MAT 274 GCU Probability Dice Rolls Data Sets & Confidence Intervals Discussion

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funuenz13

Mathematics

MAT 274

Grand Canyon University

MAT

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I need solution just for part B, and question 2, please.

Part A: Roll a single die 50 times and record the results. Now use that data set to compute the mean, median, mode, variance, and standard deviation of the set.

Part B: Then Calculate the 95% confidence interval for the mean.

Question 2- What is the relationship between confidence intervals and levels of significance?

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Topic 4 DQ 2: MAT 274 GCU Part A: Roll a single die 50 times and record the results. Now use that data set to compute the mean, median, mode, variance, and standard deviation of the set. Part B: Then Calculate the 95% confidence interval for the mean. Part A: Roll a single die 50 times and record the results. Now use that data set to compute the mean, median, mode, variance, and standard deviation of the set. The results of rolling: 1, 3, 2, 2, 5, 4, 4, 2, 5, 5, 2, 1, 4, 6, 6, 2, 2, 3, 1, 1, 2, 2, 4, 6, 6, 2, 3, 1, 1, 1, 2, 3, 1, 5, 4, 4, 3, 6, 6, 1, 1, 1, 3, 4, 1, 1, 6, 3, 6, 4. There are 13 1’s, 10 2’s, 7 3’s, 8 4’s, 4 5’s, 8 6’s. The mean is the arithmetic mean, the sum divided by the number of rolls (50). The sum is 13 ∙ 1 + 10 ∙ 2 + 7 ∙ 3 + 8 ∙ 4 + 4 ∙ 5 + 8 ∙ 6 = 13 + 20 + 21 + 32 + 20 + 48 = = 34 + 40 + 80 = 154, so the mean is 154 50 308 = 100 = 𝟑. 𝟎𝟖. The median is the center number in sorted list (average between two most centered numbers for an even quantity of numbers). Here the sorted list is 11111111111112222222222333333344444444555566666666. Remove 12 items from the left and from the right: 12222222222333333344444444. Then remove 8 more items: 2223333333. Now we see that both center numbers are 3’s, so the median is 3. The mode is the number which occurs most often, here it is 1. Topic 4 DQ 2: MAT 274 GCU The variance is the arithmetic mean of squared differences between all outcomes and their mean, i.e. 1 13 ∙ (1 − 3.08)2 + 10 ∙ (2 − 3.08)2 + 7 ∙ (3 − 3.08)2 + ( )= 50 +8 ∙ (4 − 3.08)2 + 4 ∙ (5 − 3.08)2 + 8 ∙ (6 − 3.08)2 = 1 (13 ∙ 4.3264 + 10 ∙ 1.1664 + 7 ∙ 0.0064 + 8 ∙ 0.8464 + 4 ∙ 3.6864 + 8 ∙ 8.5264) = 50 = 1 ∙ 157.68 = 𝟑. 𝟏𝟓𝟑𝟔. 50 The standard deviation is the square root of the variance, here it is √3.1536 ≈ 𝟏. 𝟕𝟕𝟓𝟖. Part B:
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Topic 4 DQ 2:
MAT 274 GCU
Part A: Roll a single die 50 times and record the results. Now use that data set to compute
the mean, median, mode, variance, and standard deviation of the set.
Part B: Then Calculate the 95% confidence interval for the mean.
Part A: Roll a single die 50 times and record the results. Now use that data set to compute the
mean, median, mode, variance, and standard deviation of the set.

The results of rolling: 1, 3, 2, 2, 5, 4, 4, 2, 5, 5, 2, 1, 4, 6, 6, 2, 2, 3, 1, 1, 2, 2, 4, 6, 6, 2, 3, 1, 1, 1,
2, 3, 1, 5, 4, 4, 3, 6, 6, 1, 1, 1, 3, 4, 1, 1, 6, 3, 6, 4.
There are 13 1’s, 10 2’s, 7 3’s, 8 4’s, 4 5’s, 8 6’s.

The mean is the arithmetic mean, the sum divided by the number of rolls (50). The sum is
13 ∙ 1 + 10 ∙ 2 + 7 ∙ 3 + 8 ∙ 4 + 4 ∙ 5 + 8 ∙ 6 = 13 + 20 + 21 + 32 + 20 + 48 =
= 34 + 40 + 80 = 154,
so th...


Anonymous
Really useful study material!

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