Answer:
symmetric matrix is the square matrix and it is equal to its transpose
Step-by-step explanation:
solution
a symmetric matrix is the square matrix and it is equal to its transpose
As A is symmetric matrix then
A =
here only square matrices will be symmetric
and matrix A is symmetric its mean its matrices have equal dimension
and every square diagonal matrix is also symmetric when all off diagonals element is zero
symmetric matrix for all indices i and j
A = aij = aji
Answer:
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is significantly lower than 10 minutes.
Step-by-step explanation:
Data given and notation
represent the sample mean
represent the population standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
z would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is less than 10 minutes, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:
(1)
z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
P-value
Since is a left tailed test the p value would be:
Conclusion
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is significantly lower than 10 minutes.
Answer:
We want to find the percentage of values between 147700 and 152300
And one way to solve this is use a formula called z score in order to find the number of deviations from the mean for the limits given:
And replacing we got:
So then we are within 1 deviation from the mean so then we can conclude that the percentage of values between $147,700 and $152,300 is 68%
Step-by-step explanation:
We define the random variable representing the prices of a certain model as X and the distirbution for this random variable is given by:
The empirical rule states that within one deviation from the mean we have 68% of the data, within 2 deviations from the mean we have 95% and within 3 deviations 99.7 % of the data.
We want to find the percentage of values between 147700 and 152300
And one way to solve this is use a formula called z score in order to find the number of deviations from the mean for the limits given:
And replacing we got:
So then we are within 1 deviation from the mean so then we can conclude that the percentage of values between $147,700 and $152,300 is 68%