Question

In: Statistics and Probability

An Izod impact test was performed on 20 specimens of PVC pipe. The sample mean is...

An Izod impact test was performed on 20 specimens of PVC pipe. The sample mean is x Overscript bar EndScripts equals 1.44 and the sample standard deviation is s = 0.27. Find a 99% lower confidence bound on the true Izod impact strength. Assume the data are normally distributed. Round your answer to 3 decimal places. less-than-or-equal-to

Solutions

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 1.44

sample standard deviation = s = 0.27

sample size = n = 20

Degrees of freedom = df = n - 1 = 19

At 99% confidence level the t0.005 is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t /2,df = t0.005,19 = 2.861

Margin of error = E = t/2,df * (s /n)

= 2.861 * ( 0.27/ 20)

= 0.173

The 99% confidence interval estimate of the population mean is,

- E + E

1.44 - 0.173 1.44 + 0.173

1.267 1.613

(1.267 , 1.613)

orchestra answered 1 year ago
Next > < Previous

Related Solutions

An Izod Impact Test was performed on 20 specimens of PVC pipe. The sample mean is...
An Izod Impact Test was performed on 20 specimens of PVC pipe. The sample mean is ? = 1.25, and the sample ??? ??????? ? standard deviation is ? = 0.25. You need to test if the true mean Izod Impact Strength is less than 1.5. a.Write down the Null and Alternative Hypotheses to be tested b.What is the appropriate type of statistical test? Explain. c.Construct a 95% ?????????? ???????? and test the Hypotheses. Clearly interpret the test result. d.Test...
An Izod impact test was performed on 20 specimens of PVC pipe. The ASTM standard for...
An Izod impact test was performed on 20 specimens of PVC pipe. The ASTM standard for this material requires that Izod impact strength must be greater than 1.0 ft-lb/in. The sample average and standard deviation obtained were x over Bar = 1.121 and s = 0.328, respectively. (a) Test the hypothesis that σ2 = 0.10 against an alternative specifying that σ2 ≠ 0.10, using α = 0.01 (if reject enter a value of 1, if not, enter a value of...
An Izod impact test was performed on 20 specimens of PVC pipe. The obtained standard deviation...
An Izod impact test was performed on 20 specimens of PVC pipe. The obtained standard deviation was s = 0.328. Assume that the random sample was drawn form a normal population N (µ, σ^2 ), with unknown mean value µ and unknown variance σ^2 . a) Give a 99% confidence interval for the variance σ^2 . b) Give a 99% upper confidence bound for the variance σ^2 . c) Test the hypothesis H0 : σ^2 = 0.1, against the two-sided...
An Izod impact test was performed on 20 specimens of PVC pipe. The ASTM standard for this material requires that Izod impact strength must be greater than 1.0 ft-lb/in.
An Izod impact test was performed on 20 specimens of PVC pipe. The ASTM standard for this material requires that Izod impact strength must be greater than 1.0 ft-lb/in. The sample average and standard deviation obtained were x = 1.121 and s = 0.328, respectively. (a) Test H0: µ = 1.0 versus H1: µ 1.0 using α = 0.01 and draw conclusions. (b) Use the P-value approach to confirm your inference (c) Construct the 99% lower confidence bound on the...
An ANOVA test is performed using 5 groups, each with a sample size of 20. The...
An ANOVA test is performed using 5 groups, each with a sample size of 20. The level of significance is α=0.05. The F-value is calculated as F=2.17. Give the results of the test with a brief explanation.
An ANOVA test is performed using 5 groups, each with a sample size of 20. The...
An ANOVA test is performed using 5 groups, each with a sample size of 20. The level of significance is α=0.05. The F-value is calculated as F=2.17. Give the results of the test with a brief explanation.
To test H0: mean = 20 vs H1: mean < 20 a simple random sample of...
To test H0: mean = 20 vs H1: mean < 20 a simple random sample of size n = 18 is obtained from a population that Is known to be normally distributed (a) If x-hat = 18.3 and s = 4.3, compute the test statistic (b) Draw a t-distribution with the area that represents the P-value shaded (c) Approximate and interpret the P-value (d) If the researcher decides to test this hypothesis at the a = 0.05 level of significance,...
A one-sample z-test for a population mean is to be performed. Let z 0 denote the...
A one-sample z-test for a population mean is to be performed. Let z 0 denote the observed value of the test statistic, z. Assume that a two-tailed test is being performed. True or false: If z0 is negative, the P-value is twice the area under the standard normal curve to the right of z0. 2) A) True B) False
In order to conduct a hypothesis test for the population mean, a random sample of 20...
In order to conduct a hypothesis test for the population mean, a random sample of 20 observations is drawn from a normally distributed population. The resulting mean and the standard deviation are calculated as 12.9 and 2.4, respectively. Use the critical value approach to conduct the following tests at α = 0.05. H0: μ ≤ 12.1 against HA: μ > 12.1 a-1. Calculate the value of the test statistic. (Round your answer to 2 decimal places.)   Test statistic    a-2....
A sample of 13 joint specimens of a particular type gave a sample mean proportional limit...
A sample of 13 joint specimens of a particular type gave a sample mean proportional limit stress of 8.56 MPa and a sample standard deviation of 0.75 MPa. (a) Calculate and interpret a 95% lower confidence bound for the true average proportional limit stress of all such joints. (Round your answer to two decimal places.) (b) Calculate and interpret a 95% lower prediction bound for proportional limit stress of a single joint of this type. (Round your answer to two...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT