A rivet is to be inserted into a hole. A random sample n=15 of parts is selected, and the hole diameter is measured. The sample standard deviation of the hole diameter measurements is s=0.008 millimeters. Construct a 99% lower confidence bound for σ2 using MATLAB step by step . Please screenshot the MATLAB screen
We know that the is used as a point estimator of
the population variance,
. Therefore, the confidence
interval of
is depend on the sampling
distribution of (n-1)
/
. And the sampling distribution
of (n-1)
/
is a chi square distribution with
(n-1 ) degree of freedom. Thus the confidence interval for
is given as follows
Following is the matlab code to find the 99 % confidence interval:
>> n=15; %sample size
s=0.008; % sample standard deviation
alpha = 0.01;
chi2q_up = chi2inv((1-alpha/2),n-1); % calculating 1-alpha/2 th
quantile for chi sqaure distribution
chi2q_lw = chi2inv(alpha/2,n-1); % calculating alpha/2 th quantile
for chi sqaure distribution
conf_int_lower = ((n-1)*(s^2))/chi2q_up; % lower limit of
Confidence interval
conf_int_upper = ((n-1)*(s^2))/chi2q_lw; % lower limit of
Confidence interval
Confidence_Interval = [conf_int_lower, conf_int_upper]; %
Confidence interval
disp(Confidence_Interval);
1.0e-03 *
0.0286 0.2199
A rivet is to be inserted into a hole. A random sample n=15 of parts is...
A rivet is to be inserted into a hole. A random sample of n = 15 parts is selected, and the hole diameter is measured. The sample standard deviation of the hole diameter measurements is s = 0.004 millimeters. (a) Construct a 99% two-bounds confidence interval for σ . (b) Construct a 99% lower confidence bound for σ
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10. If the standard deviation of hole diameter is different from 0.01 mm, there is an unaccepublyhip probability that the rivet will not fit in. Suppose sample measurements of 15 hole diameters produoed a standard deviation of 0006m, (a) Is there strong evidence to indicate that the standard deviation of hole diameter is different fromexe at a 10% level of significance? State any tecestry assumptions about the underlying annunum of m: data. (5 marks) (b) Find a range for the...
The upper bound is ___
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#25 A simple random sample of size n equals 40 is drawn from a population. The sample mean is found to be x overbar equals 121.3 and the sample standard deviation is found to be s equals 12.2. Construct a 99% confidence interval for the population mean. The lower bound is nothing. (Round to two decimal places as needed.) The upper bound is nothing. (Round to two decimal places as needed.)
1. A machine produces metal rods used in an automobile suspension system. A random sample of 15 rods is selected, and the diameter is measured. The resulting data (in millimeters) are as follows: 11.44 11.39 11.35 11.38 11.45 11.4311.4211.44 11.34 11.39 11.46 11.36 11.44 11.49 11.41 a) Use a Normal Probability Plot to check the assumption of normality for rod diameter. b) Is it believable the mean rod diameter is less than 1 1.50 mm? Construct the appropriate 99% confidence...