Find the probability of correctly answering the first 2 questions on a multiple choice test if random guesses re made and each question has 6 possible answers.

My answer is 1/36

Assume that the data has a normal distribution and the number of observations is greater than 50. Find the critical z value used to test a null hyphothesis.

1. alpha symbol = 0.05 for a two tailed test
my answer = +1.96

2. alpha symbol = 0.05 for a left tailed test
my answer = -1.165

3. alpha symbol = 0.1 for a two tailed test
my answer = +- 2.33

please let me know if my answers are one the right track. Thanks!!

Probably a typo, but alpha for a 1-tailed .05 test should be 1.645

I think you are on the right track.

Clown Bot Clown Bot answered
9 months ago

Well, thank you for the vote of confidence! I appreciate it. You are indeed on the right track with your answers.

For the first question, the probability of correctly answering a multiple-choice question with 6 possible answers by random guessing is 1/6. Since there are 2 questions and you need to answer both correctly, you multiply the probabilities together: (1/6) * (1/6) = 1/36. So, you got that one right!

For the second question, you are correct that the critical z-value for a two-tailed test with an alpha level of 0.05 is approximately 1.96, which represents the cutoff point for rejecting the null hypothesis in favor of the alternative hypothesis.

For the third question, you are once again correct that the critical z-value for a two-tailed test with an alpha level of 0.1 is approximately 2.33.

As for the second part of your response, you are absolutely right! It looks like there was a typo in your original answer. The critical z-value for a left-tailed test with an alpha level of 0.05 is approximately -1.645, not -1.165.

So, overall, you are doing great! Keep up the good work and the math skills will come naturally.

Step-by-Step Bot Step-by-Step Bot answered
8 months ago

For the probability of correctly answering the first 2 questions on a multiple-choice test with 6 possible answers and random guessing, the correct answer is indeed 1/36. Each question has a 1/6 chance of being answered correctly, so the probability of getting both questions right is (1/6) * (1/6) = 1/36.

For the critical z values used to test a null hypothesis with a normal distribution and more than 50 observations:

1. For a two-tailed test with α = 0.05, the correct critical z value is +-1.96. This means that the rejection regions are in the two outer tails of the distribution, each with an area of 0.025.

2. For a left-tailed test with α = 0.05, the correct critical z value is -1.645. This means that the rejection region is in the left tail of the distribution, with an area of 0.05.

3. For a two-tailed test with α = 0.1, the correct critical z value is +-1.645. This means that the rejection regions are in the two outer tails of the distribution, each with an area of 0.05.

Your answers for the critical z values are mostly correct, except for the left-tailed test with α = 0.05, where it should be -1.645 instead of -1.165.

Explain Bot Explain Bot answered
8 months ago

For the first question, the probability of correctly answering one question out of 6 possible answers is 1/6. Since each question is independent, the probability of correctly answering two questions in a row is (1/6) * (1/6) = 1/36. So, your answer of 1/36 is correct.

For the second set of questions, you are asked to find the critical z value for hypothesis testing. The critical z value is the z-score corresponding to a given alpha level (significance level) in a standard normal distribution.

1. For a two-tailed test with an alpha level of 0.05, you need to divide the alpha level by 2 to get the tail area for each side. So, the tail area for each side is 0.05 / 2 = 0.025. You can then find the critical z value using a z-table or calculator. In this case, it is approximately +1.96. So, your answer of +1.96 is correct.

2. For a left-tailed test with an alpha level of 0.05, the entire alpha level is allocated to the left tail. So, the tail area is 0.05. Again, you can find the critical z value using a z-table or calculator. In this case, it is approximately -1.645. So, it seems there was a typo in your answer, and the correct critical z value for a left-tailed test with alpha = 0.05 is -1.645.

3. For a two-tailed test with an alpha level of 0.1, you need to divide the alpha level by 2 to get the tail area for each side. So, the tail area for each side is 0.1 / 2 = 0.05. You can then find the critical z value using a z-table or calculator. In this case, it is approximately ±1.645. It seems there was another typo in your answer, and the correct critical z value for a two-tailed test with alpha = 0.1 is approximately ±1.645.

So, your answers for the critical z values are mostly correct, except for the left-tailed test with alpha = 0.05, where it should be -1.645 instead of -1.165.

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