Question

In: Statistics and Probability

For a random sample of 50 measurements of the breaking strength of cotton threads resulting in...

For a random sample of 50 measurements of the breaking strength of cotton threads resulting in a mean of 210 grams and standard deviation of 18 grams.

A. Calculate an 80% confidence interval for the true mean breaking strength of cotton threads.

B. Is your interval statistically valid? Explain.

C. Without recalculating, would a 90% confidence result in a wider or narrower interval? Explain.

D. A co-worker offers the following partial interpretation of your interval: We are confident that 80% of all breaking strength measurements of cotton threads will be within this calculated confidence interval. Explain why this interpretation is not correct.

E. Provide an interpretation of your confidence interval.

F.Use R to find the confidence interval you found by hand in the question. Include a copy of your interval and the R commands.

Solutions

Expert Solution

orchestra answered 1 year ago
Next > < Previous

Related Solutions

In a sample of 75 steel wires, the average breaking strength is 50 kN, with a...
In a sample of 75 steel wires, the average breaking strength is 50 kN, with a standard deviation of 1.9 kN. a) Find a 99% confidence interval for the mean breaking strength of this type of wire. b) An engineer claims that the mean breaking strength is between 49.7 kN and 50.3 kN With what level of confidence can this statement be made? c) How many wires must be sampled so that a 99% confidence interval specifies the mean breaking...
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?
A random sample of n=9 pieces of Manila rope has a mean breaking strength of 82500...
A random sample of n=9 pieces of Manila rope has a mean breaking strength of 82500 pounds and a standart deviation of 3154 pounds. Assuming that it is reasonable to treat these data as a sample from a normal population, what can we assert with 95% confidence about the maximum error if µ =82500 pounds is used as an estimate of the mean breaking strength of such rope? And construct a %98 confidence interval for the mean breaking strenght of...
given a random sample of 50 measurements of acid levels in the water on one day...
given a random sample of 50 measurements of acid levels in the water on one day recorded a sample mean of 210 with a standard deviation of 55. Create a 95% confidence interval for the parameter.
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 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 significance?(b) What is the p-value?(c) What is the smallest value of α for which the claim will be rejected?
A random sample of 49 measurements from one population had a sample mean of 10, with...
A random sample of 49 measurements from one population had a sample mean of 10, with sample standard deviation 3. An independent random sample of 64 measurements from a second population had a sample mean of 12, with sample standard deviation 4. Test the claim that the population means are different. Use level of significance 0.01. (a) What distribution does the sample test statistic follow? Explain. (b) State the hypotheses. (c) Compute x1 2 x2 and the corresponding sample test...
A random sample of 49 measurements from one population had a sample mean of 16, with...
A random sample of 49 measurements from one population had a sample mean of 16, with sample standard deviation 3. An independent random sample of 64 measurements from a second population had a sample mean of 18, with sample standard deviation 4. Test the claim that the population means are different. Use level of significance 0.01. (a) What distribution does the sample test statistic follow? Explain. The standard normal. We assume that both population distributions are approximately normal with known...
Data analysis of the breaking strength of a certain fabric shows that it is normally
Data analysis of the breaking strength of a certain fabric shows that it is normally distributed with a mean of 300 lb and a variance of 9. a. Estimate the percentage of fabric samples that will have a breaking strength no less than 294 lb. b. Estimate the percentage of fabric samples that will have a breaking strength no less than 297 lb and no greater than 303 lb.
The relationship between "strength" and "fineness" of cotton fibers was the subject of a study that...
The relationship between "strength" and "fineness" of cotton fibers was the subject of a study that produced the following data. (Give your answers correct to two decimal places.) x, Strength 75 78 74 69 80 82 80 86 70 88 y, Fineness 3.8 4 4.5 3.7 4.3 3.8 3.8 4.7 4.8 3.7 (a) Find the 98% confidence interval for the mean measurement of fineness for fibers with a strength of 76. Upper Limit - Lower Limit- (b) Find the 99%...
The relationship between "strength" and "fineness" of cotton fibers was the subject of a study that...
The relationship between "strength" and "fineness" of cotton fibers was the subject of a study that produced the following data. (Give your answers correct to two decimal places.) x, Strength 75 87 70 78 74 75 86 71 71 70 y, Fineness 4.4 3.9 4 4.5 3.8 4 4.1 3.7 4.9 4.9 (a) Draw a scatter diagram. (Do this on paper. Your instructor may ask you to turn in this work.) (b) Find the 90% confidence interval for the mean...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT