. 14 19 15 20 15 12 15 18 16 12 (i) Use a calculator with sample...
Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters...
Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of whole blood. Then x has a distribution that is approximately normal, with population mean of about 14 for healthy adult women. Suppose that a female patient has taken 10 laboratory blood tests during the past year. The HC data sent to the patient's doctor are as follows. 14 17 17 18 15 12 14 18 15 12 (i) Use a calculator with sample...
Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters...
Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of whole blood. Then x has a distribution that is approximately normal, with population mean of about 14 for healthy adult women. Suppose that a female patient has taken 10 laboratory blood tests during the past year. The HC data sent to the patient's doctor are as follows. 16 19 17 20 13 11 13 18 17 11 (i) Use a calculator with sample...
The random variable X is normally distributed. Also, it is known that P(X > 161) =...
The random variable X is normally distributed. Also, it is known that P(X > 161) = 0.04. [You may find it useful to reference the z table.] a. Find the population mean μ if the population standard deviation σ = 13. (Round "z" value to 3 decimal places and final answer to 2 decimal places.) b. Find the population mean μ if the population standard deviation σ = 24. (Round "z" value to 3 decimal places and final answer to...
Let x be a random variable that represents the weights in kilograms (kg) of healthy adult...
Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean μ = 67.0 kg and standard deviation σ = 8.0 kg. Suppose a doe that weighs less than 58 kg is considered undernourished. (a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your...
Let x be a random variable that represents the weights in kilograms (kg) of healthy adult...
Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean μ = 64.0 kg and standard deviation σ = 8.9 kg. Suppose a doe that weighs less than 55 kg is considered undernourished. (a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your...
Let x be a random variable that represents the weights in kilograms (kg) of healthy adult...
Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean μ = 67.0 kg and standard deviation σ = 8.1 kg. Suppose a doe that weighs less than 58 kg is considered undernourished. (a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your...
Let x be a random variable that represents the weights in kilograms (kg) of healthy adult...
Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean μ = 59.0 kg and standard deviation σ = 8.1 kg. Suppose a doe that weighs less than 50 kg is considered undernourished. (a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your...
Let x be a random variable that represents the weights in kilograms (kg) of healthy adult...
Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean μ = 56.0 kg and standard deviation σ = 8.8 kg. Suppose a doe that weighs less than 47 kg is considered undernourished. (a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your...
Let x be a random variable that represents the weights in kilograms (kg) of healthy adult...
Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean μ = 67.0 kg and standard deviation σ = 8.7 kg. Suppose a doe that weighs less than 58 kg is considered undernourished. (a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT