Respuesta :
Answer:
a) The sample proportion is 0.06.
b) The test statistic is z = -1.89.
c) 0.0294
d) 0.294 < 0.05, which means that there is enough evidence that p is less than 0.1, which means that we reject the null hypothesis, and accept the shipment.
Step-by-step explanation:
The null hypothesis is:
[tex]H_{0} = 0.1[/tex]
The alternate hypotesis is:
[tex]H_{1} < 0.1[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
a. Calculate the sample proportion p.
200 potatoes, 12 defective.
This means that [tex]p = \frac{12}{200} = 0.06[/tex]
The sample proportion is 0.06.
b. Calculate the test statistic.
For a proportion p, we have that:
[tex]\sigma = \sqrt{p(1-p)}[/tex]
In this question, since [tex]\mu = 0.1[/tex]
[tex]\sigma = \sqrt{0.1}{0.9}[/tex]
SRS of 200 means that [tex]n = 200[/tex]
[tex]H{0} = 0.1[/tex] means that [tex]\mu = 0.1[/tex]. So
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.06 - 0.1}{\frac{\sqrt{0.1*0.9}}{\sqrt{200}}}[/tex]
[tex]z = -1.89[/tex]
The test statistic is z = -1.89.
c. Find the p-value.
Looking at the z-table, [tex]z = -1.89[/tex] has a pvalue of 0.0294, which is the pvalue of this hypothesis test.
d. Given α=0.05 what is your conclusion? Should he reject the shipment?
0.294 < 0.05, which means that there is enough evidence that p is less than 0.1, which means that we reject the null hypothesis, and accept the shipment.
