Which one of the following statements is true?
2 answers:
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Answer:
0.04,0.25.0.52
Step-by-step explanation:
Given that you throw a dart at a circular target of radius 10 inches.
Assuming that you hit the target and that the coordinates of the outcomes are chosen at random,
probability that the dart falls
(a) within 2 inches of the center
Here favourable region has area of a circle with radius 2 inches and sample space has area of 10 inches
Prob =
(b) within 2 inches of the rim.
For within two inches from the rim we have to select area of the ring i.e. area of big circle with 10 inches - area of smaller circle with 10-2 inches
Prob=
c) within I quadrant
area of I quadrant / area of circle=0.25
d) within I quadrant and within 2 inches of the rim
= I quadrant area + 2 inches ring area - common area
=
Answer:
If we compare the p value obtained and the significance level assumed we see that
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 is not significantly higher than 0.2 or 20%.
Step-by-step explanation:
How would you make the decision if you were Callaway management? Would you use hypothesis testing?
The best way to test the claim if with a proportion test. The procedure is explained below.
1) Data given and notation
n=624 represent the random sample taken
X=140 represent the golf ball purchasers will buy a Callaway golf ball
estimated proportion of golf ball purchasers will buy a Callaway golf ball
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 true proportion is more than 0,2 or 20%:
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 is not provided but let's assume . The next step would be calculate the p value for this test.
Since is a right tailed test the p value would be:
If we compare the p value obtained and the significance level assumed we see that
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 is not significantly higher than 0.2 or 20%.