Evaluate the following expression for a = 12 and b = 4 2a/2b
1 answer:
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Answer:
(a) Decision rule for 0.01 significance level is that we will reject our null hypothesis if the test statistics does not lie between t = -2.651 and t = 2.651.
(b) The value of t test statistics is 1.890.
(c) We conclude that there is no difference in the mean number of times men and women order take-out dinners in a month.
(d) P-value of the test statistics is 0.0662.
Step-by-step explanation:
We are given that a recent study focused on the number of times men and women who live alone buy take-out dinner in a month.
Also, following information is given below;
Statistic : Men Women
The sample mean : 24.51 22.69
Sample standard deviation : 4.48 3.86
Sample size : 35 40
<em>Let </em><em> = mean number of times men order take-out dinners in a month.</em>
<em /><em> = mean number of times women order take-out dinners in a month</em>
(a) So, Null Hypothesis, :
= 0 {means that there is no difference in the mean number of times men and women order take-out dinners in a month}
Alternate Hypothesis, :
0 {means that there is difference in the mean number of times men and women order take-out dinners in a month}
The test statistics that would be used here <u>Two-sample t test statistics</u> as we don't know about the population standard deviation;
T.S. = ~
where, = sample mean for men = 24.51
= sample mean for women = 22.69
= sample standard deviation for men = 4.48
= sample standard deviation for women = 3.86
= sample of men = 35
= sample of women = 40
Also, =
= 4.16
So, <u>test statistics</u> = ~
= 1.890
(b) The value of t test statistics is 1.890.
(c) Now, at 0.01 significance level the t table gives critical values of -2.651 and 2.651 at 73 degree of freedom for two-tailed test.
Since our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <u>we fail to reject our null hypothesis</u>.
Therefore, we conclude that there is no difference in the mean number of times men and women order take-out dinners in a month.
(d) Now, the P-value of the test statistics is given by;
P-value = P( > 1.89) = 0.0331
So, P-value for two tailed test is = 2 0.0331 = <u>0.0662</u>
Answer:
6 segments are required to connect each point to every other point.
Step-by-step explanation:
If four points are placed on a circle.Then as we know the segment is a line that join two points.
Now as we are given four points on the circle.
- so we will firstly start with the first point; the first point requires 3 segments to connect to the remaining three points.
- Next second point will just require 2 segments to connect to the two points as it is already connected to the first point.
- similarly third point requires just one segment to connect to the last point as it is already connected to first and second point as done above.
- and hence by the above three steps the fourth point is connected to all the points.
Hence, 6 segments are required to connect each point to every other point.
