Two cyclists, 96 miles apart, start riding toward each other at the same time. one cycles 2 times as fast as the other. if they meet 4 hours later, what is the speed (in mi/h) of the faster cyclist?
a. write an equation using the information as it is given above that can be solved to answer this problem. use the variable
r
r to represent the speed of the slower cyclist.

We use .  The distance covered is miles.  The rate is , as both of the cyclists are covering part of this ground.  The time is hours.  So we have:





This is your equation, the solution to part (a).  

If you need to solve it, you can just divide by twelve, giving .

a) Null hypothesis:  

Alternative hypothesis:  

b)  

c) 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 we can said that at 1% of significance the proportion of American families owning stocks or stock funds is significantly less than 0.53 .  

Step-by-step explanation:

Data given and notation

n=300 represent the random sample taken

estimated proportion of American families owning stocks or stock funds

is the value that we want to test

represent the significance level

Confidence=99% or 0.99

z would represent the statistic (variable of interest)

represent the p value (variable of interest)  

Concepts and formulas to use  

Part a

We need to conduct a hypothesis in order to test the claim that proportion is less than 0.53 or 53%.:  

Null hypothesis:  

Alternative hypothesis:  

Part b

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 left tailed test the p value would be:  

Part c  

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 we can said that at 1% of significance the proportion of American families owning stocks or stock funds is significantly less than 0.53 .