Estimate how many times large (6.1) x 10⁷ is than (2.1) x 10⁻⁴ ?
2 answers:
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Answer:
Null hypothesis:
Alternative hypothesis:
The p value is a very low value and using any significance level for example always
so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion of Canadians is not significantly higher than the porportions of readers at Britons.
Step-by-step explanation:
1) Data given and notation
represent the number of Canadians randomly sampled by Gallup that read at least one book in the past year
represent the number of Britons randomly sampled that read at least one book in the past year
sample of Gallup selected
sample of Britons selected
represent the proportion of Canadians randomly sampled by Gallup that read at least one book in the past year
represent the proportion of Britons randomly sampled that read at least one book in the past year
z would represent the statistic (variable of interest)
represent the value for the test (variable of interest)
2) Concepts and formulas to use
We need to conduct a hypothesis in order to check if the proportion for men with red/green color blindness is a higher than the rate for women , the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
We need to apply a z test to compare proportions, and the statistic is given by:
(1)
Where
3) Calculate the statistic
Replacing in formula (1) the values obtained we got this:
4) Statistical decision
For this case we don't have a significance level provided , but we can calculate the p value for this test.
Since is a one side test the p value would be:
So the p value is a very low value and using any significance level for example always
so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion of Canadians is not significantly higher than the porportions of readers at Britons.
Answer:
a) There is a 59.87% probability that none of the LED light bulbs are defective.
b) There is a 31.51% probability that exactly one of the light bulbs is defective.
c) There is a 98.84% probability that two or fewer of the LED light bulbs are defective.
d) There is a 100% probability that three or more of the LED light bulbs are not defective.
Step-by-step explanation:
For each light bulb, there are only two possible outcomes. Either it fails, or it does not. This means that we use the binomial probability distribution to solve this problem.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinatios of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
In this problem we have that:
a) None of the LED light bulbs are defective?
This is P(X = 0).
There is a 59.87% probability that none of the LED light bulbs are defective.
b) Exactly one of the LED light bulbs is defective?
This is P(X = 1).
There is a 31.51% probability that exactly one of the light bulbs is defective.
c) Two or fewer of the LED light bulbs are defective?
This is
There is a 98.84% probability that two or fewer of the LED light bulbs are defective.
d) Three or more of the LED light bulbs are not defective?
Now we use p = 0.95.
Either two or fewer are not defective, or three or more are not defective. The sum of these probabilities is decimal 1.
So
In which
There is a 100% probability that three or more of the LED light bulbs are not defective.