Answer:
<h2>X =Step-by-step explanation:
We need to find the translation for which, (-3, 1) becomes (1, 5).
-3 will become 1, if it is divided by -3.
Hence, the translation for x axis is X = .
1 will become 5, when it is multiplied by 5.
Hence, The translation for y axis is Y = 5y.
Answer:
The pvalue of the test is 0.0007 < 0.01, which means that we reject the null hypothesis and accept the alternate hypothesis that the percentage of defective items produced by this machine is greater than 5%.
Step-by-step explanation:
A machine, when working properly, produces 5% or less defective items.
This means that the null hypothesis is:
Test if the percentage of defective items produced by this machine is greater than 5%.
This means that the alternate hypothesis is:
The test statistic is:
In which X is the sample mean, is the value tested at the null hypothesis,
is the standard deviation and n is the size of the sample.
0.05 is tested at the null hypothesis:
This means that
A random sample of 300 items taken from the production line contained 27 defective items.
This means that
Value of the test statistic:
Pvalue of the test:
Testing if the mean is greater than a value, which means that the pvalue of the test is 1 subtracted by the pvalue of Z = 3.18, which is the probability of a finding a sample proportion of 0.09 or higher.
Looking at the Z-table, Z = 3.18 has a pvalue of 0.9993
1 - 0.9993 = 0.0007
The pvalue of the test is 0.0007 < 0.01, which means that we reject the null hypothesis and accept the alternate hypothesis that the percentage of defective items produced by this machine is greater than 5%.