9.3.2 Listed below are body temperatures from five different subjects measured at 8 AM and again at 12 AM. Find the values of d
1 answer:
Answer:
= −0.26
= 0.4219
Step-by-step explanation:
Given:
Sample1: 98.1 98.8 97.3 97.5 97.9
Sample2: 98.7 99.4 97.7 97.1 98.0
Sample 1 Sample 2 Difference d
98.1 98.7 -0.6
98.8 99.4 -0.6
97.3 97.7 -0.4
97.5 97.1 0.4
97.9 98.0 -0.1
To find:
Find the values of and
d overbar ( ) is the sample mean of the differences which is calculated by dividing the sum of all the values of difference d with the number of values i.e. n = 5
= ∑d/n
= (−0.6 −0.6 −0.4 +0.4 −0.1) / 5
= −1.3 / 5
= −0.26
s Subscript d is the sample standard deviation of the difference which is calculated as following:
= √∑(
-
)²/ n-1
=
√
= √ (−0.6 − (−0.26 ))² + (−0.6 − (−0.26))² + (−0.4 − (−0.26))² + (0.4 −
(−0.26))² + (−0.1 − (−0.26))² / 5−1
=
=
=
= 0.4219
= 0.4219
Subscript d represent
μ represents the mean of differences in body temperatures measured at 8 AM and at 12 AM of population.
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Answer:
Null hypothesis:
Alternative hypothesis:
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so then we can conclude that the mean pressure for the automobile engines is not significantly less than 7.3 at 1% of significance.
Step-by-step explanation:
1) 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)
2) State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean pressure is lower than the specificated value 7.3, the system of hypothesis are :
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".
3) Calculate the statistic
We can replace in formula (1) the info given like this:
4) P-value
Since is a one-side lower test the p value would given by:
5) 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 FAIL to reject the null hypothesis, so we can conclude that the mean pressure for the automobile engines is not significantly less than 7.3 at 1% of significance.
