If the distance from the Sharks to the dolphins is 12ft, what is the distance from
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Answers:
(a) Possible values of X are: 0, 1, 2, 3, 4, 5
(b) See attached image below; specifically figure 2
(c) No, it is <u>not</u> symmetric
(d) As a fraction, the answer is 1/6. In decimal form, the answer is approximately 0.1667 (converts to roughly 16.67%)
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Explanations:
(a) The largest possible roll we can get on one die is 6, the smallest is 1, so the largest possible difference is 6-1 = 5. The smallest difference is 0 as we could get doubles (eg: both dice show a "3" at the same time). We can get any difference in between 0 and 5. So X can take on whole numbers from 0 to 5, ie, X can be any number from the set {0, 1, 2, 3, 4, 5}
(b) Consult the attached image. Figure 1 shows a 6 by 6 grid of values that represent all the possible ways to roll two dice. Each value in the interior of the grid is the result of subtracting the outer header values. Figure 2 is where the answer is shown for part b. The idea is that you list out the X values along the top of the table and the probability P(X) values along the bottom row. I show the work on how to compute each probability in the attachment. The probability is equal to the number of occurences over the number total. Example: X = 3 shows up 6 times out of 36, so P(X) is 6/36 = 1/6 when X = 3.
(c) The distribution is not symmetric as figure 3 shows a lop-sided diagram. The mode should be at the center, but this figure shows the mode off to the left side.
(d) Count how many copies of '4' or '5' show up in the interior of the grid shown in figure 1. There are four copies of '4' and two copies of '5'. Overall there are 4+2 = 6 instances of either '4' or '5'. This is out of 36 total, so 6/36 = 1/6 is the fractional form of the answer which approximates to 0.1667 and converts to 16.67% approximately.
Step-by-step explanation:
hope you can understand
Answer:
Part A:
The null and alternative hypothesis are:
Part B:
- A Type I error is when the null hypothesis is rejected although it is true. In this case, it would mean that we conclude that the hiring process is discriminatory, when in reality it is a random result and the process is not discriminatory.
- A Type II error is when the null hypothesis fails to be rejected although it is false. In this case, the hiring process is discriminatory, but statistically the result is not significant enough to prove that.
Part C:
A reduction in the significance level causes a reduction in the power of the test.
Part D:
The power of the test is increased with a larger sample.
Step-by-step explanation:
We have a restaurant with hire a proprotion of 15 % of people in the age ragne of 30-50 years. The expected proportion, according to the applicants, is 50%.
The test will tell us if the actual 15% is a result of a discriminatory practice or a random result.
Part A:
The null and alternative hypothesis are:
Part B:
- A Type I error is when the null hypothesis is rejected although it is true. In this case, it would mean that we conclude that the hiring process is discriminatory, when in reality it is a random result and the process is not discriminatory.
- A Type II error is when the null hypothesis fails to be rejected although it is false. In this case, the hiring process is discriminatory, but statistically the result is not significant enough to prove that.
Part C:
The power of an hypothesis test is the probability that the test rejects the null hypothesis (H_0) when a specific alternative hypothesis (H_1) is true.
If the significance level is reduced (from 5% to 1%), the rejection region is reduced, so the probability of rejecting the null hypothesis is also reduced.
Then, a reduction in the significance level causes a reduction in the power of the test.
Part D:
A bigger sample size gives robustness to the sample statistic. Then, if the alternative hypothesis is true, the probabilities of detecting the effect are increased with increased sample size.
Then, the power of the test is increased with a larger sample.