Answer:
So the p value obtained was a very low value and using the significance level given we have
so we can conclude that we have enough evidence to reject the null hypothesis
And the best conclusion would be:
There is enough evidence to show that more than 35% of community college students own a smart phone (Pvalue = 0.034).
And for the second case the correct system of hypothesis is:
H0: p = 0.078; Ha: p > 0.078
Step-by-step explanation:
Data given and notation
n=300 represent the random sample taken
estimated proportion of college students that have a smart phone
is the value that we want to test
represent the significance level
Confidence=90% or 0.90
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 proportion is >0.35.:
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:
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 provided . The next step would be calculate the p value for this test.
Since is a right tailed test the p value would be:
So the p value obtained was a very low value and using the significance level given we have
so we can conclude that we have enough evidence to reject the null hypothesis
And the best conclusion would be:
There is enough evidence to show that more than 35% of community college students own a smart phone (Pvalue = 0.034).
And for the second case the correct system of hypothesis is:
H0: p = 0.078; Ha: p > 0.078