Answer:
3,952,512
Step-by-step explanation:
A: P(green)= 2/7, P(yellow)=2/7
B: P(green)=3/8, P(yellow)=1/8
C: P(green)=1/4 P(yellow)=1/4
D: P(green)= 5/21 Pyellow)= 11/21 E. P(green)= 3/7 P(yellow)=1/14
Answer:
The answer is "Option D".
Step-by-step explanation:
In this question, the shape of the model is not declared that why we assume that it has four sides in which two sides are given that is:
other probabilities are:
B. There is evidence to conclude that p1C.There is evidence to conclude that p1>p2 because all values in the interval are positive.
D. There is evidence to conclude that p1E. There is evidence to conclude that p2>p1 because 0.247 and 0.325 are both greater than 0.05.
You can use the fact that the 90% confidence interval given is all positive value for the test statistic being the difference of and .
The conclusion that is supported by the given confidence interval is given by:
Option C: There is evidence to conclude that because all values in the interval are positive.
Since it is given that the difference is measured by ,
and since the given confidence interval at 90% confidence for that difference is obtained to be (0.247,0.325), thus we can say that 90% difference value of , will be lying in that given interval.
Since the interval is all positive, thus we can say that 90% of the times, the difference will be positive which indicates that
Thus, the conclusion that is supported by the interval is given by:
Option C: There is evidence to conclude that because all values in the interval are positive.
Learn more about confidence interval here:
Answer:
C
Step-by-step explanation:
Statistics!!
When we have a confidence interval for the difference in proportions or means, our null hypothesis is always that there's no difference. (H0 = p1-p2 = 0.)
If the difference is positive, that means we have sufficient evidence p1>p2.
If it's negative, then we have sufficient evidence p2>p1.
Why not A: incorrect interpretation of the interval
Why not B: doesn't look like a complete answer
Why not D: also doesn't look like a complete answer
Why not E: this confuses the definition of alpha-level and p-value with confidence interval values. If those were p-values and greater or less than an alpha-level, we would reject or fail to reject the null hypothesis. That isn't the case here.
Answer:
1 and 2) Null hypothesis:
Alternative hypothesis:
When we conduct a proportion test we need to use the z statistic, and the is given by:
(1)
3)
4)
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 5% of significance the proportion of correct answers is not significantly higher than 0.5
Step-by-step explanation:
Data given and notation
n=90 represent the random sample taken
X=58 represent the number of correct answers
estimated proportion of correct answers
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)
Step 1 and 2: Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the true proportion of correct answers is higher than 0.5.:
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 right tailed test the p value would be:
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 5% of significance the proportion of correct answers is not significantly higher than 0.5
Answer:
Step-by-step explanation:
Hello!
The variable of interest is X: the number of correct answers on a true/false test out of 90 questions.
The parameter of interest is p: population proportion of correct answers in a true/false test.
The passing grade is 58/90 correct questions.
The claim is that if the students answer more than half of the answers, then he is not guessing, i.e. if the proportion of correct answers is more than 50%, the student did not guess the answers, symbolically: p>0.5
Then the hypotheses are:
H₀: p ≤ 0.5
H₁: p > 0.5
α: 0.05
since the sample size is large enough, n= 90 questions, you can apply the Central Limit Theorem to approximate the distribution of the sample proportion to normal, p'≈N(p;[p(1-p])/n) and use the standard normal as a statistic:
≈N(0;1)
The sample proportion is the passing grade of the student p': 58/90= 0.64
Then under the null hypothesis the statistic is:
This test is one-tailed (right) and so is the p-value, you can calculate it as:
P(Z≥2.66)= 1 - P(Z<2.66)= 1 - 0.996093= 0.003907
With this p-value, the decision is to reject the null hypothesis.
Then at a 5% level, there is significant evidence to conclude that the proportion of correctly answered questions is greater than 50%, this means that the student didn't guess the answers.
I hope this helps!
Answer:
The 90% for the average weights of men is between 137.24 lb and 185.76 lb.
Step-by-step explanation:
We have the standard deviation for the sample, so we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 14 - 1 = 14
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of . So we have T = 1.7709
The margin of error is:
M = T*s = 1.7709*13.7 = 24.26
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 161.5 - 24.26 = 137.24 lb
The upper end of the interval is the sample mean added to M. So it is 161.5 + 24.26 = 185.76 lb
The 90% for the average weights of men is between 137.24 lb and 185.76 lb.
B 0.46 liters
C 4.6 liters
D 46 liters
Answer:
B. 0.46 liters
Step-by-step explanation:
Using 0.5 of the container is the same thing as using half of the container.
We can calculate how much she used by dividing:
0.92/2 = 0.46