Answer:
Null hypothesis:
[tex]\mathbf{H_o: \mu = 444}[/tex]
Alternative hypothesis:
[tex]\mathbf{H_1: \mu < 444}[/tex]
Step-by-step explanation:
From the given information:
the population mean = 444
the sample mean = 443
number of samples = 40
standard deviation = 23
The null hypotheses and he alternative hypotheses can be computed as:
Null hypothesis:
[tex]\mathbf{H_o: \mu = 444}[/tex]
Alternative hypothesis:
[tex]\mathbf{H_1: \mu < 444}[/tex]
Thus, this is left-tailed since the alternative hypothesis is less than the population mean
The test statistics can be computed as follows:
[tex]Z = \dfrac{\overline x - \mu }{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]Z = \dfrac{443 - 444 }{\dfrac{23}{\sqrt{40}}}[/tex]
Z = - 0.275
At the level of significance of 0.02;
the critical value of [tex]Z_{\alpha/2} = Z_{0.02/2}=-2.05[/tex]
Decision rule: To reject the null hypothesis if the value of the Z score is lesser than the critical value.
Conclusion:
We fail to reject the null hypothesis and we conclude that sufficient evidence to support the claim that the machine bags were underfilled.
