Respuesta :
Answer:
For the critical value we know that the significance is 5% and the value for [tex] \alpha/2 = 0.025[/tex] so we need a critical value in the normal standard distribution that accumulates 0.025 of the area on each tail and for this case we got:
[tex] Z_{\alpha/2}= \pm 1.96[/tex]
Since we have a two tailed test, the rejection zone would be: [tex] z<-1.96[/tex] or [tex] z>1.96[/tex]
Step-by-step explanation:
Data given and notation
n represent the random sample taken
[tex]\hat p[/tex] estimated proportion of interest
[tex]p_o=0.15[/tex] is the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level
Confidence=95% or 0.95
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the proportion of graduates with degrees in engineering who earn more than $75,000 in their first year of work is not 15%.:
Null hypothesis:[tex]p=0.15[/tex]
Alternative hypothesis:[tex]p \neq 0.15[/tex]
When we conduct a proportion test we need to use the z statistic, and the is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].
For the critical value we know that the significance is 5% and the value for [tex] \alpha/2 = 0.025[/tex] so we need a critical value in the normal standard distribution that accumulates 0.025 of the area on each tail and for this case we got:
[tex] Z_{\alpha/2}= \pm 1.96[/tex]
Since we have a two tailed test, the rejection zone would be: [tex] Z<-1.96[/tex] or [tex] z>1.96[/tex]
