9. Hypothesis Testing for One Sample

Test the claim about the population mean $\mu$ at the given level of significance. Assume the population is normally distributed. Find the $P$-value and determine whether you should reject or fail to reject the null hypothesis.

Claim: $\mu >52$, $\alpha =0.10$

Sample: $\bar{x}=53.1$, $s=4.7,$ $n=20$

A company manufactures precision metal bolts designed to have a diameter of 10.00mm. The quality control department periodically tests samples from the production line. A random sample of 12 bolts is measured, with the results shown below. Assume $\sigma =0.04$.

$\left(A\right)$ Use $\alpha =0.05$ to test if the mean diameter is different from 10.00 mm.

A company manufactures precision metal bolts designed to have a diameter of 10.00mm. The quality control department periodically tests samples from the production line. A random sample of 12 bolts is measured, with the results shown below. Assume $\sigma =0.04$.

$\left(B\right)$ Should management pause production to investigate?

Test the claim about the population mean $\mu$ at the given level of significance. Assume the population is normally distributed. Find the $P$-value and determine whether you should reject or fail to reject the null hypothesis.

Claim: $\mu \ne 1020$, $\alpha =0.01$, $\sigma =85$

Sample: $\bar{x}=990$, $n=40$

BeanZone Coffee is testing a new brand of espresso beans that the supplier claims will increase average customer satisfaction, which is currently 7.8 (out of 10). A sample of 35 stores using the new beans reports an average satisfaction score of 8.1 & standard deviation 0.5.

$\left(B\right)$ Should BeanZone switch espresso bean suppliers at all stores?

BeanZone Coffee is testing a new brand of espresso beans that the supplier claims will increase average customer satisfaction, which is currently 7.8 (out of 10). A sample of 35 stores using the new beans reports an average satisfaction score of 8.1 & standard deviation 0.5.

$\left(A\right)$ Use $\alpha =0.10$ to test if the true mean satisfaction score increased.