Respuesta :
Answer:
[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{0.06-0.10}{\sqrt{\frac{0.10(1-0.10)}{200}}}=-1.89[/tex]
And the p value would be given by:
[tex]p_v =P(z<-1.89)=0.0294[/tex]
Step-by-step explanation:
Information given
n=200 represent the random sample taken
X=12 represent the potatoes with major defects
[tex]\hat p=\frac{12}{200}=0.06[/tex] estimated proportion of potatoes with major defects
[tex]p_o=0.10[/tex] is the value that we want to test
z would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to check if the true proportion is less than 0.10 so then the system of hypothesis are:
Null hypothesis:[tex]p\geq 0.1[/tex]
Alternative hypothesis:[tex]p < 0.10[/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{0.06-0.10}{\sqrt{\frac{0.10(1-0.10)}{200}}}=-1.89[/tex]
And the p value would be given by:
[tex]p_v =P(z<-1.89)=0.0294[/tex]
Considering the hypothesis tested, the p-value is of 0.0294.
The null hypothesis is:
[tex]H_0: p = 0.1[/tex]
The alternative hypothesis is:
[tex]H_a: p < 0.1[/tex]
The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
- [tex]\overline{p}[/tex] is the sample proportion.
- p is the proportion tested at the null hypothesis.
- n is the sample size.
For this problem, the parameters are:
[tex]p = 0.1, n = 200, \overline{p} = \frac{12}{200} = 0.06[/tex]
The value of the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.06 - 0.1}{\sqrt{\frac{0.1(0.9)}{200}}}[/tex]
[tex]z = -1.89[/tex]
The p-value for this test is the probability of finding a sample proportion of 0.06 or below, which is the p-value of z = -1.89.
- Looking at the z-table, z = -1.89 has a p-value of 0.0294.
A similar problem is given at https://brainly.com/question/24166849
