A rectangular picture frame has the dimensions shown in

Head movement evaluations are important because disabled individuals may be able to operate communications aids using head motio

earnstyle [38]

Answer:

$t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{1.307 -0}{\frac{7.798}{\sqrt{14}}}=0.6271$

df=n-1=14-1=13

$p_v =P(t_{(13)}>0.6271) =0.2707$

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 (This problem) we can use it.

Let put some notation

x=test value CL , y = test value CO

x: 57.8 35.7 54.5 56.8 51.1 70.8 77.3 51.6 54.7 63.6 59.2 59.2 55.8 38.5

y: 44.7 52.1 60.2 52.7 47.2 65.6 71.4 48.8 53.1 66.3 59.8 47.5 64.5 34.4

The system of hypothesis for this case are:

Null hypothesis: $\mu_x- \mu_y \leq 0$

Alternative hypothesis: $\mu_x -\mu_y >0$

The first step is calculate the difference $d_i=x_i-y_i$ and we obtain this:

d: 13.1, -16.4,-5.7,4.1,3.9,5.2,5.9,2.8,1.6,-2.7,-0.6,11.7,-8.7,4.1

The second step is calculate the mean difference

$\bar d= \frac{\sum_{i=1}^n d_i}{n}= \frac{29}{8}=1.307$

The third step would be calculate the standard deviation for the differences, and we got:

$s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1} =7.798$

The 4 step is calculate the statistic given by :

$t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{1.307 -0}{\frac{7.798}{\sqrt{14}}}=0.6271$

The next step is calculate the degrees of freedom given by:

$df=n-1=14-1=13$

Now we can calculate the p value, since we have a right tailed test the p value is given by:

$p_v =P(t_{(13)}>0.6271) =0.2707$

So the p value is higher than the significance level provided of 0.01, so then we can conclude that we FAIL to reject the null hypothesis that the difference mean between after and before is higher or equal than 0. So we can't conclude that the mean neck rotation is greater in the clockwise direction than in the counterclockwise direction at 1% of significance.

8 0

4 years ago

A student found the solution below for the given inequality.

Pavel [41]

Correct option is A) The student is completely correct because the student correctly wrote and solved the compound inequality.

<u>Step-by-step explanation:</u>

Here we have , A student found the solution below for the given inequality.

1x-91<-4

x-9>4 and x-9 <-4

x> 13 and x<5

We need to find Which of the following explains whether the student is correct . Let's find :

We will be solving equation 1x-91<-4 or , $|x-9|$ . We know that for Modulus function , value inside modulus function is both positive & negative depending on particular value of x ! So ,