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1 answer:
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Answer:
a)
Using the symmetrical property we can write this like this:
We can solve for the probability like this:
And we can find the value using the following excel code: "=T.INV(0.05,7)"
So on this case the answer would be
b) For this case we can use the complement rule and we got:
We can solve for the probability and we got:
And we can use the following excel code to find the value"=T.INV(0.95;7)"
And the answer would be
Step-by-step explanation:
Previous concepts
The t distribution (Student’s t-distribution) is a "probability distribution that is used to estimate population parameters when the sample size is small (n<30) or when the population variance is unknown".
The shape of the t distribution is determined by its degrees of freedom and when the degrees of freedom increase the t distirbution becomes a normal distribution approximately.
The degrees of freedom represent "the number of independent observations in a set of data. For example if we estimate a mean score from a single sample, the number of independent observations would be equal to the sample size minus one."
Solution to the problem
For this case we know that
And we want to find:
Part a
We can rewrite the expression using properties for the absolute value like this:
Using the symmetrical property we can write this like this:
We can solve for the probability like this:
And we can find the value using the following excel code: "=T.INV(0.05,7)"
So on this case the answer would be
Part b
For this case we can use the complement rule and we got:
We can solve for the probability and we got:
And we can use the following excel code to find the value"=T.INV(0.95;7)"
And the answer would be
Answer:
The p value is higher than any significance level given for example , so then we can conclude that we FAIL to reject the null hypothesis. So we don't have enough evidence to conclude that the mean reading is greater for the auscultatory method at 5% or 10% of significance.
Step-by-step explanation:
A paired t-test is used to compare two population means where you have two samples in which observations in one sample can be paired with observations in the other sample. For example if we have Before-and-after observations we can use it.
Let put some notation
x=Auscultatory method , y = Oscillatory method
x: 74 86 84 79 70 78 79 70
y: 70 85 90 110 71 80 69 74
The system of hypothesis for this case are:
Null hypothesis:
Alternative hypothesis:
The first step is define the difference , that is given so we have:
d: 6.6, 4.2, -5.5, -3.1, 9.3, -3.9
The second step is calculate the mean difference
The third step would be calculate the standard deviation for the differences, and we got:
The fourth step is calculate the statistic given by :
The next step is calculate the degrees of freedom given by:
Now we can calculate the p value, since we have a right tailed test the p value is given by:
The p value is higher than any significance level given for example , so then we can conclude that we FAIL to reject the null hypothesis. So we don't have enough evidence to conclude that the mean reading is greater for the auscultatory method at 5% or 10% of significance.