Use the law of cosines:
We have:
substitute:
A company makes toy plastic soccer balls each with a radius of 3 inches. How many square inches of plastic does the company need
1 answer:
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Answer:
a) Number = 60 *0.35=21
b) Since is a left tailed test the p value would be:
c) If we compare the p value obtained 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 5% the proportion of business owners providing holiday gifts had decreased from the 2008 level.
We can use as smallest significance level 0.044 and we got the same conclusion.
Step-by-step explanation:
Data given and notation
n=60 represent the random sample taken
X represent the business owners plan to provide a holiday gift to their employees
estimated proportion of business owners plan to provide a holiday gift to their employees
is the value that we want to test
represent the significance level
Confidence=95% or 0.95
z would represent the statistic (variable of interest)
represent the p value (variable of interest)
Part a
On this case w ejust need to multiply the value of th sample size by the proportion given like this:
Number = 60 *0.35=21
2) Part b
We need to conduct a hypothesis in order to test the claim that the proportion of business owners providing holiday gifts had decreased from the 2008 level:
Null hypothesis:
Alternative hypothesis:
When we conduct a proportion test we need to use the z statisitc, 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
If we compare the p value obtained 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 5% the proportion of business owners providing holiday gifts had decreased from the 2008 level.
We can use as smallest significance level 0.044 and we got the same conclusion.
Answer: 999 games
Step-by-step explanation:
There are many ways to illustrate the rooted tree model to calculate the number of games that must be played until only one player is left who has not lost.
We could go about this manually. Though this would be somewhat tedious, I have done it and attached it to this answer. Note that when the number of players is odd, an extra game has to be played to ensure that all entrants at that round of the tournament have played at least one game at that round. Note that there is no limit on the number of games a player can play; the only condition is that a player is eliminated once the player loses.
The sum of the figures in the third column is 999.
We could also use the formula for rooted trees to calculate the number of games that would be played.
where i is the number of "internal nodes," which represents the number of games played for an "<em>m</em>-ary" tree, which is the number of players involved in each game and l is known as "the number of leaves," in this case, the number of players.
The number of players is 1000 and each game involves 2 players. Therefore, the number of games played, i, is given by
