this is part two. I got the answer wrong and i trying to figure out the answers before this test.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, withσ = 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 isμ = 2.0 µg/L.However, a random sample ofn = 10water samples showed thatx = 2.54 µg/L.Does this indicate that the lead concentration population mean is higher than the industrial plant claims? Usea = 1%(i) the level of significance which is 0.01and the value of the sample test statistic is 2.44(iii)p-value<0.010  (iv) Based on your answers in parts (i) to (iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α? At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.     At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.  (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 limitupper limit(c) How large a sample should be taken to be 95% confident that the sample meanxis within a margin of errorE = 0.4 µg/Lof the population mean? (Round your answer up to the nearest whole number.)      ?  water samples

Question
Asked Dec 11, 2019
4 views

this is part two. I got the answer wrong and i trying to figure out the answers before this test.

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 = 2.54 µg/L.
Does this indicate that the lead concentration population mean is higher than the industrial plant claims? Use
a = 1%
(i) the level of significance which is 0.01
and the value of the sample test statistic is 2.44
(iii)p-value<0.010
 
 
(iv) Based on your answers in parts (i) to (iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?
At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.     At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.
 
 
(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
upper limit

(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
 
 
 
check_circle

Expert Answer

Step 1

(a) (iv)

The null and the alternative hypotheses used for testing are given below:

help_outline

Image Transcriptionclose

Н, : иs2.0ugL > 2.0µg/L Н:и>2.0ug/1L

fullscreen
Step 2

By using the results obtained in part (i) and (iii) the conclusion is made.

Decision Rule:

Reject the null hypothesis when the p-value is lesser than or equal to the level of significance. Otherwise, do not reject the null hypothesis.

Conclusion:

It is given that the p-value is lesser than 0.010 and the level of significance is 0.010.

The p-value is less than the level of significance.

Thus, the null hypothesis is rejected.

 

Hence, there is sufficient evidence to conclude that the lead concentration population mean is higher than the industrial plant claims at 1% level of significance.

 

The conclusion is that we reject the null hypothesis and conclude that the data are statistically significant

Step 3

(b)

The 95% confidence interval ...

help_outline

Image Transcriptionclose

C.I =F±Z, Vn, 0.7 = 2.54+1.96 V10 = 2.54+0.43 = 2.11,2.97 Thus, the 95% confidence interval is (2.11, 2.97)

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Statistics

Related Statistics Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: A study collects samples of water from the tap in Vacaville and from bottled water available from th...

A: The observed pH value is 6.32.The mean pH of Tap water is calculated as follows:

question_answer

Q: The FiveThirtyEight website a survey of people about their financial situation and their social well...

A: Formulation of HypothesisNull Hypothesis H0: - People’s social well being and their wealth is not re...

question_answer

Q: A clinical trial is being conducted in order to determine the efficacy of a new drug used to treat R...

A: It is given that both standard deviations, σ1 = σ2 = 8.Margin of error, E = 3.0The z-critical value ...

question_answer

Q: A regression of the LDL cholesterol level on the Body Mass Index (BMI) is shown below:LDL Cholestero...

A: According to the provided information, regression line of the LDL cholesterol level on the Body Mass...

question_answer

Q: Using the following data, calculate the χ2, the degrees of freedom, and the effect size.  Would the ...

A: The appropriate Null and Alternative Hypotheses are given below: Null hypothesis: H0: The variables ...

question_answer

Q: HELP

A: The null and alternative hypotheses are as:Null hypothesis,Ho: The distribution of hockey player’s b...

question_answer

Q: Why should researchers be very cautious about comparison of correlations that involve different vari...

A: Researchers should be very cautious about comparisons of correlations that involve different variabl...

question_answer

Q: Listed below are student evaluation ratings of courses, where a rating of 5 is for "excellent." The ...

A: Given data and calculation for mean and sample standard deviation is shown below

question_answer

Q: The probability distribution of x, the number of defective tires on a randomly selected automobile c...

A: Note:Thank you for the question. Since multiple questions are posted, according to our policy, we ar...