You have just entered a very competitive rock-paper-scissors tournament sponsored by the world rock paper scissors society. since the first-place prize is $10,000, you spend some time researching the various strategies to increase your chances of winning. a claim that you see repeatedly in your research is that paper is a good strategy since scissors is chosen less than (1/3) of the time in competitive tournaments. to test this claim you obtain a record of 634 rock-paper-scissors choices in competitive tournaments and observe 190 scissors. let p denote the population proportion of choices in competitive tournaments that are scissors. answer the following questions about the hypothesis test
h0: p = (1/3) vs. ha: p < (1/3).

question 1. what is the value of the test statistic z? (use 1 decimal place in your answer)
question 2. what is the p-value? (use 3 decimal places in your answer)
question 3. what is an appropriate conclusion for this hypothesis test? (1 submission allowed)

a. do not reject h0: p = (1/3); there is insufficient evidence to conclude that the population proportion p of scissors choices in competitive rock-paper-scissors tournaments differs from (1/3).
b. reject h0: p = (1/3); there is sufficient evidence to conclude that p is greater than (1/3).
c. reject h0: p = (1/3); there is sufficient evidence to conclude that p is less than (1/3).

1.  

2.  

2. c. Reject H0: p = (1/3); there is sufficient evidence to conclude that p is less than (1/3).

Step-by-step explanation:

1) Data given and notation

n=634 represent the random sample taken

X=190 represent the choices in competitive tournaments that are Scissors

estimated proportion of choices in competitive tournaments that are Scissors

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 that the proportion is less than 0.33.:  

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 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:  

If we compare the p value and using the significance level assumed we have so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion it's significantly less than 0.333.  

c. Reject H0: p = (1/3); there is sufficient evidence to conclude that p is less than (1/3).

reduce the friction between its moving parts

step-by-step explanation:

in fact, by reducing the friction between the moving parts of the machine, it is possible to reduce the energy wasted due to this friction; therefore, more input energy is converted into useful work, and this will improve the efficiency of the machine.