Walter is helping to make cookies for a basketball tournament. He's made 15 cookies so far. His coach asked him to make at least
1 answer:
Answer:
Here, denotes the additional cookies that need to be made by Walter besides 15 cookies made by him so far
Step-by-step explanation:
Number of cookies made by Walter so far = 15
He is asked by his coach to make at least 20 cookies but no more than 55.
Let denotes the additional cookies that need to be made by Walter besides 15 cookies made by him so far.
The inequality is
Now solve this inequality.
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Answer:
If we compare the p value obtained and the significance level given we have
so we can conclude that we have enough evidence to FAIL reject the null hypothesis, and we can said that at 2% of significance the proportion of arrests that were not prosecuted is not significanlty less than 0.31.
Step-by-step explanation:
1) Data given and notation
n=500 represent the random sample taken
X represent the number of arrests that were not prosecuted.
estimated proportion of arrests that were not prosecuted
is the value that we want to test
represent the significance level
Confidence=98% or 0.98
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 true proportion is less than 0.31.:
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
.
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 obtained and the significance level given we have
so we can conclude that we have enough evidence to FAIL reject the null hypothesis, and we can said that at 2% of significance the proportion of arrests that were not prosecuted is not significanlty less than 0.31.