# GMU Statistics Excel

You have until 5:45PM on Thursday Dec 3rd
Problem #
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Point value
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2
Total
15
Topic
multinomial distribution
test for independence / randomness
test for independence / randomness
test for independence / randomness
nonparametric test for the center
test for distribution of a population
multinomial distribution
8
59.8
97.0
133.4
88.6
27.6
128.2
138.0
73.2
45.2
32.0
80.6
141.6
170.6
75.2
94.6
68.2
38.0
66.6
67.8
51.4
19.6
71.2
39.2
69.8
126.0
49.4
70.0
52.8
65.4
87.2
74.2
151.4
110.0
156.6
77.8
17.4
20.8
144.2
77.0
61.2
73.2
82.6
35.6
97.4
58.4
47.4
44.0
16.2
82.8
32.8
#6 data
67.8
105.0
141.4
96.6
35.6
136.2
146.0
81.2
53.2
40.0
88.6
149.6
178.6
83.2
102.6
76.2
46.0
74.6
75.8
59.4
27.6
79.2
47.2
77.8
134.0
57.4
78.0
60.8
73.4
95.2
82.2
159.4
118.0
164.6
85.8
25.4
28.8
152.2
85.0
69.2
81.2
90.6
43.6
105.4
66.4
55.4
52.0
24.2
90.8
40.8
In craps, the shooter rolls 2 dice. Depending on the result,
three things can happen:
Dice show
7 or 11
2, 3, or 12
4, 5, 6, 8, 9, 10
Outcome
Immediate win
Immediate loss
Game continues
If the shooter plays the game 5 times, what are the chances of having
1 immediate win, 1 immediate loss, and 3 cases where the game continues?
0.222222
0.111111
0.666667
A casino decides to test whether there is a “best seat” at the blackjack table.
Note that, in blackjack, each player compares their cards to the dealer’s cards to determine whether they win or lose.
You can assume that the house has a 2% advantage, ie out of 1000 games the player expects to win 490 times.
1,000 games are observed, with these results:
Seat #
Number of Winners
1
468
2
481
Test the hypothesis that all seats are equal using 5% significance
Pearson’s “D” statistic is:
The 5% critical value is:
The decision is:
(accept or reject)
3
483
4
495
5
502
r they win or lose.
6
511
Do husbands and wives vote independently of each other?
Here are the data from 152 households:
husband
Trump
Biden
Green
wife
Trump
Biden
Green
28
38
8
24
27
8
8
8
3
60
73
19
74
59
19
152
Test the hypothesis of independence using 2.5% significance
The test statistic is:
The 2.5% critical value is:
The decision is:
(accept or reject)
Does the stock market “remember” what happened yesterday, or is each day indpendent of the day before?
We observe the closing S&P 500 average for each of the 252 trading days over the past year:
Day
S&P Avg
move
W
11/29/2019
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3140.97998
3113.870117
3093.199951
3112.76001
3117.429932
3145.909912
3135.959961
3132.52002
3141.629883
3168.570068
3168.800049
3191.449951
3192.52002
3191.139893
3205.370117
3221.219971
3224.01001
3223.379883
3239.909912
3240.02002
3221.290039
3230.780029
3257.850098
3234.850098
3246.280029
3237.179932
3253.050049
3274.699951
3265.350098
3288.129883
3283.149902
3289.290039
3316.810059
3329.620117
3320.790039
3321.75
3325.540039
3295.469971
3243.629883
3276.23999
3273.399902
3283.659912
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The test statistic is:
The 5% critical value is:
The decision is:
In one sentence, indicate a possible flaw in th
1/31/2020
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3225.52002
3248.919922
3297.590088
3334.689941
3345.780029
3327.709961
3352.090088
3357.75
3379.449951
3373.939941
3380.159912
3370.290039
3386.149902
3373.22998
3337.75
3225.889893
3128.209961
3116.389893
2978.76001
2954.219971
3090.22998
3003.370117
3130.120117
3023.939941
2972.370117
2746.560059
2882.22998
2741.379883
2480.639893
2711.02002
2386.129883
2529.189941
2398.100098
2409.389893
2304.919922
2237.399902
2447.330078
2475.560059
2630.070068
2541.469971
2626.649902
2584.590088
2470.5
2526.899902
2488.649902
2663.679932
2659.409912
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2749.97998
2789.820068
2761.629883
2846.060059
2783.360107
2799.550049
2874.560059
2823.159912
2736.560059
2799.310059
