Question

In: Statistics and Probability

A simple random sample of 25 ball bearings is selected. The mean diameter of the ball...

A simple random sample of 25 ball bearings is selected. The mean diameter of the ball bearings is 3mm with a standard deviation of 0.05mm. Previous investigations suggest that the diameters measures are normally distributed. Construct a 95% confidence interval for the standard deviation of the diameters of the ball bearings in this population. Explain how you found your answer.

Solutions

Expert Solution

We have given here,                          
                          
              
Sample standard deviation=0.05              
Sample size =25                  
                          
Degree of freedom =n-1=   24              
Level of significance given =0.05              
Chi square critical value for lower tail=12.401          
                          
Chi square critical value for upper tail=39.364  

       

orchestra answered 1 year ago
Next > < Previous

Related Solutions

Manufacturing Ball bearings are manufactured with a mean diameter of 6 millimeter (mm).
Manufacturing   Ball bearings are manufactured with a mean diameter of 6 millimeter (mm). Because of variability in the manufacturing process, the diameters of the ball bearings are approximately normally distributed with a standard deviation of 0.03 mm. a) What proportion of ball bearings has a diameter more than 6.04 mm ? b)   Any ball bearings that have a diameter less than 5.95 mm or greater than 6.05 mm are discarded. What proportion of ball bearings will be discarded ? c)  ...
The diameters of ball bearings are distributed normally. The mean diameter is 89 millimeters and the...
The diameters of ball bearings are distributed normally. The mean diameter is 89 millimeters and the standard deviation is 5 millimeters. Find the probability that the diameter of a selected bearing is between 91 and 97 millimeters. Round your answer to four decimal places.
1. A simple random sample of 25 items resulted in a sample mean of 28 and...
1. A simple random sample of 25 items resulted in a sample mean of 28 and a standard deviation of 7.5. Construct a 95% confidence interval for the population mean. Select one: A. 24.904 to 31.096 B. 25.905 to 32.096 C. 26.324 to 29.432 D. None of the above answers is correct 2. A simple random sample of 25 items resulted in a sample mean of 28 and a standard deviation of 7.5. Construct a 99% confidence interval for the...
A manufacturer produces ball bearings, normally distributed, with unknown mean and standard deviation. A sample of...
A manufacturer produces ball bearings, normally distributed, with unknown mean and standard deviation. A sample of 25 has a mean of 2.5cm. The 99% confidence interval has length 4cm (double-sided). Which statement is correct (use t-distribution): s2 = 23.42cm2        b) s2 = 12.82cm2              c)   s= 3.58cm                   d) s= 4.84cm      The 99% prediction interval measures (use t-distribution): a) 20.38 cm                  b) 10.21 cm                      c) 20.42 cm                               d) 10.19 cm From a box containing oatmeal...
The true average diameter of ball bearings of a certain type is supposed to be 0.5...
The true average diameter of ball bearings of a certain type is supposed to be 0.5 in. A one-sample t test will be carried out to see whether this is the case. What conclusion is appropriate in each of the following situations? (a)     n = 10, t = 1.51, α = 0.05 Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in. Reject the null hypothesis. There is not sufficient evidence that the true...
The true average diameter of ball bearings of a certain type is supposed to be 0.5...
The true average diameter of ball bearings of a certain type is supposed to be 0.5 inch. What conclusion is appropriate when testing H0: μ = 0.5 versus Ha: μ ≠ 0.5 inch in each of the following situations? (a)     n = 15, t = 1.8, α = 0.05 1. Reject H0 2.Fail to reject H0     (b)     n = 15, t = −1.8, α = 0.05 1. Reject H0 2. Fail to reject H0     (c)     n = 27, t =...
The mean tar content of a simple random sample of 25 unfiltered king-size cigarettes is 20.8...
The mean tar content of a simple random sample of 25 unfiltered king-size cigarettes is 20.8 mg, with a standard deviation of 4 mg. The mean tar content of a simple random sample of 25 filtered 100 mm cigarettes is 13.4 mg with a standard deviation of 3.9 mg. Assume that the two samples are independent, simple, random samples, selected from normally distributed populations. Do not assume that the population standard deviations are equal. o Use a 0.05 significance level...
An industrial sewing machine uses ball bearings that are targeted to have a diameter of 0.75...
An industrial sewing machine uses ball bearings that are targeted to have a diameter of 0.75 inch. The lower and upper specification limits under which the ball bearing can operate are 0.735 inch​ (lower) and 0.765 inch​ (upper). Past experience has indicated that the actual diameter of the ball bearings is approximately normally​ distributed, with a mean of 0.755 inch and a standard deviation of 0.006 inch. Suppose a random sample of 2121 ball bearings are selected. Complete parts​ (a)...
An industrial sewing machine uses ball bearings that are targeted to have a diameter of 0.74...
An industrial sewing machine uses ball bearings that are targeted to have a diameter of 0.74 inch. The lower and upper specification limits under which the ball bearings can operate are 0.72 inch and 0.76 ​inch, respectively. Past experience has indicated that the actual diameter of the ball bearings is approximately normally​ distributed, with a mean of 0.743 inch and a standard deviation of 0.005 inch. A. What is the probability that a ball bearing is between the target and...
An industrial sewing machine uses ball bearings that are targeted to have a diameter of 0.73...
An industrial sewing machine uses ball bearings that are targeted to have a diameter of 0.73 inch. The lower and upper specification limits under which the ball bearing can operate are 0.715 inch​ (lower) and 0.745 inch​ (upper). Past experience has indicated that the actual diameter of the ball bearings is approximately normally​ distributed, with a mean of 0.734 inch and a standard deviation of 0.006 inch. Suppose a random sample of 22 ball bearings are selected. Complete parts​ (a)...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT