Answer
The answer and procedures of the exercise are attached in the following archives.
Step-by-step explanation:
You will find the procedures, formulas or necessary explanations in the archive attached below. If you have any question ask and I will aclare your doubts kindly.
Answer:
We conclude that the new procedure will not decrease the population mean amount of time required to produce the part.
Step-by-step explanation:
We are given that a large manufacturing plant has analyzed the amount of time required to produce an electrical part and determined that the times follow a normal distribution with mean time μ = 45 hours.
A random sample of 25 parts will be selected and the average amount of time required to produce them will be determined. The sample mean amount of time is = 43.118 hours with the sample standard deviation s = 5.5 hours
<em>Let </em><em> = population mean amount of time required to produce an electrical part using new procedure</em>
SO, <u>Null Hypothesis</u>, :
45 hours {means that the new procedure will remain same or increase the population mean amount of time required to produce the part}
<u>Alternate Hypothesis,</u> :
< 45 hours {means that the new procedure will decrease the population mean amount of time required to produce the part}
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 amount of time = 43.118 hours
s = sample standard deviation = 5.5 hours
n = sample of parts = 25
So, <u><em>test statistics</em></u> = ~
= -1.711
<em>Now at 0.025 significance level, the t table gives critical value of -2.064 at 24 degree of freedom for left-tailed test. Since our test statistics is more than the critical value of t so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.</em>
Therefore, we conclude that the new procedure will remain same or increase the population mean amount of time required to produce the part.
Answer: The correct option is
(A) The measures of corresponding angles of ABCD and KLMN are equal, but the lengths of corresponding sides of ABCD are half those of KLMN.
Step-by-step explanation: We are given to select the correct condition that might be true if polygons ABCD and KLMN are similar.
Two polygons are said to be SIMILAR if corresponding angles are congruent and corresponding sides are proportional.
So, options (B), (C), (D) and (E) are not correct because they contradict conditions of similarity.
In option (A), we have
The measures of corresponding angles of ABCD and KLMN are equal. So, they must be congruent.
And the lengths of corresponding sides of ABCD are half those of KLMN.
So, we can write
Therefore, the corresponding sides are proportional.
Thus, option (A) is true if two polygons are similar.