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Answer:
Null hypothesis:[tex]p \leq 0.65[/tex]
Alternative hypothesis:[tex]p > 0.65[/tex]
[tex]z=\frac{0.66 -0.65}{\sqrt{\frac{0.65(1-0.65)}{1500}}}=0.812[/tex]
[tex]p_v =2*P(z>0.812)=0.208[/tex]
So the p value obtained was a very high value and using the significance level assumed [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the true proportion it's not significantly higher from 0.65.
We don't have enough evidence to conclude that the true % it's higher than 65%, since we fail to reject the null hypothesis on this case.
Step-by-step explanation:
1) Data given and notation
n=1500 represent the random sample taken
X represent the adults that said television was one of their main sources of news.
[tex]\hat p=0.66[/tex] estimated proportion of adults that said television was one of their main sources of news.
[tex]p_o=0.65[/tex] is the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level
Confidence=95% or 0.95
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value (variable of interest)
2) Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the proportion is higher than 0.65:
Null hypothesis:[tex]p \leq 0.65[/tex]
Alternative hypothesis:[tex]p > 0.65[/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].
3) Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
[tex]z=\frac{0.66 -0.65}{\sqrt{\frac{0.65(1-0.65)}{1500}}}=0.812[/tex]
4) Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level assumed [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.
Since is a right tailed test the p value would be:
[tex]p_v =P(z>0.812)=0.208[/tex]
So the p value obtained was a very high value and using the significance level assumed [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the true proportion it's not significantly higher from 0.65.
Do we find evidence that more than 65% of all US adults use television as one of their main sources for news?
We don't have enough evidence to conclude that the true % it's higher than 65%, since we fail to reject the null hypothesis on this case.
The hypothesis for adults who use tv as their main source of news are:
- null hypothesis says population is equal to 65%
- alternate hypothesis says it is greater.
What is a hypothesis?
This is a statement that is made during a research study which is put through statistical testing to determine if it is true.
a. The null hypothesis
H0: P = 0.65
The alternate hypothesis
H1: P > 0.65
b. How to solve for the test statistics.
We have to solve using the z test statistics
[tex]z = \frac{p-P}{SE} \\\\z = \frac{0.66-0.65}{0.013}[/tex]
z = 0.01/0.013
= 0.77
c. Next we have to solve for the p value. Note that this is a right tailed test
Enter z(0.77) on a p value calculator
= 0.2206
The p value is 0.2206
d. The conclusion of the test is given that the p value that has been calculated is very high, we fail to reject the null hypothesis.
e. There is no evidence that more than 65 percent of adults use the television as their source of news
Read more on test statistics here: https://brainly.com/question/4621112
