Respuesta :
Answer:
The significance level is [tex]\alpha=0.02[/tex] and [tex]\alpha/2=0.01[/tex] we want to find the decision rule. Since is a bilateral test the critical values are:
[tex] z_{\alpha/2}= \pm 2.326[/tex]
And for this case the decision rule would be reject the null hypothesis if the calculated value is:
[tex] |t_{calculated}| >2.326[/tex]
And for this case the calculated value is higher than 2.326 so then we have enough evidence to reject the null hypothesis at the significance level given.
Step-by-step explanation:
Information given
n=900 represent the random sample mean
[tex]\hat p=0.58[/tex] estimated proportion of the chips fail in the first 1000 hours of their use
[tex]p_o=0.54[/tex] is the value to verify
[tex]\alpha=0.02[/tex] represent the significance level
z would represent the statistic
System of hypothesis
We want to test if the actual percentage that fail is different from the stated percentage, the system of hypothesis are.:
Null hypothesis:[tex]p=0.54[/tex]
Alternative hypothesis:[tex]p \neq 0.54[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{0.58 -0.54}{\sqrt{\frac{0.54(1-0.54)}{900}}}=2.41[/tex]
The significance level is [tex]\alpha=0.02[/tex] and [tex]\alpha/2=0.01[/tex] we want to find the decision rule. Since is a bilateral test the critical values are:
[tex] z_{\alpha/2}= \pm 2.326[/tex]
And for this case the decision rule would be reject the null hypothesis if the calculated value is:
[tex] |t_{calculated}| >2.326[/tex]
And for this case the calculated value is higher than 2.326 so then we have enough evidence to reject the null hypothesis at the significance level given.