2797.800049
2836.73999
2878.47998
2863.389893
2939.51001
2912.429932
2830.709961
2842.73999
2868.439941
2848.419922
2881.189941
2929.800049
2930.189941
2870.120117
2820
2852.5
2863.699951
2953.909912
2922.939941
2971.610107
2948.51001
2955.449951
2991.77002
3036.129883
3029.72998
3044.310059
3055.72998
3080.820068
3122.870117
3112.350098
3193.929932
3232.389893
3207.179932
3190.139893
3002.100098
3041.310059
3066.590088
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3124.73999
3113.48999
3115.340088
3097.73999
3117.860107
3131.290039
3050.330078
3083.76001
3009.050049
3053.23999
3100.290039
3115.860107
3130.01001
3179.719971
3145.320068
3169.939941
3152.050049
3185.040039
3155.219971
3197.52002
3226.560059
3215.570068
3224.72998
3251.840088
3257.300049
3276.02002
3235.659912
3215.629883
3239.409912
3218.439941
3258.439941
3246.219971
3271.120117
3294.610107
3306.51001
3327.77002
3349.159912
3351.280029
3360.469971
3333.689941
3380.350098
3373.429932
3372.850098
3381.98999
3389.780029
3374.850098
3385.51001
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3431.280029
3443.620117
3478.72998
3484.550049
3508.01001
3500.310059
3526.649902
3580.840088
3455.060059
3426.959961
3331.840088
3398.959961
3339.189941
3340.969971
3383.540039
3401.199951
3385.48999
3357.01001
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3281.060059
3315.570068
3236.919922
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3298.459961
3351.600098
3335.469971
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3348.419922
3408.600098
3360.969971
3419.439941
3446.830078
3477.139893
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3511.929932
3488.669922
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3483.810059
3426.919922
3443.120117
3435.560059
3453.48999
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3269.959961
3310.23999
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3443.439941
3510.449951
3509.439941
3550.5
3545.530029
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3537.01001
3585.149902
3626.909912
3609.530029
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3581.870117
3557.540039
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(accept or reject)
dicate a possible flaw in this test
The following data come from an unknown distribution, and you cannot assume that its variance is finite
Test the hypothesis that the median = 60 using a 2-tail test with a 5% chance of committing a Type I error
Data
67.8
105
141.4
96.6
35.6
136.2
146
81.2
53.2
40
88.6
149.6
178.6
83.2
102.6
76.2
46
74.6
75.8
59.4
27.6
79.2
47.2
77.8
134
57.4
78
60.8
73.4
95.2
82.2
159.4
118
164.6
85.8
25.4
28.8
152.2
85
69.2
The test statistic is:
The 5% critical value is:
The decision is:
(accept or reject)
Test the hypothesis that the following data come from a normal distribution
with mean equal to the sample mean, and variance equal to the unbiased estimator from the sample.
Use 5% significance.
Data
Sample statistics
67.8
n
(max likelihood estimate of μ)
105.0

141.4
96.6
35.6
136.2
146.0
81.2
53.2
40.0
88.6
149.6
178.6
83.2
102.6
76.2
46.0
74.6
75.8
59.4
27.6
79.2
47.2
77.8
134.0
57.4
78.0
60.8
73.4
95.2
82.2
159.4
118.0
164.6
85.8
25.4
28.8
152.2
85.0
69.2
81.2
90.6
s2
s
(the unbiased estimate of σ2, using n-1 as divisor)
Test of H0
test statistic
dof
critical value
decision
(7 strata; subtract 1 because it was a sample; subt
(accept or reject)
To do this problem, use these 7 strata
Low
High
0
40
60
70
80
90
110
40
60
70
80
90
110
1000
43.6
105.4
66.4
55.4
52.0
24.2
90.8
40.8
because it was a sample; subtract 2 because we estimated 2 parameters)
Fit these data with an exponential model and perform
the appropriate goodness-of-fit test at 5% significance.
Remember to combine ranges with sparse data to the extent appropriate.
Range
0–1
1–2
2–3
3–4
4–5
5–6
6–7
7–8
D-statistic
Critical value
Decision
Observed Frequency
136
41
25
8
2
3
1
1
(accept or reject)

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