The national percent of adults who have a laptop computer is 62%. in san francisco, a simple random sample of 100 adults is taken and 69% of these adults have a laptop. is this strong evidence that more adults in sf have laptops than the national average?

a) state the null hypothesis and the alternative in terms of a box model.
b) find z and p values.
c) what do you conclude?

a) Null hypothesis:  

Alternative hypothesis:  

b)  

c) The p value obtained was a high low value and using the significance level assumed for example we have 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 proportion of adults who have a laptop is not significantly higher than 0.62 .  

Step-by-step explanation:

1) Data given and notation

n=100 represent the random sample taken

X represent the adults that have a laptop

estimated proportion of adults that have a laptop

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)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim the proportion is higher than 0.62 the national proportion:  

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 .

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

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 next step would be calculate the p value for this test.  

Since is a right tailed test the p value would be:  

The p value obtained was a high low value and using the significance level assumed for example we have 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 proportion of adults who have a laptop is not significantly higher than 0.62 .  

0 is its x and y coordinate