MATH SOLVE

8 months ago

Q:
# Use the given information to find the p-value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis). With Upper H 1: pgreater than0.554, the test statistic is zequals1.34.

Accepted Solution

A:

Answer:[tex]p_v =P(z>1.34)=1-P(z<1.34)=0.0901[/tex] Step-by-step explanation:1) Data given and notation n n represent the random sample taken
Xrepresent the people with a characterisitc in the sample
[tex]\hat p[/tex] estimated proportion of people with the characteristic desired
[tex]p_o=0.554[/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 [tex]p_v[/tex] represent the p value (variable of interest) 2) Concepts and formulas to use We need to conduct a hypothesis in order to test the claim that the population proportionis higher than 0.554.: Null hypothesis:[tex]p\leq 0.554[/tex] Alternative hypothesis:[tex]p > 0.554[/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].
3) Calculate the statistic The value of the statisitc is already calculate and given: [tex]z=1.34[/tex] 4) Statistical decision It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis. The significance level provided [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test. Since is a one right tailed test the p value would be: [tex]p_v =P(z>1.34)=1-P(z<1.34)=0.0901[/tex] So the p value obtained was a very low value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we don't have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of interest is not significantly higher than 0.554 .