Question

Pressing pills A drug manufacturer forms tablets by compressing a granular material that contains the active ingredient and various fillers. The hardness of a sample from each batch of tablets produced is measured to control the compression process. The target value for the hardness is $\mu =11.5$. The hardness data for a random sample of $20$tablets are

$11.62711.61311.49311.60211.36011.37411.59211.45811.55211.46311.38311.71511.48511.50911.42911.47711.57011.62311.47211.531$

Is there significant evidence at the$5\%$ level that the mean hardness of the tablets differs from the target value? Carry out an appropriate support your answer.

Short answer

We do not have enough evidence to conclude that the hardness of these tablets is something other than $11.5$.

Step-by-step solution

Given information

The hardness data for a random sample of $20$tablets are

$11.62711.61311.49311.60211.36011.37411.59211.45811.55211.46311.38311.71511.48511.50911.42911.47711.57011.62311.47211.531$

Explanation

State: $H_0:\mu =11.5,H_a:\mu \ne 11.5$

Plan: Random: Random sample.

Normal: The histogram indicates that the distribution is roughly symmetric with no outliers.

Independent: There are more than $200$tablets.

Do:$t=0.772,P-value=0.4494.$

Conclude: Since the P-value is greater than $0.05$, we fail to reject $H_0$.

We do not have enough evidence to conclude that the hardness of these tablets is something other than $11.5$.