Respuesta :
Answer:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
[tex]z=\frac{0.36 -0.41}{\sqrt{\frac{0.41(1-0.41)}{100}}}=-1.017[/tex]
Step-by-step explanation:
Data given and notation
n=100 represent the random sample taken
[tex]\hat p=0.36[/tex] estimated proportion with the survey
[tex]p_o=0.41[/tex] is the value that we want to test
[tex]\alpha[/tex] represent the significance level
z would represent the statistic (variable of interest)
[tex]p_v[/tex] 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:[tex]p\geq 0.41[/tex]
Alternative hypothesis:[tex]p < 0.41[/tex]
When we conduct a proportion test we need to use the z statistic, and the is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].
Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
[tex]z=\frac{0.36 -0.41}{\sqrt{\frac{0.41(1-0.41)}{100}}}=-1.017[/tex]
Answer:
z test statistic is -1.042 .
Step-by-step explanation:
We are given that based on the Nielsen ratings, the local CBS affiliate claims its 11 p.m. newscast reaches 41% of the viewing audience in the area. In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station.
Let Null Hypothesis, [tex]H_0[/tex] : p = 0.41 {means that % of the viewing audience in the area is 41%}
Alternate Hypothesis, [tex]H_1[/tex] : p [tex]\neq[/tex] 0.41 {means that % of the viewing audience in the area is different from 41%}
The z-test statistics we will use here is One sample proportion test ;
T.S. = [tex]\frac{\hat p - p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, p = % of the viewing audience based on the Nielsen ratings = 41%
[tex]\hat p[/tex] = % of the viewing audience based on a survey of 100 viewers = 36%
n = sample of viewers = 100
So, test statistics = [tex]\frac{0.36 - 0.41}{\sqrt{\frac{0.36(1-0.36)}{100} } }[/tex]
= -1.042
Therefore, the z test statistic is -1.042 .
