Tanya and Cam can each wash a car and vacuum its interior in 2 hours. Pat needs 3 hours to do this same job by himself. If Pat,
2 answers:
You might be interested in
A cylinder with a circumference of about 50 units is formed.
Step-by-step explanation:
Step 1:
The perimeter of the square is 32 units. The perimeter of a square is given by 4 times its side length.
So the side length of the square is 8 units.
If a square is rotated a cylinder will be formed. So the options with a cone are wrong as a cone is formed when a triangle is rotated.
Step 2:
To calculate the circumference of the cylinder, we multiply 2π with the radius. The radius is the same as the side length of the square. So r is 8 units.
The circumference of the cylinder
So the circumference of the cylinder is approximately equal to 50 units so the answer is the fourth option, a cylinder with a circumference of about 50 units.
Answer:
1. M=108
2. μ=110
3. In the explanation.
4. Test statistic t = -1.05
5. P-value = 0.1597
Step-by-step explanation:
The question is incomplete: to solve this problem, we need the sample information: size, mean and standard deviation.
We will assume a sample size of 10 matches, a sample mean of 108 points and a sample standard deviation of 6 points.
1. The mean points is the sample points and has a value of 108 points.
2. The null hypothesis is H0: μ=110, meaning that the mean score is not significantly less from 110 points.
3. This is a hypothesis test for the population mean.
The claim is that the mean score is significantly less than 110.
Then, the null and alternative hypothesis are:
The significance level is 0.05.
The sample has a size n=10.
The sample mean is M=108.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=6.
The estimated standard error of the mean is computed using the formula:
4. Then, we can calculate the t-statistic as:
The degrees of freedom for this sample size are:
5. This test is a left-tailed test, with 9 degrees of freedom and t=-1.05, so the P-value for this test is calculated as (using a t-table):
As the P-value (0.1597) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the mean score is significantly less than 110.
Answer:
For this case the statistic calculated is
So the p value is a very high value and using the significance level given we see that
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and there is enough evidence to conclude that we have a difference between the two means at 10% of significance.
Step-by-step explanation:
Data given and notation
represent the mean for the sample for A
represent the mean for the sample B
represent the sample standard deviation for the sample A
represent the sample standard deviation for the sample B
sample size for the group poisoned
sample size for the group unpoisoned
t would represent the statistic (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to check if the two means are equal or not , the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
For this case is better apply a t test to compare means, and the statistic is given by:
(1)
t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.
Calculate the statistic
For this case the statistic calculated is
Statistical decision
The significance level is 0.1 , but we can calculate the p value for this test. The first step is calculate the degrees of freedom, on this case:
The p value on this case is given
So the p value is a very high value and using the significance level given we see that
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and there is enough evidence to conclude that we have a difference between the two means at 10% of significance.