Tea Bags

$5\mathrm{.}32$

$5\mathrm{.}34$

$5\mathrm{.}39$

$5\mathrm{.}38$

$5\mathrm{.}40$

$5\mathrm{.}41$

$5\mathrm{.}44$

$5\mathrm{.}47$

$5\mathrm{.}46$

$5\mathrm{.}46$

$5\mathrm{.}49$

$5\mathrm{.}48$

$5\mathrm{.}48$

$5\mathrm{.}48$

$5\mathrm{.}50$

$5\mathrm{.}50$

$5\mathrm{.}52$

$5\mathrm{.}50$

$5\mathrm{.}53$

$5\mathrm{.}53$

$5\mathrm{.}52$

$5\mathrm{.}57$

$5\mathrm{.}57$

$5\mathrm{.}53$

$5\mathrm{.}57$

$5\mathrm{.}59$

$5\mathrm{.}56$

$5\mathrm{.}56$

$5\mathrm{.}56$

$5\mathrm{.}58$

$5\mathrm{.}59$

$5\mathrm{.}58$

$5\mathrm{.}60$

$5\mathrm{.}59$

$5\mathrm{.}60$

$5\mathrm{.}60$

$5\mathrm{.}61$

$5\mathrm{.}64$

$5\mathrm{.}62$

$5\mathrm{.}63$

$5\mathrm{.}64$

$5\mathrm{.}64$

$5\mathrm{.}68$

$5\mathrm{.}66$

$5\mathrm{.}68$

$5\mathrm{.}70$

$5\mathrm{.}70$

$5\mathrm{.}71$

$5\mathrm{.}71$

$5\mathrm{.}80$bag exceeds the label weight. The accompanying data are the weights, in grams, of a sample of $50$ tea bags produced in one hour by a single machine. Complete parts $($a$)$ through $($c$)$ below.

$$ Click the icon to view the tea bag weight data.

a$.$ Construct a $99\%$ confidence interval estimate for the population mean weight of the tea bags.

$$

$($Round to two decimal places as needed.$)$

b$.$ Is the company meeting the requirement set forth on the label that the mean amount of tea in a bag is $5\mathrm{.}55$ grams?

The company

meeting the requirement set forth on the label that the mean amount of tea in a bag is $5\mathrm{.}55$ grams, since $5\mathrm{.}55$

contained within the interval.

c$.$ Do you think the assumption needed to construct the confidence interval estimate in $($a$)$ is valid?

The assumption needed to construct the confidence interval estimate in $($a$)$ is that

the weights are uniformly distributed.

the sample standard deviation is equal to the population standard deviation.

at least five tea bags are below the target.

the weights are normally distributed.