Can anyone please help me with this question? : A target consists of two concentric circles. The larger circle has diameter 1m.
When a complete novice fires at the target, the probability of hitting the blue circle is the same as the probability of hitting the green region. Find the diameter of the blue circle.
1 answer:
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Answer:
1) n=48
2) n=298
3) n=426
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
represent the real population proportion of interest
represent the estimated proportion for the sample
n is the sample size required (variable of interest)
represent the critical value for the margin of error
The population proportion have the following distribution
Part 1
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by and
. And the critical value would be given by:
The margin of error for the proportion interval is given by this formula:
(a)
And on this case we have that and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
We can assume that the estimated proportion is 0.23 for the 25 to 30 group. And replacing into equation (b) the values from part a we got:
And rounded up we have that n=48
Part 2
The margin of error on this case changes to 0.04 so if we use the same formula but changing the value for ME we got:
And rounded up we have that n=298
Part 3
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by and
. And the critical value would be given by:
The margin of error for the proportion interval is given by this formula:
(a)
And on this case we have that and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
We can assume that the estimated proportion is 0.23 for the 25 to 30 group. And replacing into equation (b) the values from part a we got:
And rounded up we have that n=426
Answer:
Step-by-step explanation:
<u><em>Step(i):-</em></u>
<em>Given first random sample size n₁ = 500</em>
Given Roper survey reported that 65 out of 500 women ages 18-29 said that they had the most say when purchasing a computer.
<em>First sample proportion </em>
<em> </em>
<em>Given second sample size n₂ = 700</em>
<em>Given a sample of 700 men (unrelated to the women) ages 18-29 found that 133 men said that they had the most say when purchasing a computer.</em>
<em>second sample proportion </em>
<em> </em>
<em>Level of significance = α = 0.05</em>
<em>critical value = 1.96</em>
<u><em>Step(ii)</em></u><em>:-</em>
<em>Null hypothesis : H₀: There is no significance difference between these proportions</em>
<em>Alternative Hypothesis :H₁: There is significance difference between these proportions</em>
<em>Test statistic </em>
<em></em><em></em>
<em>where </em>
<em> </em><em></em>
<em> Q = 1 - P = 1 - 0.165 = 0.835</em>
<em></em><em></em>
<em>Z = -2.76</em>
<em>|Z| = |-2.76| = 2.76 > 1.96 at 0.05 level of significance</em>
<em>Null hypothesis is rejected at 0.05 level of significance</em>
<em>Alternative hypothesis is accepted at 0.05 level of significance</em>
<u><em>Conclusion:</em></u><em>-</em>
<em>There is there is a difference between these proportions at α = 0.05</em>