A analog clock (with hour and minute hands) is set to 5:00 P.M. After 30 min, what will the measure of the major arc formed by h
1 answer:
Answer:
180 degrees
Step-by-step explanation:
Given
Required
The measure of the major arc, 30 minutes after
First, we calculate the time after 30 minutes
At 5:30pm, the hour and the minute hand will be directly opposite each other.
In other words, the hands divide the time into two equal parts (180 degrees each)
At this point, there is no major or minor arc as both sides have the same measurement
<em>Hence, the measure of the arcs is 180 degrees</em>
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Answer:
We conclude that the true average percentage of organic matter in such soil is something other than 3% at 10% significance level.
We conclude that the true average percentage of organic matter in such soil is 3% at 5% significance level.
Step-by-step explanation:
We are given a random sample of soil specimens was obtained, and the amount of organic matter (%) in the soil was determined for each specimen;
1.10, 5.09, 0.97, 1.59, 4.60, 0.32, 0.55, 1.45, 0.14, 4.47, 1.20, 3.50, 5.02, 4.67, 5.22, 2.69, 3.98, 3.17, 3.03, 2.21, 0.69, 4.47, 3.31, 1.17, 0.76, 1.17, 1.57, 2.62, 1.66, 2.05.
Let = <u><em>true average percentage of organic matter</em></u>
So, Null Hypothesis, :
= 3% {means that the true average percentage of organic matter in such soil is 3%}
Alternate Hypothesis, :
3% {means that the true average percentage of organic matter in such soil is something other than 3%}
The test statistics that will be used here is <u>One-sample t-test statistics</u> because we don't know about the population standard deviation;
T.S. = ~
where, = sample mean percentage of organic matter = 2.481%
s = sample standard deviation = 1.616%
n = sample of soil specimens = 30
So, <u><em>the test statistics</em></u> = ~
= -1.76
The value of t-test statistics is -1.76.
(a) Now, at 10% level of significance the t table gives a critical value of -1.699 and 1.699 at 29 degrees of freedom for the two-tailed test.
Since the value of our test statistics doesn't lie within the range of critical values of t, so we have <u><em>sufficient evidence to reject our null hypothesis</em></u> as it will fall in the rejection region.
Therefore, we conclude that the true average percentage of organic matter in such soil is something other than 3% at 10% significance level.
(b) Now, at 5% level of significance the t table gives a critical value of -2.045 and 2.045 at 29 degrees of freedom for the two-tailed test.
Since the value of our test statistics lies within the range of critical values of t, so we have <u><em>insufficient evidence to reject our null hypothesis</em></u> as it will not fall in the rejection region.
Therefore, we conclude that the true average percentage of organic matter in such soil is 3% at 5% significance level.
