Use the given information to find the ​p-value. ​Also, use a 0.05 significance level and state the conclusion about the null hypothesis​ (re

Question

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 than​0.554, the test statistic is zequals1.34.

in progress 0
Aaliyah 1 week 2021-09-15T20:57:14+00:00 1 Answer 0

Answers ( )

    0
    2021-09-15T20:58:14+00:00

    Answer:

    p_v =P(z>1.34)=1-P(z<1.34)=0.0901  

    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

    \hat p estimated proportion of people with the characteristic desired

    p_o=0.554 is the value that we want to test

    \alpha=0.05 represent the significance level

    Confidence=95% or 0.95

    z would represent the statistic  

    p_v 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:p\leq 0.554  

    Alternative hypothesis:p > 0.554  

    When we conduct a proportion test we need to use the z statistic, and the is given by:  

    z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

    The One-Sample Proportion Test is used to assess whether a population proportion \hat p is significantly different from a hypothesized value p_o.

    3) Calculate the statistic  

    The value of the statisitc is already calculate and given:  

    z=1.34  

    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 \alpha=0.05. The next step would be calculate the p value for this test.  

    Since is a one right tailed test the p value would be:  

    p_v =P(z>1.34)=1-P(z<1.34)=0.0901  

    So the p value obtained was a very low value and using the significance level given \alpha=0.05 we have p_v>\alpha 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 .  

Leave an answer

Browse
Browse

27:3+15-4x7+3-1=? ( )