Thread: Trouble calculating a confidence interval

1. Trouble calculating a confidence interval

Your company plans to buy disks that are supposed to come in containers of exactly 100 disks. A random sample of 49 containers is taken and the mean is found to be 102 disks with a standard deviation of 3 disks.
(a) Using a .05 significance level, should the disk -packing machinery be adjusted?
(b) Construct a two-sided 95% confidence interval about the mean using the above data.

2. hi

hi

$\displaystyle \left[\mu^{*} -\lambda_{0.05} \cdot \sigma^{*} , \mu^{*} +\lambda_{0.05} \cdot \sigma^{*} \right]$ - Asymptotic normality

where $\displaystyle \mu^{*} \mbox{ is the estimated mean, and } \sigma^{*}$ is the estimated standard deviation.

If the number of observations n is not large enough, use

$\displaystyle \left[ \mu^{*} -t_{\frac{\alpha}{2}}(n-1) \frac{s_{n-1}}{\sqrt{n}}, \mu^{*} +t_{\frac{\alpha}{2}}(n-1) \frac{s_{n-1}}{\sqrt{n}} \right]$

The later is the so-called Students t-distribution, with $\displaystyle f=n-1$
degrees of freedom. For this you need the t-distribution table.