What is the greatest common factor of 42a5b3, 35a3b4, and 42ab4?
1 answer:
For this case we have that by definition, the Greatest Common Factor (GCF) is the largest factor that 2 numbers have in common.
So, we have the following expressions:
We look for the positive integers that divide to 35 and 42 without leaving residue:
42: 1,2,3,6,7,14,21
35: 1,5,7
Thus, the GCF of 42 and 35 is 7
Then, the GCF of the three expressions is:
Answer:
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Answer:
(a) The significance level of the test is 0.002.
(b) The power of the test is 0.3487.
Step-by-step explanation:
We are given that a coin is thrown independently 10 times to test the hypothesis that the probability of heads is 0.5 versus the alternative that the probability is not 0.5.
The test rejects the null hypothesis if either 0 or 10 heads are observed.
Let p = <u><em>probability of obtaining head.</em></u>
So, Null Hypothesis, : p = 0.5
Alternate Hypothesis, : p
0.5
(a) The significance level of the test which is represented by is the probability of Type I error.
Type I error states the probability of rejecting the null hypothesis given the fact that the null hypothesis is true.
Here, the probability of rejecting the null hypothesis means we obtain the probability of observing either 0 or 10 heads, that is;
P(Type I error) =
P(X = 0/ is true) + P(X = 10/
is true) =
Also, the event of obtaining heads when a coin is thrown 10 times can be considered as a binomial experiment.
So, X ~ Binom(n = 10, p = 0.5)
P(X = 0/ is true) + P(X = 10/
is true) =
=
=
= 0.0019
So, the significance level of the test is 0.002.
(b) It is stated that the probability of heads is 0.1, and we have to find the power of the test.
Here the Type II error is used which states the probability of accepting the null hypothesis given the fact that the null hypothesis is false.
Also, the power of the test is represented by (1 - ).
So, here, X ~ Binom(n = 10, p = 0.1)
= P(X = 0/
is true) + P(X = 10/
is true)
=
=
= 0.3487
Hence, the power of the test is 0.3487.