What is -282 -20,320 written out
2 answers:
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Answer:
No, we don't have sufficient evidence to support the claim that the doors are either too long or too short.
Step-by-step explanation:
We are given that a lumber company is making doors that are 2058.0 millimeters tall. If the doors are too long they must be trimmed, and if the doors are too short they cannot be used.
A sample of 11 is made, and it is found that they have a mean of 2043.0 millimeters with a standard deviation of 25.0.
Let = <u><em>population mean length of doors</em></u>.
So, Null Hypothesis, :
= 2058.0 millimeters {means that the mean length of doors is 2058.0 millimeters}
Alternate Hypothesis, :
2058.0 millimeters {means that the doors are either too long or too short}
The test statistics that will be used here is <u>One-sample t-test statistics</u> because we know about the population standard deviation;
T.S. = ~
where, = sample mean = 2043.0 millimeters
s = sample standard deviation = 25.0 millimeters
n = sample of doors = 11
So, <u>the test statistics</u> =
= -1.989
The value of t-test statistics is -1.989.
Now, at a 5% level of significance, the t table gives a critical value between -2.228 and 2.228 at 10 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 <u><em>we have insufficient evidence to reject our null hypothesis</em></u> as it will not fall in the rejection region.
Therefore, we conclude that the mean length of doors is 2058.0 millimeters.
The decision rule for rejecting the null hypothesis, considering the t-distribution, is of:
- |t| < 1.9801 -> do not reject the null hypothesis.
- |t| > 1.9801 -> reject the null hypothesis.
At the null hypothesis, it is tested if there is not enough evidence to conclude that the mean voltage for these two types of batteries is different, that is, the subtraction of the sample means is of zero, hence:
At the alternative hypothesis, it is tested if there is enough evidence to conclude that the mean voltage for these two types of batteries is different, that is, the subtraction of the sample means different of zero, hence:
We have a two-tailed test, as we are testing if the mean is different of a value.
Considering the significance level of 0.05, with 75 + 46 - 2 = 119 df, the critical value for the test is given as follows:
|t| = 1.9801.
Hence the decision rule is:
- |t| < 1.9801 -> do not reject the null hypothesis.
- |t| > 1.9801 -> reject the null hypothesis.
More can be learned about the t-distribution in the test of an hypothesis at brainly.com/question/13873630
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