Answer:
(1)
Step-by-step explanation:
Data given and notation
n=100 represent the random sample taken
estimated proportion with the survey
is the value that we want to test
represent the significance level
z would represent the statistic (variable of interest)
represent the p value (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the true proportion is lower than 0.41.:
Null hypothesis:
Alternative hypothesis:
When we conduct a proportion test we need to use the z statistic, and the is given by:
(1)
The One-Sample Proportion Test is used to assess whether a population proportion
is significantly different from a hypothesized value
.
Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
Answer:
4
Step-by-step explanation:
It's ok! This is simple. Simply plug in your given values. Since g(x) = -1, plug that into the equation.
g(x) = -x + 3
g(-1) = -(-1) + 3
=1+3
=4
The answer to the question
Answer: It is believed that exactly 20% of Evergreen Valley college students attended the opening night midnight showing of the latest harry potter movie.
Step-by-step explanation:
Since we have given that
n = 84
x = 11
So, ![\hat{p}=\dfrac{x}{n}=\dfrac{11}{84}=0.13](https://tex.z-dn.net/?f=%5Chat%7Bp%7D%3D%5Cdfrac%7Bx%7D%7Bn%7D%3D%5Cdfrac%7B11%7D%7B84%7D%3D0.13)
p = 0.20
So, hypothesis:
![H_0:p=\hat{p}\\\\H_a:\hat{p}](https://tex.z-dn.net/?f=H_0%3Ap%3D%5Chat%7Bp%7D%5C%5C%5C%5CH_a%3A%5Chat%7Bp%7D%3Cp)
so, test statistic value would be
![z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\\\\z=\dfrac{0.13-0.20}{\sqrt{\dfrac{0.2\times 0.8}{84}}}\\\\z=-1.604](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7B%5Chat%7Bp%7D-p%7D%7B%5Csqrt%7B%5Cdfrac%7Bp%281-p%29%7D%7Bn%7D%7D%7D%5C%5C%5C%5Cz%3D%5Cdfrac%7B0.13-0.20%7D%7B%5Csqrt%7B%5Cdfrac%7B0.2%5Ctimes%200.8%7D%7B84%7D%7D%7D%5C%5C%5C%5Cz%3D-1.604)
At 1% level of significance, critical value would be
z= 2.58
Since 2.58>-1.604
So, We will accept the null hypothesis.
Hence, It is believed that exactly 20% of Evergreen Valley college students attended the opening night midnight showing of the latest harry potter movie.