2) What is the five-digit number, no zeroes, in which the second digit is three times the first, the third is one more than the
1 answer:
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Answer:
If we compare the the p value with the significance level provided , we see that
, so then we can reject the null hypothesis. and there is a significant increase in the miles per gallon from 2017 to 2019 at 10% of significance.
Step-by-step explanation:
Previous concepts
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 (This problem) we can use it.
Let put some notation :
x=test value 2017 , y = test value 2019
x: 28.7 32.1 29.6 30.5 31.9 30.9 32.3 33.1 29.6 30.8 31.1 31.6
y: 31.1 32.4 31.3 33.5 31.7 32.0 31.8 29.9 31.0 32.8 32.7 33.8
Solution to the problem
The system of hypothesis for this case are:
Null hypothesis:
Alternative hypothesis:
Because if we have an improvement we expect that the values for 2019 would be higher compared with the values for 2017
The first step is calculate the difference and we obtain this:
d: 2.4, 0.3, 1.7,3,-0.2, 1.1, -0.5, -3.2, 1.4, 2, 1.6, 2.2
The second step is calculate the mean difference
The third step would be calculate the standard deviation for the differences, and we got:
We assume that the true difference follows a normal distribution. The 4th 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:
If we compare the the p value with the significance level provided , we see that
, so then we can reject the null hypothesis. and there is a significant increase in the miles per gallon from 2017 to 2019 at 10% of significance.
Answer:
(A)
Step-by-step explanation:
Scott cycled for 10 minutes in first week, 15 minutes in second week,20 minutes in third week and 25 minutes in the fourth week which maintains a consistency in the line as there is consistent slope when drawn on a graph.
On, the other hand, harry cycled for 10 minutes in first week, 20 minutes in second, 40 minutes in third and 80 minutes in fourth week in which there is no consistency in the timings according to the weeks. Therefore, only, scott's method is linear as the number of minutes increased by an equal factor every week.
