Question

In: Statistics and Probability

An article presents voltage measurements for a sample of 66 industrial networks in Estonia. Assume the...

An article presents voltage measurements for a sample of 66 industrial networks in Estonia. Assume the rated voltage for these networks is 232 V. The sample mean voltage was 231.5 V with a standard deviation of 2.19 V. Let μ represent the population mean voltage for these networks.

a) Find the P-value for testing H0 : μ = 232 versus H1 : µ ≠ 232. Round the answer to four decimal places.

b) Either the mean voltage is not equal to 232, or the sample is in the most extreme % of its distribution. Round the answer to two decimal places.

Solutions

Expert Solution

Given that,
population mean(u)=232
sample mean, x =231.5
standard deviation, s =2.19
number (n)=66
null, Ho: μ=232
alternate, H1: μ!=232
level of significance, alpha = 0.05
from standard normal table, two tailed t alpha/2 =1.997
since our test is two-tailed
reject Ho, if to < -1.997 OR if to > 1.997
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =231.5-232/(2.19/sqrt(66))
to =-1.855
| to | =1.855
critical value
the value of |t alpha| with n-1 = 65 d.f is 1.997
we got |to| =1.855 & | t alpha | =1.997
make decision
hence value of |to | < | t alpha | and here we do not reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != -1.8548 ) = 0.0682
hence value of p0.05 < 0.0682,here we do not reject Ho
ANSWERS
---------------
null, Ho: μ=232
alternate, H1: μ!=232
test statistic: -1.855
critical value: -1.997 , 1.997
decision: do not reject Ho
a.
p-value: 0.0682
we do not have enough evidence to support the claim that the rated voltage for these networks is 232 V
b.
Either the mean voltage is not equal to 232, or the sample is in the most extreme % of its distribution
is 6.82%


Related Solutions

An article presents voltage measurements for a sample of 66 industrial networks in Estonia. Assume the...
An article presents voltage measurements for a sample of 66 industrial networks in Estonia. Assume the rated voltage for these networks is 232 V. The sample mean voltage was 231.5 V with a standard deviation of 2.19 V. Let μ represent the population mean voltage for these networks. a) Find the P-value for testing H0 : μ = 232 versus H1 : µ ≠ 232. Round the answer to four decimal places. b) Either the mean voltage is not equal...
An article presents an analysis of the profit of international construction projects. In a sample of...
An article presents an analysis of the profit of international construction projects. In a sample of 126 projects, the average profit margin (in percent) was 8.27 with a standard deviation of 16.33. A test is made of H0 : μ ≥ 10 versus H1 : μ < 10. - Find the P-value. Round the answer to four decimal places. This is what i have, but for some reason I'm being told it is wrong. (8.27 - 10 ) / (16.33...
2.3. Each of the following scenarios presents a claim by a researcher. Assume that the sample...
2.3. Each of the following scenarios presents a claim by a researcher. Assume that the sample sizes in each case was in the range of 20 to 25 observations per sample in each case. Answer the following for each scenario: (i) state the appropriate null (HO) and alternate hypothesis (HA) in symbolic form (e.g. Hx : Meanleft = Meanright); (ii) indicate whether it is a 1or 2-tailed test, and if a 1-tailed tests which tail is the area of rejection...
Assume that a simulation model of an industrial process has just been completed. A sample of...
Assume that a simulation model of an industrial process has just been completed. A sample of output from the process and the simulation model appears below: Observation History Simulation 1 111 109 2 113 106 3 76 126 4 83 98 5 104 96                         Is there evidence to believe that the simulation adequately represents the real system with relation to this particular metric? Why or why not? State any assumptions you make. Later, the simulation is run under three...
Assume that a simulation model of an industrial process has just been completed. A sample of...
Assume that a simulation model of an industrial process has just been completed. A sample of output from the process and the simulation model appears below: Observation History Simulation 1 111 109 2 113 106 3 76 126 4 83 98 5 104 96 Is there evidence to believe that the simulation adequately represents the real system with relation to this particular metric? Why or why not? State any assumptions you make.
Refer to the accompanying data set and use the 25 home voltage measurements to construct a...
Refer to the accompanying data set and use the 25 home voltage measurements to construct a frequency distribution with five classes. Begin with a lower class limit of 127.7127.7 ​volts, and use a class width of 0.2 volt. Does the result appear to have a normal​ distribution? Why or why​ not? LOADING... Click the icon to view the data. Complete the frequency distribution below. Voltage​ (volts) Frequency 127.7127.7minus−nothing nothing nothingminus−nothing nothing nothingminus−nothing nothing nothingminus−nothing nothing nothingminus−nothing nothing ​(Type integers or...
Summarize the article on measurements, Focus on the Logistics Service Capability Measurement System Article: Research on...
Summarize the article on measurements, Focus on the Logistics Service Capability Measurement System Article: Research on Measurement of Service Capability of Logistics Enterprise
Assume -122 and -66 are signed 8-bit decimal integers. Calculate -122 + (- 66). and -122...
Assume -122 and -66 are signed 8-bit decimal integers. Calculate -122 + (- 66). and -122 - (- 66). Do we have overflow or underflow after each operation? Why?
A 66 year-old male presents to the local ER at 6 AM. The patient reports that...
A 66 year-old male presents to the local ER at 6 AM. The patient reports that he has been having severe chest pain since last night before he went to bed. The patient says that he just simply thought that he was having a “bad case of indigestion and gas” after eating a bunch of fatty foods while watching the football with his friends last night. He says he took Pepto Bismol to help ease the pain. The patient says...
A random sample of 50 measurements resulted in a sample mean of 62 with a sample...
A random sample of 50 measurements resulted in a sample mean of 62 with a sample standard deviation 8. It is claimed that the true population mean is at least 64. a) Is there sufficient evidence to refute the claim at the 2% level of signifigance? b) What is the p-vaule? c) What is the smallest value of alpha for which the claim will be rejected?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT