Question

A computer random number generator was used to generate 550 random digits (0,1,...,9). The observed frequences of the digits are given in the table below. 0 1 2 3 4 5 6 7 8 9 58 55 45 50 53 50 57 57 46 79 Test the claim that all the outcomes are equally likely using the significance level ?=0.05.

The expected frequency of each outcome is

E=

The test statistic is

?2=

The p-value is

Is there sufficient evidence to warrant the rejection of the claim that all the outcomes are equally likely?

A. Yes

B. No

Answer 1

(a)

The Expected Frequency (E) of each outcome = 550/10 = 55

(b)

O                     (O - E)²/E

58                       0.1552

55                           0

45                           2.2222

50                           0.5

53                             0.0755

50                           0.5

57                              0.8596

57                             0.8596

46                             1.7609

79                              7.2911

----------------------------------------------

                        = 13.7241

Test statistic is:

13.7241

(c)

= 13.7241

ndf = 10 - 1 = 9

By Technology,

p-value = 0.1325

(d) Since p-value is greater than , Fail to reject H0.

Correct option:

B. No