Question

In: Statistics and Probability

The data below is suspected to be part of a normal distribution - unknown mean and...

The data below is suspected to be part of a normal distribution - unknown mean and variance. perform goodness of fit test to confirm if the data really comes from a normal distribution.

a) Estimate the normal distribution:

b) Partition the range of the data into 4 mutually exclusive intervals.

c) Calculate the relative frequency of each interval you selected using the observed data.

d)

Calculate the theoretical probabilities of the intervals you selected assuming the data came from a

normal distribution, that is, what are the probabilities of the intervals using the normal distribution.

What are the probabilities of the intervals?

e)

Using the goodness of fit test, calculate the p-value of the null hypothesis that the data did come from

a normal distribution.

- sampling distribution of the test statistic

- degrees of freedom

- value of t

data

X
-41.7993
-6.75551
-4.57207
6.473999
8.043334
10.03882
10.1176
10.24299
10.92813
12.26577
14.31572
14.55558
14.66927
16.04167
16.18602
16.7623
16.79184
17.17429
17.23557
18.42297
18.59053
19.03812
19.88943
19.93733
20.15449
20.70884
20.79775
21.62833
21.70961
21.94015
21.97315
21.99528
22.08135
22.08294
22.38798
22.73674
22.75807
22.76812
22.82578
22.83249
22.90806
22.96188
23.23283
23.32808
23.36745
23.45859
23.95804
24.00811
24.06396
24.56042
24.59346
24.7885
24.81072
24.95474
24.98597
24.99861
25.04665
25.07295
25.13607
25.39688
25.41033
25.51445
25.61327
25.627
25.65928
25.79173
25.79198
26.12293
26.13035
26.88713
26.88921
27.04299
27.06587
27.75357
27.95948
28.05283
28.09865
28.94248
28.98953
29.15215
29.17561
29.42956
29.59153
29.78948
29.8014
29.94943
30.09963
30.43334
30.44267
30.53582
30.61413
30.95647
31.05248
31.29321
31.47292
31.56255
31.89942
32.53614
32.70575
33.27085
34.32168
34.58493
36.25383
37.16522
37.92006
37.92295
39.30411
40.49066
46.59491

Expert Solution

H0: The given data is follows Normal distribution

H1: The given data is not follows Normal distribution

From the given data

Since Chi-square value > Chisquare critical value so we reject H0

Thus we conclude that the given data is not follows Normal distribution

orchestra answered 2 years ago

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