Respuesta :
Answer:
The pvalue of the test is 0.3844 > 0.1, which means that there is not sufficient evidence at the 0.10 level to support the executive's claim
Step-by-step explanation:
A publisher reports that 35% of their readers own a laptop.
This means that the null hypothesis is:
[tex]H_0: p = 0.35[/tex]
A marketing executive wants to test the claim that the percentage is actually different from the reported percentage.
This means that the alternate hypothesis is:
[tex]H_{a}: p \neq 0.35[/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.
0.35 is tested at the null hypothesis:
This means that [tex]\mu = 0.35, \sigma = \sqrt{0.35*0.65}[/tex]
A random sample of 190 found that 32% of the readers owned a laptop.
This means that [tex]X = 0.32, n = 190[/tex]
Z-statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.32 - 0.35}{\frac{\sqrt{0.35*0.65}}{\sqrt{190}}}[/tex]
[tex]z = -0.87[/tex]
pvalue of the test and decision:
As we are testing that the mean is different from a value and z is negative, the pvalue of the test is 2 multiplied by the pvalue of z = -0.87
Looking at the z-table, z = -0.87 has a pvalue of 0.1922
2*0.1922 = 0.3844
0.3844 > 0.1, which means that there is not sufficient evidence at the 0.10 level to support the executive's claim
