Question

A standardized procedure is expected to produce washers with very small deviation in their thicknesses. The thickness of these washers is known to be normally distributed. A random sample of 10 such washers are chosen and measured, resulting in a sample mean 0.1259 and sample standard deviation 0.0037.

Consider the case where we have the true population variance. If the variance is 10^-5, calculate a two-sided 90% confidence interval for the population mean of the thickness of a washer produced by this procedure.

What is the lower bound of the two-sided 90% confidence interval?

What is the upper bound of the two-sided 90% confidence interval?

Consider the case where the true population variance is unknown. Calculate a 90% upper bound for the population mean.

Please use the appropriate table to provide the value of z or t critical value that you would use in building this confidence interval.

What is the 90% upper bound for the population mean?

Answer 1

Consider the case where we have the true population variance. If the variance is 10^-5, calculate a two-sided 90% confidence interval for the population mean of the thickness of a washer produced by this procedure.

The provided sample mean is 0.1259 and the population standard deviation is σ=0.00316. The size of the sample is n = 10 and the required confidence level is 90%.

Based on the provided information, the critical z-value for α=0.1 is z_c = 1.645

The 90% confidence for the population mean μ is computed using the following expression

Therefore, based on the information provided, the 90 % confidence for the population mean μ is

CI = (0.124, 0.128)

What is the lower bound of the two-sided 90% confidence interval?

0.124

What is the upper bound of the two-sided 90% confidence interval?

0.128

Consider the case where the true population variance is unknown. Calculate a 90% upper bound for the population mean.

Please use the appropriate table to provide the value of z or t critical value that you would use in building this confidence interval.

What is the 90% upper bound for the population mean?

The provided sample mean is 0.1259 and the sample standard deviation is s=0.0037. The size of the sample is n = 10 and the required confidence level is 90%.

The number of degrees of freedom are df = 10 - 1 = 9, and the significance level is α=0.1.

Based on the provided information, the critical t-value for α=0.1 and df = 9 degrees of freedom is t_c = 1.833

The 90% confidence for the population mean μ is computed using the following expression

Therefore, based on the information provided, the 90 % confidence for the population mean μ is

CI = (0.1259 - 0.002, 0.1259 + 0.002)

CI = (0.124,0.128)